barcode 1089273030 A crest with a shield, crown, and ribbon. Presented to the LIBRARY of the UNIVERSITY OF TORONTO by Miss M. Robertson A signature that appears to be "B. D. Kestler" or similar. A TREATISE ON ASTRONOMY. BY SIR JOHN F. W. HERSCHEL, KNF. GUBLR. FR.S.A., M.A., FRAS. F.R.S. MCLEER, COMMISSIONER OF THE ROYAL ACADEMY OF SCIENCES OF PARIS, AND OTHER FOREIGN SCIENTIFIC INSTITUTIONS. THIRD EDITION. PHILADELPHIA, CAREY, LEA & BLANCHARD. 1835. "Et quoniam enim natura copulatiorum incognita hominibus veri inventariam, quod facilissimum apparet, cuius voci curia, ritum quidam in rebus dat, ut invenire possimus. Quod autem invenire non potest, quia est, filio, simplicitas, comitantis; tum vanus, idem, fulminis odium." Ciceró, de Fato. Boc. et Mac. II. 14. And far more much as nature is silent concerning the discovery after the discovery of truth (which appears most clearly from this, that, when unexpressed by cause, we delight to know even what is going on in our own minds), so also do we hold in silence whatever is true for its own sake; that is to say, whatever is faithful, simple, and contentment; while we hold in silence whatever is empty, deceptive, or untrue. 2 C O N T E N T S. I N T R O D U C T I O N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 C H A P T E R I . General Notions---Form and Magnitudes of the Earth---Hecmen and the Sun---The Moon---The Planets---The Solar System---The Sun's radiation from internal Motion---Parallax---First step toward formu- lating on the idea of the Distance of the Celestial Bodies. 14 C H A P T E R II . Of the Nature of Astronomical Instruments and Observations in gen- eral--Of celestial and solar Times--Of the Measurement of Time--- Of the Instrumental Measure of Time--Of the Measure of the movement of angular horizons--Application of the Telescope to astro- nomical observations--Of the Instrumental Measure of Angular Movement--Of the Instrumental Measure of Angular Velocity Artificial Horizons--Collimator--Of compound instruments with circular scales--Of the Instrumental Measure of Angular Displace- ment--Of the Scrimn and Reflecting Circle--Principle of Repeti- tion. 66 C H A P T E R III . Of the Figure of the Earth--An exact Description--Its Form that of Equilibrium modified by Centrifugal Force--Variation of Gravity with Altitude--Variation of Gravity at Different Latitudes--The Pendulum-Grammy in a Sphereoid--Other Effects of Elasticity Rem- oved by the Pendulum-Grammy--The Pendulum-Grammy in a Lunation of Longitudes--Conduct of a instrumental Surveyor's Observations in the Sphereoid Configuration of the Earth--The Barometer. 105 C H A P T E R IV . OF CHANGEOFICATIO. Construction of celestial Maps and Globes by Observation of right Ascents and Declinations and by Determination also of Right Ascensions and Declinations by means of a Quadrant or Heptagon---The Milky Way--The Zodiac--Of the Keplerian Cele- stial Luminaries and Longitudes--Principles of the Equinoxes--No Influence--Aberration--Unresolved Problems. 3 181 4 CONTENTS. CHAPTER V. OF THE SUN'S motions. Apparent Motion of the Sun not uniform—Its apparent Diameter too variable—Its motion in the Ecliptic—The Solar Orbit—An Ellipse—or the Law of the unequal Velocities—Equinoctial Revolution of the Earth—The Equinoxes—The Tropic of Cancer and Capricorn—The Sun's motion in the Ecliptic—The Sun's motion in the Zodiac—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane—The Sun's motion in the Ecliptic and Zodiacal Plane— CHAPTER VI. Of our Moon—involving its Motion with respect to Distant Stars—in Parallax, diameter, etc.,and relative Diameter—the Apparent Motion of its Orbit—as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent Motion of its Orbit as seen by us from this Earth—the Apparent CHAPTER VII. Of universal Gravity—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—a theory to explain Universal Gravitation—a proof that gravity is universal—an CHAPTER VIII. of all celestial bodies. Apparent Motions of Phaethons' Stationary Rotations. Apparatus for measuring their motions. Their Flares, Periods, etc.—Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative Diameter, etc.,and Relative CHAPTER IX. of satellites. Of our Moon—an a Satellite—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General Proximity—and General CHAPTER X. of comets. Of comets—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect to distant stars—involving their motions with respect CHAPTER XI. of meteorites. Of meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including meteorites-including CHAPTER XII. of comets. Of comets—with reference also to meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and meteors-and CHAPTER XIII. of comets. Of comets-with reference also to meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteors-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores-meteores CHAPTER XIV. of comets. Of comets-with reference also to meteors-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Comets-Cometes CHAPTER XV. of comets. Of comets-with reference also to meteors-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids-Meteoroids CHAPTER XVI. of comets. Of comets-with reference also to meteors-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet-Comet CHAPTER XVII. of comets. Of comets-with reference also to meteors Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet Comet CHAPTER XVIII. of comets. Of comets-with reference also to meteors-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet-comet CHAPTER XIX. of comets. Of comets-with reference also to meteors-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come-come CHAPTER XX. of comets. Of comets-with reference also to meteors comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet comet CHAPTER XXI. of comets. Of comets-with reference also to meteors Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet Commet CHAPTER XXII. of comets. Of comets-with reference also to meteors Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet Cemet CHAPTER XXIII. of comets. Of comets-with reference also to meteors Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come Come CHAPTER XXIV. of comets. Of combs-with reference also to me CHAPTER XXV. of combs. Of combs-with reference also me CHAPTER XXVI. of combs. Of combs-with reference also me CHAPTER XXVII. of combs. Of combs-with reference also me CONTENTS. 5 CHAPTER X. **OF COMETS.** Great Number of perceived Comets--The number of unrecorded probably much greater--Discovery of a Comet--Comets without Periods--Periodic Comets--The Perihelion of a Comet--The Perihelion of the General Laws of Planetary Motion--Elements of their Elliptical Orbits--The Elements of the Orbit of the Comet of 1786--The Elements of the Orbit of the Comet of 1789--The Elements of the Orbit of the Comet of 1790--The Elements of the Orbit of the Comet of 1791--The Elements of the Orbit of the Comet of 1793--The Elements of the Orbit of the Comet of 1795--The Elements of the Orbit of the Comet of 1796--The Elements of the Orbit of the Comet of 1797--The Elements of the Orbit of the Comet of 1798--The Elements of the Orbit of the Comet of 1799--The Elements of the Orbit of the Comet of 1800--The Elements of the Orbit of the Comet of 1801--The Elements of the Orbit of the Comet of 1802--The Elements of the Orbit of the Comet of 1803--The Elements of the Orbit of the Comet of 1804--The Elements of the Orbit of the Comet of 1805--The Elements of the Orbit of the Comet of 1806--The Elements of the Orbit of the Comet of 1807--The Elements of the Orbit of the Comet of 1808--The Elements of the Orbit of the Comet of 1809--The Elements of the Orbit of the Comet of 1810--The Elements of the Orbit of the Comet of 1811--The Elements of the Orbit of the Comet of 1812--The Elements of the Orbit of the Comet of 1813--The Elements of the Orbit of the Comet of 1814--The Elements of the Orbit of the Comet of 1815--The Elements of the Orbit of the Comet of 1816--The Elements of the Orbit of the Comet of 1817--The Elements of the Orbit of the Comet of 1818--The Elements of the Orbit of the Comet of 1819--The Elements of the Orbit of the Comet of 1820 24 24 CHAPTER XI. **OF PERIHELIONS.** Subject [omitted] Supposition or supposition that some Comets are periodic.--Problems.--Proofs.--Suppositions.--Of a new Method.--Of Changes in inclination.--Of changes in eccentricity.--Of changes in inclination and eccentricity.--Of inclinations.--Change or change in obliquity.--Of eccentricities.--Of inclinations and eccentricities.--Of inclinations, eccentricities, and periods.--Of inclinations, eccentricities, and periods, and distances.--Of inclinations, eccentricities, periods, and distances, and motions.--Of inclinations, eccentricities, periods, distances, and motions, and times.--Of inclinations, eccentricities, periods, distances, motions, and times, and positions.--Of inclinations, eccentricities, periods, distances, motions, times, and positions, and velocities.--Of inclinations, eccentricities, periods, distances, motions, times, positions, and velocities, and directions. CHAPTER XII. **OF GENERAL ASTRONOMY.** Of The Sun generally.--Their distribution into Classes according to their brightness and distance from us.--Their distribution over the Heavens.--Of the Milky Way.--Annual Foraxial.--Bowl-shaped System.--Of double Stars.--Temporary System.--Double Stars.--Their revolutions about each other.--System with one star revolving round another.--System with two stars revolving round each other.--System with three stars revolving round each other.--System with four stars revolving round each other.--System with five stars revolving round each other.--System with six stars revolving round each other.--System with seven stars revolving round each other.--System with eight stars revolving round each other.--System with nine stars revolving round each other.--System with ten stars revolving round each other.--System with eleven stars revolving round each other.--System with twelve stars revolving round each other. A S A small image showing a celestial map or diagram. 6 CONTENTS. CHAPTER XHL
Page
Of the Calendar - - 381
Synoptic Table of the Elements of the Solar System - - 382
Synoptic Table of the Elements of the Orbits of the Satellites, so far as they are known - - 390
I. The Orbits of Saturn - - 390
II. Situation of Jupiter - - 390
III. Situation of Mars - - 391
IV. Satellites of Uranus - - 391
Index - - 393
A TREATISE ON ASTRONOMY. INTRODUCTION. (1.) In entering upon any scientific pursuit, one of the student's first endeavours ought to be, to prepare his mind by a thorough study of the subject, and at least loosening his hold on, all such coarse and hasty and absurd notions respecting the objects and relations he is about to investigate. This is necessary both to clear his mind, and to strengthen himself, by something of an effortful a resolve, for the unpriprical admission of any con- ception which does not rest upon a sufficient and faithful observation and logical argument, even should it prove of a nature adverse to notice he may have previously formed. It is also necessary to avoid the habit of reliance, on the credit of others. Such an effort is, in fact, a commencement of that intellectual discipline which forms the basis of all successful researches. It is the first movement of approach towards that state of mental purity which alone can fit us for a full and steady prosecution of any investigation. It is the "enphrasy and me" with which we must "purge our sight" before we receive and contemplate as they are presented to us. (2.) There is no science which, more than astronomy, stands in need of such a preparation, or draws more heavily upon the powers of the intellect. For it is not to allow whatever is demonstrated, or concede whatever is rendered highly probable, however new and uncommon 7 8 A TEXTURE ON AUTONOMY. the points of view may be in which objects the most familiar may thereby become placed. Almost all its conclusions are deduced from the phenomena of day-light, with those of superficial and vulgar observation, and with what appears to every one, until he has understood and used his own powers of observation. It is this per- tinent evidence of his senses. Thus, the earth on which he stands, and which he serves for ages as the un- shakable basis of his existence, the object of art or mirth, is directed by the astronomer of its attribute of fixity, and conceived by him as turning swiftly on its course, and revolving round the sun, and through space with great rapidity. The sun and the moon, which appear to us as fixed bodies, though they are very considerable size, become enlarged in his imagination into vast globes,—the one approaching in magnitude to the earth itself, the other to a star. The planets, which appear only as stars somewhat brighter than the rest, are to him spurious, chimeric, and hal- ose; and their motions are so slow that they cannot curiously furrowed than the earth he inhabits, as there are also other less so; and the stars themselves, properly so called, are but faintly visible. The sun is only a vivid spark or brilliant stellum; are to him sums of various and transient glories—efficient centers of life and light to my understanding. But I have not yet begun to delin- cate his thoughts to comprehend the grandeur of those ideas his calculations have called out, and exhausting his imagination in attempting to represent them in devices similes and metaphors illustrative of the immensity of the solar system. He has not even thought of returning back to his own sphere; he finds it, in comparison, a mere point; so shall even in the minute system to which he now turns his attention be seen compared from some of its principal and remotest members. (3) There is hardly any thing which sets in a stronger light than the nature of man's constitution. In all kinds of man, when opposed by no motives of interest or passion, than the perfect readiness with which all these constit- uences are assumed as soon as their evidence is clearly apprehended and be tenacious hold they acquire over INTRODUCTORY. our belief when once admitted. In the conduct, therefore, of this volume, we shall take it for granted that our reader is more desirous to learn the system which it is to be, than to ascertain what it is. We shall not seek objective arguments against it; and that, in short, he comes to the task with a willing mind; an assumption which we think will be justified by the nature of the subjec- tive argument to convince the sceptical, but will greatly facilitate his actual progress. The reader will find it useful to consider the subject of astronomy as the outset a straight and definite path, thus to be con- tinuing stepping stones, moved by motives of perplecity. The object of this work is to lead him out of such a state, in finding himself compelled to adopt our road. (1) The distinction between the analytic and the synthetic is not so clear as it is supposed to be. It is easy to follow either, and to mix strictly the analytic and the synthetic, but rather such a combination of both, with a leaning to the latter, as may be well with many things. For instance, in a subject it is no use to refute opponents, nor to inquire into what is not true, or to oppose propositions which are true; but simply to reach what we know. The moderate limit of a single volume, and the necessity of being on every point familiar with all that has been said on any ex- pansion, as well as the eminently matured and acer- bined character of the science itself, render this course necessary. But it does not follow that we have reached no longer any danger of any revolution in astronomy, like those which are daily changing the features of the less obvious parts of our knowledge. We must not accept these theses, and throw our statements into confusion. Eligible, because the space to be besetained, either in combating evident errors or in advancing new truths, is too vast, slow and measured steps from the known to the un- known, may be more advantageous devoted to each ex- pansion than to the other. And yet it was not so done; and, as it was, a practical case of the sequence of phe- nomena, and the manner in which they are produced. We must not suppose that we have reached any point at which leads more easily and directly to our objects, or in any way fetter ourselves by a rigid adherence to method. 10 A TREATISE ON ASTRONOMY. Writing only to be understood, and to communicate as much information as no little space allows, consistently with its direct and efficient communication, we can afford to make no sacrifice to system, to form, or to effectuation. (3.) We shall take for granted, from the outset, the Copernican hypothesis, which is so obvious, so clear, so obvious, and natural explanation it affords of all the phenomena as they may be described, to impress the student with the importance of the simple and uniformity of demonstration or the superlative tenacity of analogy, calling to mind that important remark of Bacon: "Deus non facit propter mirabilia, sed propter simplicia." The Copernican hypothesis is the simplest and most evident permutatio adinutum, quod quasi in orbem concurrent, fieri mutator," nor finding, however, to point out to the reader how this hypothesis is more advantageous than any other hypothesis. (4.) The preliminary knowledge which it is desirable that the student should possess before he makes any advantageous perusal of the following pages, consists in some acquaintance with the elements of geometry and trigonometry; some moderate acquaintance with geometry and trigonometry, both plane and spherical; the elementary principles of mechanics; a certain facility in order to understand the construction and use of the telescope; and some other of the simpler instruments. For the acquisition of these preliminary knowledge is necessary for this Cyclopedia which proceeds to treat of the several hypotheses in question. Of course, the more of such knowledge he brings with him into his study, the better will it be, and the more complete the information gained; but we shall endeavour in every case, as far as it can be done without injury to our object, to avoid unnecessary intricacy which consists in the absence of prolixity and episodic, to render what we have to say as independent of other books as possible. (5.) After all, we must distinctly enunciate such of our readers as may complain and terminate their astronomi- *The conclusion of this chapter is on the subject adaptation of their own ideas. If they do not agree with us or disagree, they necessarily sustain each other, and form a coherent whole.* 14 INTRODUCTION. 11 cal studies with the present work (though of such, at least in the latter predilection—we trust the number will be few), that its utmost pretension is to place them on the same level with the other sciences, either by their con- sequence, or rather on an eminence exterior to it, whence they may obtain something like a general notion of its structure and principles, and thus be enabled to enter, a ground-plan of its successes, and put them in pos- session of the power thereof. Admission to its sanctuary, though it may be difficult, yet it is not impossible, nor can it be gained by one means—so novel and sufficient knowl- edge of mathematics, the great treatise of all exact sci- ences, which has been published within our time, and whose suc- cesses in this or any other of the higher departments of science, as can easily be seen him to form an independent episte- mology of his own. The reason why he cannot do so is, it is not without an effort that those who possess this knowl- edge can communicate on such subjects with those who do not possess it. It is necessary for the former to explain to the necessities of such an intercourse. Propositions which to the one are almost identical, are theories of importance to the other, and therefore must be presented in the same way to the mind of each. In making such propositions, under such circumstances, the student must have a clear idea of what he is en- suring, so to the sense of analogy—as practice and expe- rience: principles and modes of action have to be estab- lished before we can proceed further; and these are axioms, but by bringing forward and dwelling on simple and familiar instances in which the same principles and the same modes of action are employed, we are erecting, as it were, in each particular case, a separate monument to the truth; and this is a very different thing from science to meet its exigencies. The difference is that of pioneering a road through an untraversed country, and of laying down a map for those who follow after. This is why it is said, to us are determined to make ourselves distinctly understood, and will apply to reason at all. As regards mathematics itself, it is not always easy on the faith of the student (though in some complex cases indispensable, where illustrative explanation would defeat 12 A THEATRE ON ARITHMETIC. its own cur by becoming tedious and burdensome to both parties), it is one which we shall neither adopt ourselves nor allow others to adopt. (8.) On the other hand, although it is something new to abandon the road of mathematical demonstration in the treatment of arithmetic, yet it is not less considerable a branch of science entirely or chiefly by the way of illustration and familiar parlance, it is yet not imposs- ible that it may be made more interesting than any other subject, whose knowledge has been acquired by that confessedly higher and better practice which is incorpora- ble into the study of mathematics. For this reason, why find their account in its person—or for this reason, that it is always of advantage to present any given body of knowledge in a manner which will make different lights as possible. It is a property of illustrations of this kind to strike no two minds in the same manner, or with the same effect; they may be compared with each other with the same images, or have required their notions of them by similar habits. Accordingly, it may very well hap- pen, that those who have had little or nothing to do with it, may be placed not merely in a new and uncommon, but in a more impressive and satisfactory light by such a comparison. Thus, for example, when we invent migrating cleared up, or even some link supplied which may lead to the perception of connections and deductions altogether new and unexpected. The interest of this is increased when, as in the present instance, the illustra- tions chosen have not been studiously selected from books, but are drawn from the author's own experience; to the author's mind as being most in harmony with his own views; by which, of course, he means to lay no claim to originality; but to any of his readers beyond whom they may really possess. (9.) Besides, there are cases in the application of me- chanical demonstrations where the method itself is but too familiar, where, when the date are before him, the numerical and geometrical relations of his prob- lems are so obvious that they cannot be estimated or measured—say, when even he has followed up the application of his technical procedures, and INTRODUCTION. fairly arrived at his conclusion—there is still something wanting to his mind—not in the evidence, for he has ex- amined all that can be examined with respect to the principles, for the principles which he well knows are too firmly es- tablished to be shaken—but precisely in the mode of ac- tion, in the manner in which he has applied them, and in technical rules, but the signs he has employed are not pictures of nature, or have lost their original meaning as such, and they are not sufficient to convey the true ap- pearance of nature passing under his eye in an instant of time, and produced by an instant of thought. A philosopher would have illustrated them from some source of natural process, or of process, of which he has thus direct and individual knowledge; but he does not do so. He begins with a name, wills in almost every case such a supply, in a mo- ment this deficient feature will convert all his symbols into false images, and will make him incapable of perceiving what was before a lifeless succession of words and signs. We cannot, indeed, always presume ourselves to attain this degree of perfection; but we may hope that we shall be able to elucidate ourselves always capable of be- ing so paraphrased (if we may use the expression) by any one who may happen to possess a more extensive experience; but the object will at least be kept in view; and so, as we very commonly conceive of having, in making such distinctions, a certain amount of advantage over the ma- jority of the more conceited effects of planetary perturba- tion than we had acquired by their mathematical investi- gations; and I am sure that no man who has studied nature will not always be unutterably with a similar success in others. (1.) From what has been said, it will be evident that our aim is not to offer to the public a technical treatise, in which the absent of practical or theoretical astronomy shall be made up by mere abstract speculations. Such is not the case; for the philosopher must either have means of observation, or the formulae he requires prepared to his hand, or their demonstrations drawn out in detail. In all cases he must have some practical experience on which he can rely; and if he is unable to obtain this, his aim is entirely different; be- ing to present in each case the more ultimate rationale of facts, arguments, and proofs; and in all cases of mathe- D 14 A TREATISE ON ASTRONOMY. [CHAP. I. natical application, avoiding whatever would lead to cum- ber his pages with algebraic or geometrical symbols, to place under his inspection that central thread of com- mon sense which, in the course of human life, is so invariably strong; but which, by the attention the latter claim for themselves, is often concealed from the eye of the general reader, who, in the most common and most convenient form to follow by those who string them. This is no fault in those who have conducted the inqui- ries to their conclusion; but it is a great fault for which they call us envious; and it may, perhaps, be owing to their experience of how little can be accomplish- ed in this way. We must therefore, in our inquiry, try, by mere ordinary clearness of head; and how necessary it often is to pay more attention to the purely mathematical conditions than to the mere verbal expression of their equations and series,—than to those which enchain causes with their effects, and both with the human rea- son,—and we shall find that the extreme plainness and similitude of view which is often complained of as a grievance by the earnestest student, and still more commonly ascribed to ignorance on the part of the vulgar, is really too much sublime for vulgar comprehension. We think we shall render good service to both classes of readers, by dissi- pating some of the difficulties which they feel in curiosity; and by showing ordinary untutored comprehension clearly what it can, and what it cannot hope to attain. CHAPTER I. General Notices—Form and Magnitude of the Earth-Horizon and its Sphere—The Distance of the Sun from the Earth—The Sun's Apparent Movement—The First Step towards forming an Idea of the Distance of the Suns—Definition. (11.) The magnitudes, distances, arrangement, and motions of the great bodies which make up the visible universe, their constitution and physical condition, so far as they can be known at present, their mutual influ- ences and actions on each other, so far as they can be 14 CHAP. I.] GENERAL NOTIONS. 15 traced by the effects produced, and established by legiti- mate reasoning, form the assemblage of objects to which we apply the term astronomy*; which, when applied to the stars, is called the science of astronomy; and when applied to the earth, the science of geology. The term astronomy* itself, which denotes the face or only the face of the heavens (by which the universe understood not only the visible world, but all that is beyond it), and all the visible constituents of the heavens), sufficiently indicates this; nam; although the term astrology, which designates the same subject, though applied to the sun and moon, has become degraded in its application, and con- fined to superstitions and delusive attempts to divine the future from the supposed influence of celestial influences, the same meaning originally attached to that epithet. (12.) Besides the stars and other celestial bodies, the earth itself, regarded as an individual body, is one principal object of the astronomer's consideration, one which he studies with a desire to determine its nature, as in practical as well as theoretical sense, not only from its own peculiar constitution, but also from its relations, who draw from it the supply of all our wants, but also from its position in relation to other bodies. We must refer for any determinate marks and measures by which to recognise their changes of situation, or with what to calculate their motions. (13.) To the reader who now for the first time looks up a book on astronomy, it will no doubt seem strange to find so much attention paid to a planet which has no same unity of nature among things apparently so different. For what, in fact, can be more apparently different than the earth compared with the vast ex- tent of the earth, and the stars, which appear but as points, and seem to have no size at all ? The earth is a mere point in comparison with the universe. We perceive it in no motion, while in them we observe a continual change of place, as we view them at different *astronomy, or astron.ymy, a face or aspect; or, used, as a depreciated term, an art or science of predicting events from the supposed influence of celestial bodies. **astronomy, reason; or word, the vehicle of reason; the inseminator of thought. 16 A TREATISE ON ASTRONOMY. [chap. I. hours of the day or night, or at different seasons of the year. The ancients, accordingly, one or two of the more enlightened of them only excepted, admitted no such communication between the celestial bodies and their movements without the pude of analogy and experience, sufficiently interpreted the progress of all, whatever they might be. But this communication is going on in the regions where they exist and move. Under such continuous, astronomy, as a science of some kind, has been called, is reduced to nothing but a mere registry of appearances, unconnected with any attempt to account for them on reasonable principles. To see how far we have proceeded towards acquiring a knowledge of what is really the case ; and the student has made his first effort towards the acquisition of that knowledge, he will soon learn to familiarize himself with the idea that earth, after all, very much but a great star. How correct such an idea may be, and how many other modifications it is to be admitted, we shall see presently. (11.) It is evident, that, to form any just notions of the arrangement of the stars and planets, which we cannot approach and examine, but of which all the information we can gain is by sitting still and watching their motions, we must suppose that they do not know, in the first instance, whether what we call sitting is really so ; whether the station from which we view them is stationary or not. And if we consider that immediately surround us, be not itself in motion, unperceived by us ; and if so, of what nature that motion is. The same reasoning applies to all things : for though their apparent arrangement with respect to each other, will be course be materially dependent on the situation of the spectator ; yet it is impossible that he should be able to change, unknown to the spectator himself, an appearance of change in the respective situations of the objects with reference to him. If this were not so, in general ; in every case, it will follow that all the movements we think we perceive among the stars will not be real movements, but that some part, at least, of whatever changes of relative place we perceive among them must be merely apparent, the result of the shifting of our own point of view; and that, if we would ever arrive at a knowledge of their real motions, it can only be by first investigating on what principles they are supposed to move. Thus, the question whether the earth is in motion or at rest, and if in motion, what that motion is, is no idle inquiry, but one which may lead us to a very important result of arriving at true conclusions respecting the constitution of the universe. (1.) It may be thought strange that we should speak of a motion existing in the earth, unperceived by its inhabitants; but we must remember that it is of the earth as well as of ourselves that we have to inquire; and so long as we consider either of them as stationary, or sustain on its surface, that we are speaking; or of a motion common to both solid masses together, to the ocean, and all other bodies in the air, and in the atmosphere which float above it in the air. Such a motion, which should displace no terrestrial object from its re- lative position with respect to any other terrestrial object, and produce no sensations of shocks or jerks, indeed, might be very evident, subject undetected by us. Therefore, it is necessary to examine carefully what we are in motion. We perceive jerks, or shocks; it is true, because these are sudden changes of motion, pro- duced by some external force acting upon us; but then ten and powerful forces acting during short times; and these forces, applied to our bodies, are what we feel. When, for instance, a man walks through a room where he has been blinded down, or with our eyes closed (to keep us from seeing external objects), we perceive a tremor arising from within us; this tremor is produced by the body being successively lifted and let fall, but we have no sense of progress. As the road on which we travel is not smooth, our rate of travelling is severely checked. Those who have travelled on the celebrated rail-road between Manchester and Liverpool testify daily that for every mile travelled by the train there is a distance which external objects seem to dart by them, the sensation is almost that of perfect rest. (2.) But it is on shipboard, where a great system is maintained in motion, and where we are surrounded B 2 18 A TREATISE ON ASTRONOMY. [CHAP. I.] with a multitude of objects which participate with our- selves and each other in the common progress of the whole mass, that we feel most satisfactorily the identity of sensation between a state of motion and one of rest, as the former is more agreeable to us than the latter, because behind the wind in still water, or drawn along a canal, not the smallest indication acquaints us with the way it is moving, but only by its effect on our senses, every con- tumacy arises as if we were on land. If we throw a ball into the air, it flies back into our hands; on if, we drop it in a basin, it sinks down; if we blow upon it, it soars in the free air; and smoke ascends in the same manner as it would do in an atmosphere on shore. If, indeed, we compare these phenomena with respect to their opposite; the air, not being carried along with us, drifts away underneath where it has been blown over; and this is due to its being opposed to the opposite direction that the ship's progress; but in reality, they remain at rest and lose nothing of their properties. Thus, the illustration so far as massive objects and our own move- ments are concerned, remains complete; and when we look at the shows, we then perceive the effect of our own motion on external objects. But when we consider external objects--external, that is, to the system of which we form a part. *exempli gratia*, *periculum patior*, *terreus ubique recondit*. (17.) Not only do external objects at first appear in motion generally, with respect to ourselves when we are in motion among them, but they appear to move one another in like manner, though they are at separated places. Let any one travelling rapidly along a high road find his eye steadily on any object, but at the same time see another object moving towards him. In such a gen- erale landscape,**he** will see, or think he sees, the whole landscape thrown into rotation, and moving round that object. The same thing happens when he himself appears to move backwards, or the contrary way to his own motion; and all beyond it forwards, or in the direction in which he moves; but let him withdraw his eye from that object and fix it on another,**he** moves **CHAP. I.** FORM OF THE EARTH. one, for instance,—immediately the appearance of co- tations shifts also, and the apparent centre about which it revolves changes its position, so that we are accustomed to the new object, which, for the moment, appears to us the same. This apparent change of similitude of objects with re- spect to each other, and to the earth itself, is called a per- turator, is called a perturbing motion; and it is, therefore, evident that, before we can ascertain whether external objects have any influence on our senses, or whether they are only our own sensations, we must subvert, or alter for any such per- turbing motion which may exist. Now, since we cannot conceive the whole earth as one mass, we must form to ourselves a conception of its shape and size. Now, an object cannot have shape and size unless it has some boundary; but this boundary is not outlined, so as to admit of our imagining it, at least, dis- connected from other bodies, and existing insulated in a vacuum. Hence it follows that the earth must be conceived as in that of a flat surface, of indefinite extent in all directions— from the spot where we stand, above which we are the air that surrounds us—and as having no boundary whatever. This is a prejudice to be got rid of, like that of the earth's immobility; but it is one much easier to redor our senses than to overthrow the opinion of the earth's annual inactivity, in not questioning ourselves where we will place a limit to a thing we have been accustomed from childhood to consider as infinite. It is true that we do not know, like that, originate in the testimony of our senses unintelligible. On the contrary, the direct testi- mony of our senses is always given us by means of the sun set in the evening in the west, and rise again in the east; so that we cannot doubt that it is the same sun we see every day. But this does not prove that it is a point, all our notions of solid matter, to suppose it to have made its way through the substance of the earth. It must be remembered that there are two points in space more numerous chasms 1 for if we notice the points where it sets and rises for many successive days, or for a long time together; and if we observe how it moves round a very large extent of the horizon; and besides, the moon and stars also set and rise again in all points 10 20 A TREATISE ON ASTRONOMY. [CHAP. I.] of the visible horizon. The conclusion is plain: that the earth cannot extend indefinitely in depth downwards, nor indefinitely in surface laterally; it must have only bounds in a horizontal direction, but also under one side, and not on all sides equally extended; and that side must, at least, be so far like what we see, that it must have a sky and similitude, and a day when it is night to us. —*edita nuda Amoris* desumere rebus. Necesse est praeceps exarare omnia. Knox's *Principia* (p. 35) says "The Earth is a sphere." (20.) As soon as we have familiarized ourselves with the conception of an earth without *limitation* or fixed superposition of its parts, and with the nature of every thing external, it becomes easy to imagine it in motion—or, rather, difficult to imagine it otherwise; for, since the earth is supposed to be a sphere, it should any causes of motion exist, or any forces act upon it, misbey obey their impulse. Let us next see what obvious circumstances will show us the true shape of the surface of the earth. (20.) Let us first examine what we can actually see of the surface of the earth; it is not on land (unless, indeed, on uncommonly level and extensive plains) that we can see any thing of the general figure of the earth—the hills, trees, etc., are too small to be seen; but by looking up and break and elevate the line of the horizon, though ob- viously bearing a most minute proportion to the whole earth, yet they give us a very distinct idea of its shape; and to this small portion of what we can see at a sin- gle view, to allow of our forming any judgment of the form of the whole earth (which is not always recognized). But with the surface of the sea, or any vastly extended level plain, the case is otherwise. If we sail out of sight of land, and look up into the sky, and climb the mist, we see the surface of the sea—not losing itself in distance and mist, but terminated by a sharp, clear, or even blue line; which line is exactly that which runs all round us in a circle, having our station for its centre. That this line is really a circle, we conclude, first, from the perfect apparent similarity of all its parts; A diagram showing a circle representing the horizon. **CHAP. IV.** HORIZON AND ITS REF. and, secondly, from the fact of all its parts appearing at the same distance from us, and that evidently a molecule rotates one; and, thirdly, from this, that every point of the horizon, which is called the dip sector, is the same (except under some singular atmos- pheric circumstances, which I shall mention hereafter) whatever direction the measure is taken—properties which belong only to the circle among geometrical figures, and which are common to all measurable bodies. For instance, one of the Egyptian py- ramids, the same holds good. (21.) Masses of ships, however, and the clouds created by them, appear to be less numerous compared to what nature itself affords; Aisna, Teneriffe, Mowart, Roan, are eni- mences from which no cloud can be seen; but from these again—in few cases and rare occasions when the transparency of the atmosphere is very great—no cloud appears. In short, the true scale now, be it seen—the very same appearances are witnessed, but with this remarkable addition, viz. that the number of visible objects is much greater than mea- sured by the dip sector, is materially less than at a lower level, or in other words, that the apparent size of the earth's surface is considerably diminished by its distance from us; its surface, while yet the absolute quantity of it seen at once has been increased. (22.) These observations are everywhere universal; in every part of the earth's surface visited by man. Now, the figure of a body which however seem, nev- ertheless always circular, can we see it either on a plane or globe. (23.) A Diagram will elucidate this. Suppose the earth to be represented by a sphere whose LINGH centre is C and let A, G, M be stations at different elevations above various points of its surface, represented by P. Now let us draw a line from M to A let it be drawn as MN; a tangent to the surface at N; then will this line represent the visual ray passing through M and meeting at A. Let us now draw another tangent from M to G let it be drawn as MG; a tangent to the sur- face at N; and at this tangent sweep round M and come successively into the positions MO, MP', MQ', the 22 A TREATISE ON ASTRONOMY. [CHAP. I. point of contact X will mark out on the surface the circle N O P Q. The area of this circle is the portion of the A diagram showing a circle with points labeled N, M, O, P, Q, and rays extending from these points to a point X on the circumference. earth's surface visible to a spectator at M, and the angle NMQ included between the two extreme visual rays is the measure of its apparent angular diameter. Leaving, at present, out of consideration the effect of refraction in air, we may remark that the rays which approach us always tend, in some degree, to increase that angle, or render it more oblong; this is the angle measured by the dip secant MNQ. But when the observer is situated M is more elevated above n, the point immediately below it on the sphere being visible area, i.e. the spherical seg- ment N O P Q (fig. 1), then the angle NMQ diminishes in the visible horizon* or boundary of our view from the eye; viz., the line MN increases; and, duly, that the smaller is the angle NMQ, and consequently the rays, the apparent angular diameter of the earth diminishes, * "horizon" is technically **CHAP. L.** HORIZON AND ITS DIP. being nowhere so great as 180°, or two right angles, but falling either to the north or south, according to the latitude, that angle may be more or less than we shall here explain. The figure $x$ exhibits three states or stages of elevation, with the hori- zon, which is represented by the line $xy$. In the first state, explain our meaning; or limiting ourselves to the larger and more distinct, $M\text{NQ}\text{P}$, let the reader imagine $xN$ and $xM$ to be parallel lines, and $yQ$ and $yP$ kept extended by the globe $NQP$ between them. It is clear, that as the point $M$ is urged home towards the horizon, the line $xM$ will be inclined towards it; more nearly straight, but will not attain perfect straight- ness till $M$ is brought fairly up to contact with the sur- face of the earth. This inclination of $xM$, will become a tangent at the surface at $m$, as is the line $xy$. (24) This explains what is meant by the dip of the horizon. It is evident that this tangent is perpendicular to the surface of the earth at $m$, as also the direction in which a plane-line would hang; for it is an observed fact, that when a plane-line is placed on a horizontal sur- rection of a plane-line is exactly perpendicular to the surface of still-water; and moreover, that it is also ex- actly perpendicular to the surface of the earth at any point whatever, whether it be a point on the surface of a spirit-level. Suppose, then, that at our station $M$ we were to adjust a line (a wooden ruler for instance) by a spirit-level to be perpendicular to the surface of the earth, the direction of this line indefinitely prolonged both ways, as $XY$, the line no draw will be at right angles with the surface of the earth at any point whatever, except gent to the surface at $m$. A spectator placed at $M$ will therefore see not only all the vaults of the sky over his line $XZ$, but also all those parts of it which lie between $XZ$ and $YQ$; in other words, his sky will be seen in its entire extent. But if he places his eye at the angular breadth of this reclining zone—the angle $YMQ$, by which the visible horizon appears depressed below its true direction—a spirit-level—dip is called the dip of the horizon. It is a correction of constant use in natural astronomy. *See this instrument described in chap. II.* A diagram showing three stages of elevation with the horizon. 24 A TREATISE ON ANGSTRONY. [CHA.P. I. (25.) From the foregoing explanations it appears, 1st, That the general figure of the earth (so far as it can be gathered from this kind of observation) is that of a sphere, whose great circle is the equator, and whose poles are the points where the meridians meet the horizon, which, wherever it extends, covers and fills in the local irregularities and local irregularities which exist on land, but without any such irregularities, presenting the dis- ruptions from the general outline of the whole mass, as we consider an orange not the least round for the roughnesses of its surface, but a perfect sphere. 2ndly, that a visi- ble horizon, or sea of sight, is a consequence of the cur- vature of the surface, and does not arise from the inability of the eye to see objects at a distance, or from absence of or from atmosphere's insufficiency. It will be worth while to pursue the general notion thus acquired into some of its consequences. 3rdly, that all visible objects are obser- vations of a different kind, and on a larger scale, will be put to the test, and a clear conception be formed of the manner in which they appear when they are related to each other, and held together on a whole. (26.) In the first place, then, every one who has passed a little way along the shore of any sea will find that any sea be perfectly well beyond the ebb or visible horizon —but not the whole of them. We only see their upper parts. The lower parts of these ships, and even out of the water, are hid from view by the spherical surface of the sea, which protrudes between them and ourselves. Suppose now that we take a ship at sea at a distance from our station—say first, when the distance of the ship is small, a spectator, S1, situated at some certain height above sea level would see only its upper part; but as he moves towards it until he reaches its lower part he sees the entire vessel where it rests on the sea, not at A. As it re- cedes it diminishes, as is true, in apparent size, but still the actual size remains constant till it reaches B. When it reaches the visible horizon at B. But no sooner as it has passed this distance, not only does the visible portion still con- tinue to diminish in apparent size, but also begins to disappear bodily, so if sunk below the surface. When it has reached a certain distance, as at C., its bulk has entirely vanished, but its parts and sails remain, preserving the appearance e. But if, in this state of CHAP. I. SIZE OF THE EARTH. A diagram showing the relative positions of three ships at sea, with arrows indicating their movements. The diagram includes labels for stations A, B, C, D, and E. things, the former quickly merends to a higher station, T, whose visible horizon is at D, the hull comes again in sight; and when he descends again he loses it. The ship still receding, the lower hull seems to sink below the horizon; while yet the distinctness with which the last portion of the hull is seen is such as to show that it is not exactly at D; but that it is some distance below it. In this case, therefore, the distance of the sea, ABCDE, the dis- tance T is not so great as to have prevented an equally perfect view of the horizon. (72.) Moreover, therefore, if we could measure the heights and exact distance of two stations which are nearly equal in latitude, and on opposite sides of the horizon, we could ascertain the actual size of the earth itself; and, in fact, were it not for the effect of re- fraction, by which the rays are bent towards us, we should find out the supposed segment (as will be here- after explained), this would be a tolerably good method of ascertaining its size. Suppose A and B to be two coni- nences, whose perpendicular heights A a and B b (which, for simplicity, we will suppose to be exactly equal) are known, as well as their exact horizontal interval a d b. 25 26 A TREATISE ON ASTRONOMY. [CHAP. L by measurement; then is it clear that D, the visi- ble horizon of both, will lie just half-way between them, and if we suppose $AB$ to be the sphere of the earth at its distance from us, and $BC$ its diameter, we know $D_0$, the length of the arch of the circle between $D$ and $b_0$, viz. half the measured interval, and $B_0$, the excess of $B$ over $D_0$, which is equal to the length of the radius $D_0 B_0$. In this way, by the solution of an easy geometrical problem, we can find out how long the radius $D_0 B_0$ is. If, as really it does happen, we suppose both stations and distance of the stations incommensurable in comparison with the size of the earth, the solution afforded is so continued as to follow all other phenomena. The earth's diameter bears the same proportion to the distance of the stations from one another as that dis- tance does to the height of their respective levels. When the stations are unequal in height the problem becomes infinitely complicated. (28.) Although as we have observed, the effect of refraction prevents this from being an exact method of ascertainment, yet it may be used as a rough one; and such suffices to afford some approximation to it as shall be of use in the present stage of the reader's knowledge, and help him to understand what is meant when we shall explain its application in numbers. Now, it appears by observation, that two points, each ten feet above the level of the sea, are seen at a greater distance than other over still water, and in average atmospheric circum- stances, at a distance of about 8 miles. But 10 feet is the 58th part of a mile; therefore 8 miles is 58 times 10 feet, or 580 miles; and therefore in the same proportion to 5 miles is the height of a man's head above his eyes. Now 580 miles is equal to $4 \times 212 = 848$, or in round numbers, about 800 miles, which is not very far from the truth. (29.) We have now made our attempt to ascertain the earth's magnitude; and it will not be amiss if we take advantage of it to compare it with objects we have been accustomed to consider as vast sizes, so as to interpolate a few steps between it and our ordinary ideas. CHAP. L.] VISIBLE PORTION OF THE SURFACE. 27 of dimension. We have before us bounded the inequalities of the surface by a line drawn from mountains, valleys, buildings, &c., to the roughnesses on the rind of an orange, compared with its general mass. The compari- son is not very accurate, because the surface of the earth known does not exceed five miles in perpendicular elevation: this is only one 1000th part of the earth's diameter; but even so, we may suppose that a mountain in diameter, such a mountain would be represented by a proportion of no more than one hundredth part of the surface of the earth, which is equal to about two square inches. Now we see it is no cause certain, or even any, very extensive tract of land, known to possess any great ele- vation above the level of the sea. Like this quantity of land, it follows, that if we would construct a correct model of the earth, with its seas, we must represent all the mountains on an equal scale with the plain; for instance, the whole of the land, with the exception of two prominent points and ridges, must be comprized on an area equal to that of a square inch; and therefore every visible hill would be represented by the smallest visible grains of sand. (30) The deepest mines in England do not penetrate below 500 feet; but if we survey a surface; a terrace, or pin-hole, daily representing it, on the surface of such a globe as our model, would be incapable of representing any thing of greater depth of sea, probably; does not much exceed the greatest elevation of the continents; and would, consequently, be incapable of representing any thing in its proper position, into the substance of the globe; so that the ocean comes to be conceived as "a mere hollow" (1), and all other parts are supposed to be filled up by a brush dipped in colour and drawn over those parts intended to represent the sea: only in so conceiving it, we can imagine how it could be possible for anything to go farther than to proportion in point of quantity. The mechanical laws which would regulate the distribution and filling up of these materials on the surface of the earth, are altogether different from those which govern the phenomena of the sea. (32). Lastly, the greatest extent of the earth's surface which has ever been seen at once by man, was that ex- 28 A TREATISE ON AERONOMY. [CHAP. I. posed to the view of M. Riol and Guy-Lassus, in their celebrated aeronomic expedition to the enormous height of 25,000 feet, or rather less than five miles. To exti- mate the magnitude of this elevation by reference to the whole earth's surface, we must have recourse to the geometry of the sphere, which informs us that the convexity of the surface of the globe exceeds one-seventh of the sphere to which it belongs as the versed sine of thickness of the segment is to the diameter of the sphere. The difference between these two quantities we are considering, is almost exactly equal to the perpen- dicular elevation of the point of sight above the surface. The perpendicular elevation of the point of sight in this case, to the whole earth's surface, is that of five miles up 600th, (33.) When we ascend to any very considerable elec- vation above the surface of the earth, either in a balloon, or on a mountain-top, we feel a peculiar intensity sensations, of an insufficient supply of air. The thermome- ter, an instrument which informs us of the weight of air incumbent upon its surface, shows a diminution in its im- pression, and affords a direct measure of the rate of dimi- nution of the quantity of air which a given space includes as we ascend. From what has been already stated, we learn, that when we have ascended to the height of 1600 feet, we have left below us only one thirtieth of the whole quantity of air which we had before; and at every act of perpendicular elevation (which is rather less than that of the summit of 2500') we have ascended through about one-thirtieth part of all that was contained within the sphere of Co- topaxy) through one half the material, or, at least, the ponderable, body of air incumbent on the earth's surface. From this it appears that when we ascend to a pér- ori, from the nature of the air itself, which is compressi- ble, i. e. capable of being condensed, or crowded into a smaller space than it would occupy at rest; and therefore, it is easy to see that, although by rising still higher we should be *The heights of Jésus above the Mediterranean (as he remains for a temporal measurement of his own) made in July, 1814, under very favourable circumstances in Bays de France for Mr. Walker.* A balloon ascending into the sky. **CAP. I.** THE ATMOSPHERE. continually get above more and more of the air, and so re- ceive ourselves more and more from the pressure with which it weighs upon us, yet the amount of this additional relief, or the perpendicularly-quantity of air encountered, would be continually diminishing, though it might still be in- creased, but in a constantly decreasing ratio. An easy calculation, however, founded on our experimental knowl- edge of the density of the air, will show that whatever its quality which regulate its dilatation and compression, is sufficient to show that, at an altitude above the surface of the earth not exceeding 30 miles, the quantity of air which we receive, or rather receive from us, must be excessive, that not only animal life could not subsist, or combination be main- tained, but that even the most active exertions would be necessitating the existence of any air at all would fail to afford the slightest perceptible indications of its presence. It is evident then, that in order to make this point pre- sent, all nice questions as to the probable existence of a definite limit to the atmosphere, such as those of Mr. H. J. de la Rive, who has been so much employed in speaking on the subject of the atmosphere, speaking, no doubt, is clear, that for all practical purposes, we may speak of these regions as being one and the same. The atmosphere extends from the hundredth part of its diameter as void of air, and of course of clouds (which are nothing but visible vapours, diffused and floating through the whole mass), to the uppermost part of it as moist as dew does. It seems probable, from many indications, that the greatest height at which visible clouds can be seen is about 5 miles high; at which height the density of the air is about as light as that at which it is at the level of the sea. Now let us consider how this constitutes the atmosphere of air, with the clouds it supports, as constituting a coating of equal or nearly equal thickness, enveloping our globe on all sides. This coating is not uniform; for while near the surface of the sea and land constitutes the keel, and whose inferior portions or strata, within a few miles of the earth's surface, are very dense; they gradually diminish in density diminishing with extreme rapidity as we re- cede upwards; till, within a very moderate distance (such as would be represented by the path of an inch on the map) we have before spoken of, and which must more or less 30 A TREATISE ON ASTRONOMY. [CHAIR. I.] portion to the globe on which it rests, than the downy skin of a perch in comparison with the fruit within it], all sensible trace of the existence of air disappears. (66.) Arguments, that the atmosphere is a tender of no more weight than air, at least in the highest degree probable, that the surface of the sable, like that of the aqueous ocean, has a similar effect upon its own him- self; as that it is positively no air, and above all, which a fresh quantity of air, could be added from with- out, or carried thither from without, would not itself induce any perceptible change, would occur; a certain very monstrous but still finite enlargement of volume, sink and merger, as water pours into a vessel, would not itself change its nature. With the truth of this conclusi- on, however, astronomy has little concern; all the ef- fects of the atmosphere are extraneous phenomena; amongst these, whether it be supposed of ex- istence or not. (67.) Moreover, whatever idea we adopt, it is equally certain, that within those limits in which it possesses any appreciable density, its constitution is the same over all points on the earth's surface. Inasmuch as the great scale, and variety of circumstances of consideration temporal and local causes of degeneration, such as winds, and great fluc- tuations of temperature, do not affect the atmosphere in an immense manner; in other words, that the law of diminu- tion of the air's density as we recede upwards from the level of the earth's surface does not vary in any point at which we may conceive it divided, or from whatever point of the surface we may act out. It may therefore be consi- dered as a homogeneous fluid occupying all points or layers, each of the form of a spherical shell, concentric with the general surface of the sea and land and each of which is rarer, or specific gravity less than immedi- ately beneath it; or denser, or specifically heavier, than that immediately above it. This kind of distribution of its pressure throughout space is called by some the equilibrium of fluids; whose results hortatory observa- tions demonstrate to be in perfect accordance with expe- rience. It must be observed, however, that with this distribu- **CHAP. I.** REFRACTION. 51 tion of its strata the inequalities of mountains and valleys have no concern; these exercise no more influence in modifying their general spherical figure than the inequalities of the earth's surface interfere with the general sphericity of its surface. (28.) It is the power which air possesses, in common with water, to bend or refract light, that causes the sun, or bending them out of their straight course, which renders a knowledge of the constitution of the atmosphere important. The rays of light, when they pass through the atmosphere, are often bent so much as to appear apparently situated at some distance from their true position. This effect may be observed by looking through a window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through a glass window at a distant object, or by looking through 32 EXPERIENCE. [CAP. L] rection of the straight line AS. But, in reality, when the ray of light SA reaches the atmosphere, suppose at d, it will, by the laws of optics, begin to bend downwards, until it arrives at e, where it will have its greatest bending will at first be inexplicable, owing to the extreme tem- perature of the uppermost stratum ; but it will diminish downwards, the more so as it descends, and will finally assume a com- pletely undulatory greater and greater reflection in the same di- rection ; and thus, instead of pursuing the straight line SA, it will describe a curve SDBA, which will rise more and more convexly downwards, and will reach the earth at n, not at A, but at a certain point nearer to S. This may, consequently, be observed by any one who looks through the eye by which he will see the star is there, therefore not SA, but another ray which had been there no atmosphere would have been able to produce such a reflection ; but which, being bent by the air into the curve SDBA, actually strikes on A. Now, it is a law of optics, that an object seen through a glass is always seen in front of its true position at the moment of arriving at the eye, without regard to what may have been offered in our course between the object and the eye. Therefore we must conclude that this is the di- rection AS, but in that of Aa, a tangent to the curve SDBA at A. But because the curve described by the reflection of light is not a straight line, but a curve, we will call aboe AS, the unrefracted ray : consequently the object S will appear more elevated above the horizon AL when seen through this glass than when seen without it ; and this ap- pearance were there no such atmosphere. Since, however, the disposition of the strata is the same in all directions around A., it follows that every point of this curve ABDEFGH will remain constantly in the same vertical plane SACD, passing through the eye, the object, and the earth's centre, (4th.) The rays which pass through this curve ABDEFGH will rise all the heavenly bodies higher above the horizon in ap- pearance than they are in reality. Any such body, sup- posed to be situated at H., will appear higher than it is or will have some certain apparent altitude (as it is called). Nay, even some of those actually below the horizon, and which would therefore be invisible; but for the effect of refraction, are by that effect raised above it and brought **CHAP. T. J.** REFRACTION. into sight. Thus, the sun, when situated at P below the true horizon, A1H, of the spectator, becomes visible to him, as if it stood at Q by the refracted ray PQrA, to which A1H is perpendicular (44). The exact estimation of the amount of stroma-refraction, or the strict determination of the angle SN1A1H, is difficult. In the case of the moon, the moon, HAS, is raised in appearance above its true place, is, unfortunately, a very difficult subject of physical inquiry, and we have not been able to obtain any results. We can look for any information on the subject) are not yet entirely agreed. The difficulties arising from this fact, that the degree of refraction depends upon the temperature (power depends) is affected not merely by the superincumbent beam pressure, but also by its temperature or degree of heat. It is well known that with increasing height the earth's surface the temperature of the air is constantly diminishing; yet the less, or amount of this diminution at any given altitude increases with increasing height. Moreover, the refracting power of air is perceptibly affected by its moisture; and thus, too, is not the same in every part of an atmosphere. This circumstance has been observed in some cases of its distribution. The consequence of our ignorance on these points is to introduce a corresponding degree of uncertainty into all astronomical observations. The fluctuation which affects, to a certain appreciable extent, our knowledge of several of the most important data of astronomical science, namely, the apparent motion of stars confined within such very narrow limits as to be no cause of embarrassment, except in the most delicate inquiries, and even for such purposes as a tentative like the present. *Note.* 1. *Table Refraction*. The following statement of the amount of apparent displacement arising from this cause, at all altitudes, or in every situation of the observer's eye above or below a "visible" or point of the sky vertically above the spectator, includes all the circumstances in which astronomical observations are usually performed which may influence the result, is \begin{tabular}{l} From an Arabic word of this signification. \end{tabular} 34 A TREATISE ON ASTRONOMY. [CHAP. I. one of the most important and indispensable of all astro- nomical tables, since it is only by the use of such a table we are enabled to get rid of an illusion which must otherwise pervade all our notions respecting the celestial motions. The motions of the planets appear to us with great care, and so are to be found in every collection of astronomical tables. Our design, in the present treatise, will rest upon that of explaining their nature and use, and we must, therefore, content ourselves here, and in similar cases, with referring the reader to works especially desti- ned to this purpose, rather than to treat them at length. It is, however, desirable that he should bear in mind the following general notions of its amount, and law of variation. (43.) 1st. In the zenith there is no refraction: a ce- lestial object, situated vertically over head, is seen in its true distance if it be on the horizon. 2ndly. In descending from the zenith to the horizon, the refraction continues to increase, but decreases when the horizon is more elevated by it although these two directions thus have a high altitude. 3dly. The rate of its increase is nearly in proportion to the sine of the angle between the distance of the object from the zenith. But this rule, which is not far from the truth, at moderate zenith distances, ceases to give correct results when we approach the horizon where the law becomes much more complicated in its ex- pression. 4thly. The average amount of refraction, for an ob- ject halfway between the zenith and horizon, or at an apparent altitude of 45°, is about 1° (more exactly 37°), a quantity which increases very rapidly as we go up in the vertical horizon it amounts to no less a quantity than 33°, which is rather more than the greatest apparent diameter of either sun or moon. 5thly. We see objects nearer than when we see the lower edge of the sun or moon just ap- parently resting on the horizon, his whole disk is in reality visible before it has passed beyond the horizon and will *Vide* "Requisite Tables to be used with the Nautical Almanac." See also Nautical Almanac for 1870, Dr. Peacock's Astronomical Tables, and Mr. Bailey's Nautical Tables and Ephemeris.
one of the most important and indispensable of all astro- nomical tables, since it is only by the use of such a table we are enabled to get rid of an illusion which must otherwise pervade all our notions respecting the celestial motions. The motions of the planets appear to us with great care, and so are to be found in every collection of astronomical tables. Our design, in the present treatise, will rest upon that of explaining their nature and use, and we must, therefore, content ourselves here, and in similar cases, with referring the reader to works especially desti- ned to this purpose, rather than to treat them at length. It is, however, desirable that he should bear in mind the following general notions of its amount, and law of variation.
(43.) 1st. In the zenith there is no refraction: a ce- lestial object, situated vertically over head, is seen in its true distance if it be on the horizon. 2ndly. In descending from the zenith to the horizon, the refraction continues to increase, but decreases when the horizon is more elevated by it although these two directions thus have a high altitude.
3dly. The rate of its increase is nearly in proportion to the sine of the angle between the distance of the object from the zenith. But this rule, which is not far from the truth, at moderate zenith distances, ceases to give correct results when we approach the horizon where the law becomes much more complicated in its ex- pression.
4thly. The average amount of refraction, for an ob- ject halfway between the zenith and horizon, or at an apparent altitude of 45°, is about 1° (more exactly 37°), a quantity which increases very rapidly as we go up in the vertical horizon it amounts to no less a quantity than 33°, which is rather more than the greatest apparent diameter of either sun or moon. 5thly. We see objects nearer than when we see the lower edge of the sun or moon just ap- parently resting on the horizon, his whole disk is in reality visible before it has passed beyond the horizon and will
CHAP. L.] TWILIGHT. 35 concealed by the convexity of the earth bar for the revolving round it, which the rays of light have undergone in nearly two hours, and which they will continue to undergo for forty. (4) It follows from this, that one obvious effect of refraction must to be shorten the duration of night and twilight, and increase that of day. The sun is seen at noon and moon above the horizon. But even after they are set, the influence of the atmosphere still continues to extend itself over the whole surface of the earth, and to produce its transmission, but by reflection upon the vapours, and minute solid particles, which float in it, and, perhaps, also on the surface of the sea. This is a very important circumstance how this takes place, we must resolve, that it is not only by the direct light of the sun, but also by that which is reflected from all parts of the earth's surface. For if any portion of its light which would not otherwise reach our eyes, is intercepted in its course, and thrown back, it likewise reaches us by reflection from a more distant station. Such collective obstacles always imply floating air in the room. The whole course of a sunbeams is thus interrupted by these vapours and particles. When once a beam has entered into a dark room, it is visible as a bright line in the air; and even if it be stifled, or let out through an opposite crevice, it will still remain visible until it has passed through this source is sufficient to prevent entire darkness in the room. The luminous lines occasionally seen in the air, in which the sun appears to be moving with a certain turn "the sun drawing water," are similarly caused. They are sunbeams, through apertures in clouds, per- taining to different stations of the sun. These are reflected from the surface of the air below. Thus it is with those solar rays which, after the sun is itself concealed by the convexity of the earth's surface, pass through the atmosphere above our heads, and pass through and out of it, without directly striking on the earth at any point. Some portions of them are reflected by the minute solid par- ticles above mentioned, and thrown back, or li- terally, so as to reach us, and afford us that secondary illumination which we call twilight. The remainder will be immediately understood from the annexed figure, in which ABCD is the earth; A a point on its surface, where the sun S is in the act of setting; its tail having 36 A TREATISE ON ASTRONOMY. CHAP. I ray SAM just grazing the surface at A, while its superior rays SN, SO, traverse the atmosphere above A without striking the earth, leaving it finally at the points PQJL, after being more or less bent in passing through it; the lower most, the higher less, and that which, like SRO, nearly touches the horizon, is lost by the atmosphere, not at all. Let us consider several points, A, B, C, D, each more remote than the last from A, so that each may deeply involve itself in the atmosphere through which it receives whole space from B beneath the line A M. Now, A just receives the sun's last direct ray, and, because it is surrounded by the whole sky, is called P. PQJL. It therefore receives twilight from the whole sky. The point B, to which the sun has sent its direct either light, nor any other ray whatever, is found still within the same atmosphere which is below APM; but from the lenticular figure of PQR, it appears to be much nearer to the eye, and which lies on the visible horizon BR of P. It re- ceives a twilight, which is strongest at R, the point im- mediately below which the sun is, and does not even gradu- ally diminish as we go farther away into the atmosphere thence off. At C1 only the last or thinnest portion, PQJL of the lenticular segment, thus illuminated, lies above the horizon, CQK of which it forms there; this twilight is feeble, and confined to a small space in and near the A diagram showing various points labeled with letters (N, O, P, Q, R) and lines (ABCD) representing different positions of a ray of light. S **CHAP. I.** **TERRESTRIAL REFRACTION.** 37 horizon, which the sun has quitted, while at D the twi- light has ceased altogether. (45.) When the sun is above the horizon, it illumi- nates the atmosphere, and makes it appear more dis- perse and scatter a portion of its light in all directions, so as to send some of its rays to every exposed point, from which they return to the eye with different degrees of light, therefore, which we enjoy in the daytime, is a phe- nomenon originating in the very same causes as the twi- light of the evening. Inasmuch as the atmosphere is a part of the atmosphere, no objects would be visible to us out of direct sunshine; every shadow of a passing cloud would disappear immediately; every object would be seen every day, and every apartment, into which the sun had not di- rect admission, would be inverted in nocturnal obscurity. But this is not the case; for although the light of the sun is so strong that it might be observed, it is greatly increased by the irregularity of temperature caused by the same humidity in different parts of the atmosphere; and this irregularity being itself a constant state of condensation, and by thus bringing about partial reflections from various points of the atmos- pheric boundaries, by which much light is turned aside from the direct course, and diverted to the purpose of every illuminated object. (46.) From the explanation we have given in arts. I and II., concerning terrestrial refractions, and the mode in which it is produced in the reflection of a ray of light through successive strata, or layers of atmosphere, it appears that when a ray passes obliquely from a higher level to a lower one, or vice versa, its course is not rectilinear, but concave towards the surface on which it falls. Now, if any ray of such a kind must appear deviated from its true place, whether that object be, like the celestial bodies, entirely above or below the horizon, or like mountains or other con- tains, seen from the plains, or other terrestrial stations, at different levels, seen from each other, immersed in it. It is evident that if these rays are refracted according to their with a difference of density in the aerial strata, must also have, corresponding to it, a certain amount of refraction; D 28 A TENTATIVE ON ASTRONOMY. [CHAP. I. low, indeed, than what would be produced by the whole atmosphere, but still often of very appreciable, and even considerable, amount. This refraction between terres- trial objects and the sun's rays is so great that we can distin- guish it from that total effect which is only produced on celestial objects, or such as are beyond the atmosphere, and which is called the "refraction of the horizon." (47.) Another effect of refraction is to distort the visi- ble forms and proportions of objects seen near the hori- zon. The vertical diameter of any object, whether altitude, always appears round, assumes, as it approaches the horizon, a flattened or oval outline; its horizontal diameter is also somewhat distorted in the same di- rection. When very near the horizon, this flattening is evidently more considerable on the lower side than on the upper; and when an object is exactly at the hori- zontal circle, but a species of oval, which deviates more from a circle below than above. This singular effect, which occurs with all terrestrial objects, depends on the rapid rate at which the refraction increases in approach- ing the horizon. Very every visible point in the sun's circumference may be considered as a source of light; and still appear circular, though displaced; but the lower portions being more raised than the upper, the vertical diameter is thereby increased. In consequence of this difference in hori- zontal diameter are equally raised, and in parallel direc- tions, so that its apparent length remains the same. The diffrac- tion of light by the atmosphere causes all objects near the horizon, beyond what they appear to have when high up in the sky, less nothing to do with reflec- tion. Hence it follows that terrestrial objects seen near the terrestrial objects interposed, or placed in close compari- son with them. In that situation we view and judge of them as if they were at a greater distance than they really are; and will acquire a habitual habit of attention to parts. Albeit we have no associations to guide us, and their insolation in the expanse of space does not enable us to estimate their size, to overrate their apparent magnitudes. Actual measure- ment with a proper instrument corrects our error, with- out however, dispelling our illusion. By this we learn, that the sun, when just on the horizon, subtends at our **CHAP. I.** OF THE SPHERE OF THE HEAVENS. eyes almost exactly this size, and the reason a materially finite angle, than when seen at a great altitude in the sky, owing to the effect of what is called parallax, to be ex- pressively less than it really is. (48.) After what has been said of the small extent of the atmosphere in comparison of the mass of the earth, we may now consider how much of the light which enters into our eyes comes from bodies situated within the atmos- pheres which pene- trate the sky, and which, while they obviously form no part of the earth, and receive no support from it, yet are nevertheless supported by the clouds upon the air, nor drifted by the winds, to be ex- ternal to our atmosphere. As such we have considered them to be external to us, but it is evident that in the immensity of space beyond, and esti- mated, perhaps, for any thing we can perceive to the contrary, at con- siderable distances from us, they must be internal to us. (49.) Could a spectator exist unassisted by the earth, or any solid support, he would see around him at one view all the stars which are visible to his eye, and all the suns of the universe; and, in the absence of any means of judging of their distances from him, would refer them, in his own mind, to some imaginary sphere or plane of con- tention, to the concave surface of an imaginary sphere, having his eye for a center, and its surface at some vast undulating level. But this is impossible; for every star which appear to him large and bright, is to nearer him than the smaller and less brilliant; but, independent of this fact, it is evident that they cannot all be on such a plane or surface. For if they were so arranged as to be improperly in their referring their places, geometrically speaking, to such a plane or surface of such a purely imaginary sphere, which their respective distances would require; and there would be much advantage in so doing, as by thus making their apparent relative positions could be accurately measured, according to their true distances down. This objects in a landscape at every variety of distance from one eye, yet put them all down in a picture on one plane with one diameter and one uppermost proportioned, and the likeness is not taxed with incongruity. 40 A TREATISE ON ASTRONOMY. [CHAP. L ness, though a man in the foreground should be repre- sented larger than a mountain in the distance. So it is to a spectator of the heavenly bodies pictured, projected, or suspended in the air, to represent the moon, as if she were near heaven, or to represent the sun, as if he were in the sky or heavens. Thus, we may easily conceive that the moon, which appears to us so large as the moon, though very distant, yet appears to us much nearer than it is by proximity, and may be really much less; while both the moon and sun may only appear larger and brighter than the stars, because they are nearer to our eyes. (30.) A spectator on the earth's surface is prevented, by the great mass on which he stands, from seeing into all that lies beyond his horizon. He cannot see what is behind him, nor can he see what is behind any other thing which he must look in any degree downwards. It is true that, if his place of observation be at a great eleva- tion, the earth will appear to him with such an expanse of vision a little more than a hemisphere, and reflection, wherever he may be situated, will enable him to look, as if he were at sea; but this is not sufficient to prevent that added to his visual range can hardly ever, unless in very extraordinary circumstances, exceed a couple of degrees of heaven's diameter. For instance, if a man stand on the roo- pours near the horizon. Unless then, by a change of his geographical situation, he should shift his horizon (which is always fixed) so as to include all that con- vexity of the earth at his station); or unless, by some movements proper to the heavenly bodies, they should displace themselves towards him; or unless, by some rotation of the earth itself on its centre, the point of its surface which he occupies should be moved out of his line of sight; or unless he should move away from space: he would never obtain a sight of almost one Such as the following for instance: The late Mr. Snellie, the cele- brated merchant, residing in a balloon from Dublin at about 2 o'clock in the afternoon. He was sitting in a chair placed under the balloon so as to ap- proach the English coast; when the balloon descended upon the surface of the water. He saw nothing but water; and immediately afterwards saw land to clear it. He thereupon nearly all his balls; and suddenly rising again upwards; he saw land again; and then saw water again. After this he saw another of a western nature. He subsequently descended in Wales, and without difficulty saw England and Scotland. But when he attempted to descend from Dr. Barlowe who was present at his ascent, and read his own ac- count of this voyage. CHAP. L.] CHANGE OF LOCAL SITUATION. 41 half the objects extraneous to our atmosphere. But if any of these objects happen to be near us, all may come into view according to the circumstances. (51.) A traveller, for example, shifting his locality on our globe, will find that the sun, which he has left behind from his original station, in a way which may be not in- apably illustrated by comparing him to a person standing before a mirror, appears to him to be at the same distance as when presented by its trunk ends of his view of all those parts of the landscape which it occupies as an object; but by walking round the circumference of the earth, and viewing the whole panorama may be obtained. Just in the same way, if we set off from any station, as London, and travel towards the north pole, we shall see the stars and celestial objects which are never seen from London come successively into view, as if rising up above the horizon. The same effect is produced by a ship sailing in reality our horizon, which, travelling with us southwards round the sphere, stirs in succession beneath those objects which are never seen from our station; and thus we have a series of successions thus gradually brought into view in the clear calm nights of tropical climates; in long voyages to the south, it dwells upon by all who have enjoyed this spectacle, A diagram showing three circles labeled A, B, C. and never fails to impress itself on the recollection among the most delightful and interesting of the ass- ociations connected with extensive travel. A glance at D 2 42 A TREATISE ON ASTRONOMY. [CHAP. I.] the accompanying figure, exhibiting three successive positions of the earth, with the sun at each, corres- ponding to each, will place this process in clearer evidence than any description. (50.) The earth itself will have a mo- tion of rotation on its centre. It is evident that a spec- tator at rest (as it appears to him) on any part of it will, unperceived by himself, see all the terrestrial objects un- perceived, we say, because his horizon will constantly contain, and be limited by, the several terrestrial objects. He will perceive them only when they appear before his eyes, in which all the familiar objects in it, which serve him for landmarks and directions, retain, with respect to him, their relative situation, and do not change their position. The perfect smoothness and equality of the motion of so vast a mass, in which every object he sees around him remains in the same relative position, makes his entertaining any suspicion of his actual change of place. Yet, with respect to external objects,—that it is so, all external objects remain in the same relative posi- posed rotation of the earth,—his horizon will have been all the while shifting in its relation to them, precisely as in the case of a revolving wheel or disc. Recurring to the figure of such a wheel, it is evident why the same thing, so far as its visibility is concerned, whether it be seen from one point or another, is con- successively into the situations A, B, C; or whether, the earth remaining at rest, he has transferred himself per- sonally from one point to another. In either case the spectator in the park will obtain precisely the same view of the landscape, whether he walk round the tree, or whether we suppose him to stand still and look up to an upright pylote, while he stands on a projecting step attached to it, and allows himself to be carried round by its motion. The only difference will be in his view of the tree it- self, of which, in the former case, he sees but one part; but, in the latter, only that portion of it which remains constantly opposite to him, and immediately under his eye. (53.) By such a rotation of the earth, then, as we have supposed, the horizon of a stationary spectator will **CHAP. L.** DIURNAL ROTATION OF THE EARTH. I can only state that I have observed this rotation of the earth, but I cannot pretend to give any account of its cause. It is evident that the sun does not move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the sun were moving, we should see the stars move with it. But the sun appears to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The sun is always seen in the same place in the heavens, and therefore it must be at rest; and if it were not at rest, it would be continually changing its position, and we should see it change its place every day. This is a very remarkable fact, and one which has been observed by many persons. The sun is always seen in the same place in the heavens, and therefore it must be at rest; and if it were not at rest, it would be continually changing its position, and we should see it change its place every day. It is evident that the earth also moves, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the earth were moving, we should see the stars move with it. But the earth appears to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The earth is always seen in the same place in the heavens, and therefore it must be at rest; and if it were not at rest, it would be continually changing its position, and we should see it change its place every day. It is evident that the moon also moves, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the moon were moving, we should see the stars move with it. But the moon appears to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The moon is always seen in the same place in the heavens, and therefore it must be at rest; and if it were not at rest, it would be continually changing its position, and we should see it change its place every day. It is evident that the planets also move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the planets were moving, we should see the stars move with them. But the planets appear to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The planets are always seen in the same place in the heavens, and therefore they must be at rest; and if they were not at rest, they would be continually changing their positions, and we should see them change their places every day. It is evident that the comets also move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the comets were moving, we should see them move with them. But the comets appear to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The comets are always seen in the same place in the heavens, and therefore they must be at rest; and if they were not at rest, they would be continually changing their positions, and we should see them change their places every day. It is evident that the meteors also move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the meteors were moving, we should see them move with them. But the meteors appear to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The meteors are always seen in the same place in the heavens, and therefore they must be at rest; and if they were not at rest, they would be continually changing their positions, and we should see them change their places every day. It is evident that the comets also move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the comets were moving, we should see them move with them. But the comets appear to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The comets are always seen in the same place in the heavens, and therefore they must be at rest; and if they were not at rest, they would be continually changing their positions, and we should see them change their places every day. It is evident that the meteors also move, because the stars appear to be stationary, and yet they are very distant objects; and therefore, if the meteors were moving, we should see them move with them. But the meteors appear to be at rest, and so do all other bodies which appear to us to be at rest. This is a very remarkable fact, and one which has been observed by many persons. The meteors are always seen in the same place in the heavens, and therefore they must be at rest; and if they were not at rest, they would be continually changing their positions, and we should see them change their places every day. It is evident that the meteors also move because **A TREATISE ON ASTRONOMY.** 44 stand the continual reproduction of the same phenomena, in the same order, at equal intervals of time. (56.) A free rotation of the earth round its centre, if it exists, must be accompanied by some mechanical laws which obtain in the motions of masses of matter under our immediate control, and within our ordinary experience, under similar material and terrestrial conditions. It must be invariable in its direction with respect to the sphere itself, and uniform in its velocity. The necessity of this condition is obvious. The diameter of the sphere, whose poles, or extremities, where it meets the surface, correspond always to the same points on the horizon, cannot change its position under the influence of external agency; conceivably, in which the poles of the imaginary line or axis about which it is at any moment revolving may be fixed upon the surface, but shift upon it every moment. Such changes, however, are inconsonant with the idea of a rotation of body, since they would require a motion performed in free space, and without resistance or obstruction from any surrounding medium. The complete absence of such changes is therefore necessary; the strict fulfilment of the two conditions above mentioned. (57.) Now, these conditions are in perfect accordance with what we observe, and what recorded observation teaches us in respect to the diurnal motions of the hea- venly bodies. But it is impossible to deny that in history, that any sensible change has taken place since the earliest ages in the interval of time elapsing between two successive revolutions of the earth about its axis of the sky; or, rather, it is demonstrable from astronomical records that no such change has taken place. And with respect to the apparent motions of stars—the axis of rotation—the appearances which any alteration in that respect must produce, would be marked, as we shall presently see, by a series of phenomena of a very obvious kind in the apparent motions of the stars; which again, history decidedly declares them not to have undergone. (58.) But, before we proceed to examine more in de- **CHAP. I. J.** APPARENT PERIHAL MOTION. tain how the hypothesis of the rotation of the earth about an axis accords with the phenomena which the diurnal motion of the heavenly bodies afford us to notice, it will be necessary to consider what is meant by the diurna- lal motion consists, and how far it is participated in by them self ; or whether any of them form exceptions, which require a different explanation from that of the rest. We will therefore, suppose the reader to ascend himself, on a clear evening, just after sunset, when the first stars begin to appear in the heavens. He will then have a general view of the heavens at once, and can obtain a general view of the heavens can be obtained. He will thus perceive, above all, as it were, vast congeries of stars, which seem to be composed of various magnitudes, of which the brightest only will first catch his attention; but the twinkling and the light will appear as the darkens increases, till the whole sky is surpassed with them. When he has admired this, he will observe that the stars are not fixed in one place, but move in a circle round him, and of so much thought,-spectacle which no one can view without emotion, and which is worthy of being recorded in our history. The sun is a very remarkable object in this na- ture and purpose,-but him fix his attention more particu- larly on a few of the most brilliant stars, as he can easily distinguish them from each other by their dis- tance from one another for some time, and let him refer their pre- sent situations to some surrounding objects, as build- ings, trees, mountains, etc., and compare them with dif- ferent quarters of his horizon. On comparing them again with their respective points of reference, after a moderate inter- ruption of time, he will find that they have changed their places, and advanced, as by a general movement, in a westward direction; that is to say, that those which are now seen to sede from the horizon, while those which he towards the west will see be about to approach it; and if watching long enough into the night, he will find that they rise and disappear; while others, in the eastern quarter, will be seen to rise as if out of the earth, and joining in the great circle round him with their course with the rest towards the opposite quarter. (30) If he persistia for a considerable time in watchi 46 A TREATISE ON ASTRONOMY. [CAP. I.





































































br>their motions on the same or on several successive nights, he will perceive that each star appears to describe, as far as its course lies above the horizon, a circle in the sky; that the circles so described do not differ greatly in magnitude, but vary in such a manner that those described by different stars differ greatly in respect of the parts of them which lie above the horizon, and that the parts of the circles which lie below the horizon are all equal. This is the So-called "horizon," which remains for a short time above it, and dis- appears when it sinks into sight only after one or two seg- ments of their diurnal courses have passed, while they rise and disappear between the south and east, describe larger segments of their cir- cles above the horizon than those which they describe in sight, and then proceed as far to the westward of south as they rose to the eastward; while such rise exactly in the east end just described, and fall exactly at the west end of the circle described in sight. Thus with some, again, which rise between the east and north, the same line obtains at least; while with others, whose diurnal motions are more rapid, and whose proportion of their motions above the horizon, and the proportion of their visible segment of their diurnal circles to their whole cir- cular motion, is greater in sight than in motion, their visible diurnal areas are more than semicircles. But the magnitudes of the circles themselves are not always equal; for instance, northward of south almost all of the circles being described by those which rise exactly in the east point. Carrying his eye farther northward, he will find that those which rise at a great distance motion past great horizons at its north point, or only dip below it for a moment; while others never reach it at all. In this way we see that every star, revolving about a centre round one pole, called the pole, which appears to be the common centre of all their motions, describes a circle in sight; but sometimes, may be considered immovable. Not that this point is marked by any star. It is a purely imaginary centre; but there is near it our considerably bright star, called the Pole Star, which is easily recognised by the very
*We suppose our observer to be stationed in some northern latitude; somewhere in Europe, for example.* **CHAP. I.** APPARENT DIAHETAL MOTION. small circle it describes; so small, indeed, that, without paying particular attention, and referring its position very nearly to the same point of the horizon, one would rest, and be, itself, mistaken for the common centre about which all the others in that region describe their circles; or rather, as it is more likely, one would mistake this splendid and remarkable constellation or group of stars, called by astronomers the GREAT BEAR. (60.) The reason why the apparent diaphetal motions of all the stars among one another is not changed by their diurnal motion. In whatever part of the heavens we may look at any time during the night, they form with each other the same identical groups or configurations, to which the name of constellations has been given. But though these groups are always in course, these groups stand differently with respect to the horizon; and those towards the north, when in the course of the day, are seen to rise above it; and those below it, when below that common centre of motion described in the last article, become actually inverted with respect to the horizon; so that they appear to move towards us on different points towards the pole. In short, he will perceive that the whole assembly of stars visible at once, or in successive order, forms a certain figure or constellation, which seems to recur with a uniform motion, so that if one formed one coherent mass; or as if it were in- troduced into a sphere of infinite radius, and revolving round the earth, or rather the spectre in the centre, and turning round it once in twenty-four hours; so as to pass through that fixed position p.ele already mentioned. (61.) Lastly, he will notice, if he have patience to observe carefully for some time after sunset till morning twilight, that those stars which he observed set- ting at a given hour before sunset, are those which were rising when he first began to notice them have completed their course; and are now set; and that those which rose at a given hour before sunrise are above, is now beneath him, and its place supplied by that which was at first under his feet, which he will thus disco- ver to be no less copiously furnished with stars than thi 48. A TREATISE ON ASTRONOMY. [CHAP. I. other, and bespangled with groups no less permanent and distinctly recognisable. Thus he will learn that the great constellations we have above spoken of are revolving round the pole, or centre of the sphere, and that the face of the sphere, being in reality nothing less than a universe of luminaries surrounding the earth on all sides, and brought in succession to view by the motion of the earth's circum- nomy according to its own visible ray or direction from his eye (by which means he sees the sun at noon when it him- self occupies the centre). (See art. 49.) (62.) There is, however, one portion or segment of this sphere which is never seen off the horizon. As there is a segment towards the north pole parallel to the pole above his horizon, in which the stars never set, so there is a corresponding segment towards the south pole below whose cir- cles of the more southern stars are described, in which they never rise. The stars which border upon the extreme circumference of this northern segment, and appear at any point of his horizon, and show themselves for a few moments above it, precisely as those near the circumference of the northern hemisphere appear to us at night; but for a moment below it, to reappear immediately. Every point in a spherical surface has, of course, another diametrically opposite point; and therefore every star describes its sphere into two hemispheres--a superior and inferior--there must of necessity exist a depressed pole to the south, corresponding to the elevated pole to the north; and a por- tion situated at it, perpetually beneficent, as there is another surrounding the north pole, perpetually above it. (63.) He verily sees noumen sublimis; at least, Sunturum non est sublimis; --Vitruvius. One pole rides high, one ploughed beneath the main. Such is our celestial globe. (63.) To get sight of this segment, he must travel south- wards. In so doing, a new set of phenomena come for- ward. For instance, if he travels from London to some of those constellations which, at his original station, barely grazed the northern horizon, will be observed to sink be- low it during his journey; and after having passed a short time, but gradually for a longer part of the twenty-four hours. They will continue, however, to circulate about the same **CHAP. I.** EFFECT OF CHANGE OF LATITUDE. point—that is, holding the same invisible position with respect to them in the cone of the heavens among the stars; but this point itself will become gradually depress'd with regard to the earth, and will appear to descend towards the horizon, until at that which the diurnal motion is performed, will appear to have become continually less and less inclined to the horizon, till it shall reach the northern or southern pole; and being depressed the southern pole will rise, and constellations surrounding it will come into view; at first momentarily, but afterwards more and more distinctly, till they shall form a new revolution—realizing, in short, what we have already stated in art. 51. (6.) As he travels continually southwards, he will at length reach a line on the earth's surface, called the equator, at any point of which, indifferently, if he take up his station there, he will find himself in the middle of the heavens; for he has both the centres of diurnal motion in his horizon, occupying opposite points, the northern pole having been described as such by reason of its being nearest to him. In geographical position, the diurnal rotation of the heavens will appear to him to be exactly similar to that of the sun; for he will see a circle round his head formed by the sun's apparent path during one day's course; and this circle will be divided equally between north and south by a line which he shall call his horizon above and below half beneath his horizon, remaining alternately visible for twelve hours, and consequently invisible for twelve hours each. In consequence of this rotation of the heavens he is conceived from his successer view. In a night of twelve hours (suppos- ing such a continuum) he will have seen all the stars which he will have passed in review over him—the whole hemisphere with which he began his night's observation will have been traversed; and after his return home he will once again brought up from below. (5b.) He has the equator and travel still further southwards; and as he does so, those stars which are elevated above his horizon, and the northern will sink below it; and the more, the farther he advances southwards. The same thing happens to those stars which are below the equator as that from which he started was to the north, he will find the whole phenomena of the heavens reversed; for those stars which were above his horizon when he ascended acréd their whole diurnal circles above his horizon, and never set, now describe them entirely below it, and never E 50 A TELLING ON AFTERNOON. [CHAP. 6] rise, but remain constantly visible to him; and vice versa, those sides which at his former station he never saw, he will now never cease to see. (66.) Finally, if afloat of variously southerly from his first station, and having passed the north pole, he will observe the northern pole of the heavens to become more elevated above his horizon, and the southern one depressed be- low it. This is owing to the difference in the season in less variety of stars, because a greater proportion of the whole surface of the earth is covered by water than by land; or conversely, because the circle described by each star shrinks, too, becomes more nearly parallel to the horizon ; and, in short, every appearance of a star that would have been visible from the north, he would so lengthen its altitude, a point certainly nowhere the northern pole of the heavens, at which none of the stars can be seen; but such variations occur round the horizon in circular paral- lels. Many endeavours have been made to reach this point, which is called the "equator," but without success; for it is a barrier of almost insurmountable difficulty being presented by the increasing rigour of the climate as we approach it. The same has been said, and the phenomena of those regions, though not precisely such as we have described, is what must establish the pelti itself, have no other cause than their predominance with respect to latitude. A similar reason applies to those south of the earth, which, however, is more unpre- sensible, or at least, has been less nearly approached, than the former. (67.) The above is an account of the phenomena of the diurnal rotation of the earth. There are many different geographical situations, not grounded on any specula- tion, but actually observed and recorded by travellers and voyagers. It may be worth while to reconcile with the hypothesis of a rotation of the earth round a fixed axis. In order to show this, however, it will be necessary to consider some of those appearances pre- sented by an assembly of remote objects, when viewed from different parts of a small and circum- scribed station. (68.) Imagine a landscape, in which a great multitude CHAP. L.] DISTANCE OF THE STARS. 51 of objects are placed at every variety of distance from the beholder. If he shift his point of view, though but for a moment, to any other spot, he will find that the apparent positions of the nearer objects, both with re- spect to himself and to each other. If he advance north- wards, the nearer object will appear to move westward, which were, therefore, to the east and west of his original station, will be left behind him, and appear to him as moving towards him. Objects situated between other at first, will appear to separate, and others to ap- proach, and perhaps conceal each other. Remote objects on the contrary, will appear to approach each other, indepen- dently of relative position. An object to the east of his original station, at a mile or two distance, will still be referred by him to the east point of his horizon, with hardly any perceptible deviation. The reason of this is, that the position of every object is referred by its observer to some point on an imaginary line passing through his eyes, having our eye for its centre; and as we advance in space, this line will be carried forward with us. Consequently, along with us, the visual rays AP, AQ, by which ob- jects are referred to its surface (at C), for instance), shift their place accordingly. But when we have advanced so far as A, AB being thus fixed as an axis or line of reference, and assume new positions BPp, BQq, revolving round the same axis AB, these rays will still refer themselves to Cp, qq with our visual sphere, will appear to recede on its surface, but with different degrees of im- portance according as they are more or less distant. At the same distance of advance AB subtending a greater an- gle, APBp=BPp at the near object P than at the remote one Q.
A B C D E F
P Q R S T U
52 A TREATISE ON ASTRONOMY. [CHAP. I. (60.) The perpendicular angular motion of an object on one sphere of view, with respect to another, at the same point of view, is called parallactic, and it is always expressed by the angle BAP subtended at the object P by a line joining the two points of contact of the spheres of view. For it is evident that the difference of angular position of P, with respect to the invariant direction ABD, when we consider the two spheres of view, is equal to the sum of the two angles DBP and DAP; now, DBP being the exterior angle of the triangle, ABD, ADB is equal to the sum of its interior angles, DBP, DBF=ABP+AFB, whence DBP=ABP=ADEF. (70.) It follows from this, that the amount of paral- lactic motion of an object on one sphere of view, with respect to another, at the same point of view is, exterior parallax, less, as the distance of an object viewed is greater; and when that distance is ex- tremely great, it becomes zero. On the other hand, with regard to objects near us, the parallax becomes insensible; or, in other words, objects do not appear to vary in situation at all. It is on account of this circumstance that we find for the first time we are surprised and confounded at the little progress we appear to make by a considerable change in our position. We see nothing altered, but a small parallelistic change in the relative situations of the vast and distant masses which surround us. Whether they be stars or planets or comets or suns, a real spherical surface appears to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- urally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- urally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- urally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- aturally suggests itself to our minds. But it is only a con- scious perception of sensation in the nature of eyes, which even alone cannot give us any idea of such a thing. For instance, a real spherical surface would seem to us to be round in itself, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same as- pect, whatever may be our position on earth. The ideal sphere without us, in which we refer the places of objects, and which we carry along with us wherever we go, no doubt nat- CHAP. I.] DISTANCE OF THE STARS. 53 (71.) Whatever notion, in other respects, we may form of the stars, their apparent distance must be very nearly distinct. We are not so, the apparent angular interval between any two of them seen over head would be less than that which separates the nearest of the constellations, instead of preserving the same ap- pearances and dimensions during their whole diurnal course, they appear to us to be continually moving through the sky, as we see a small cloud in the horizon swell into a great overshadowing canopy when drifted by the wind across our window, as may be seen in the nex- tigeologica, where $a$, $A$, $b$, $B$ are three different positions of A diagram showing three different positions of stars labeled \(a\), \(A\), \(b\), \(B\) with arrows indicating movement. the same stars, as they would, if near the earth, be seen from a spectator \(S\), under the visual angles \(aSb\), \(ASb\), \(ABb\). Now this difference of position is very considerable. The nearest measurements of the apparent an- gular distance of any two stars distant \(S\) taken, in any part of the heavens, will show that they do not exhibit any equal effects of refraction, or when taken at such times that this cause of distortion shall act equally on both, these measurements are found to differ but little from each other only thus, but at whatever point of the earth's surface the measurement is performed, the results are absolutely identical. This is owing to the fact that the observations are delicate enough to indicate, by an increase or diminution of angle, whether one point of the earth is nearer or further from another point of the heavens. (72.) The necessary conclusion from this is, that the dimensions of the earth, large as it is, are comparatively *nothing*, absolutely imperceptible, when compared with E 54 THEATRE ON ASTRONOMY. CHAP. L. the interval which separates the stars from the earth. If an observer walks along a straight line more than five yards in diameter, and from different points in its cir- cumference measure with a sextant, or other more exact instrument, he will find that the distance between two points P and Q, subtended at those stations by two well defined points in his visible horizon, PQ, he will not once A diagram showing a straight line AB with points P and Q on opposite sides. The line AB is labeled "AB" and has a point C marked on it. Points P and Q are connected to C by lines PP' and QQ', respectively. The diagram also shows a circle around the line AB with a point D marked on it. be advertised, by the difference of the results, of his change of distance from them arising from his change of place. This is because the stars do not produce any change in their general aspect to his un- sighted sight. This is one of the immovable instances wherein we see that the most perfect instruments means places us in a totally different situation in respect to matters of fact, and conclusions thence deducible, from what we have seen, are not affected by any case on the mere judgment of the eye. To so great a nicety have such observations been carried by the aid of an instrument so delicate as the quadrant, that this dis- meter above mentioned may thus be rendered sensible, may thus be detected to have a size, and an insensible piece, which is equal to 1000 times its own dimensions. Observations, differing, it is true, somewhat in method, but identical in principle, and extending over many years, have been applied to the stars, and with a result such as has been already stated. Hence it follows, incontrovertibly, that the distance of the stars from the earth cannot be so **CHAP. I.]** **DISTANCE OF THE STARS.** small as 100,000 of the earth's diameter. It is, indeed, incomparably greater; for we shall hereafter find it fully demonstrated that the distance of the stars from us, though may appear, is yet much undererred. (37.) From such a point of spector with our instruments, the earth would be imperceptible; and, reciprocally, an object of great magnitude would appear to us infinitely small, and be equally unperceivable. If, therefore, at the point on which a spector stands, we draw a plane touching the globular body of the earth, and passing through the centre of the region of the stars, and through the centre of the earth conceive another plane parallel to the former, and co- axial with it, we shall see that all points in this second plane, throughout their whole extent by the same interval, viz. a semi-diameter of the earth, will yet, on account of the circumstances mentioned above, appear to us infinitely small and equal together, and indistinguishable from each other in the region of the stars, when viewed by a spector on the earth. The line which connects these two planes will be broadest to his eye, and will only mark out a great circle in the heavens, which, like the vanishing point in perspec- tive in architecture, is called the horizon. This horizon, converges, in fact, the remaining line to which all planes parallel to the horizon offer a similar appearance indistinguishable from each other. (38.) The two planes just described are termed, in astronomy, the sensible and rational horizon of the ob- server's sight. The sensible horizon is that which marks its vanishing line, is also spoken of as a circle of the sphere, under the name of the celestial horizon, or simply as the horizon. From what has been said (art. 72) of the distance of the stars, it follows, that if we suppose a spector on one side of the sensible horizon to observe all points on the rational horizon, in the same manner as that of a corresponding spector on the surface by his sensible horizon; and if we consider them in all possible same relative situations, each beholding that entire hemi- sphere of the heavens which is above the celestial horizon, corresponding to their common zenith. A diagram showing two planes intersecting at a point representing a spector's position. One plane represents the region of stars while the other represents Earth's surface. The intersection forms a circle representing the horizon. 50 A TREATISE ON ASTRONOMY. CHAR. I. (75.) Now, so far as appearances go, it is clearly the same thing whether the heavens, that is, all space, with its contents, revolve round a spectator at rest in the earth's centre, or remain fixed, and have the spectator himself in the opposite direction in his place, and view them in suc- cession. The aspect of the heavens, at every instant, as referred to any one of these two positions (whether near with him), will be the same in both suppositions. And since, as has been shown, appearances are also, so far as the stars are concerned, the same whether we look upon the face as to one at the centre, it follows that, whether we surp- pose the heavens to revolve without the earth, or the earth within them, they will appear to us exactly alike. Such phenomena, to all its inhabitants, will be no way different. (76.) The Copernican astronomy adopts the latter as the true hypothesis; but this is only because it is forced by the necessity of otherwise resorting to the cumbersome mechanism of a solid but invisible sphere, to which the state of our knowledge does not admit. It may not be carried round the earth without detriment of their relative situations later on. Such a contrivance would, indeed, be necessary if we supposed that all bodies of stars, so as to say "appearances," but the movements of the sun and moon, as well as those of these planets, are in- compatible with any other hypothesis than that of a sphere about which we come to treat of these bodies. On the other hand, that a spherical mass of moderate dimensions (or rather, when we speak of it as a sphere) is not required (as appears of eremistic magnitudes), held by no tie, and free to move and to resolve, should do so, in conformity with those general laws which govern all motions. But such are the con- ditions of all material bodies, so as far from being a postu- late difficult to be conceded, that the wonder would rather be shewn how it can be denied. Hence it follows that there- fore, we shall henceforth regard it; and as, in the pro- gress of our work, analogies offer themselves in its sup- port from many parts of nature; and as this book itself, shall not fail to point them out to the reader's notice. Meanwhile, it will be proper to define a variety of terms which will be continually employed hereafter. (77.) Darnaxius 1. The axis of the earth is that di- **chap. L** **DEFINITIONS.** 57 aneter about which it revolves, with a uniform motion, from west to east; performing one revolution in the in- terior which diapizes between any star leaving a certain point in the heavens, and returning to the same point again. (78.) Decr. 2. The poles of the earth are points distant from the center of the earth. The North Pole is that nearest to Europe; the South pole that most remote from it. (79.) Decr. 3. The sphere of the heavens, or the sphere of the universe, is that which comprehends all the stars, and having the centre of the earth, or, which comes to the very same thing, the eye of any spectator on earth, as its centre. This sphere may be regarded as the vanishing point of a system of lines parallel to that radius of the sphere which passes through it, seen in perspective from any point at a great distance from it. The vanishing line of a system of planes parallels to itself. This mode of conceiving such points and circles has great advantages in a variety of cases. (80.) Decr. 4. The meridian is a plane passing through the sphere of the heavens, vertically over the specta- tor's head, and vertically under his feet; they are, there- fore, perpendicular to each other. They are also perpen- dicular to the direction of a plumb-line at his station. The plumb-line itself is, in every point of the earth, perpendi- cular to the horizon. Hence, if we consider two points be- fore, can the actual directions of two plumb-lines be re- garded as mathematically parallel? They converge to- wards each other towards their respective vanishing points (as in the area of building--in one and the same tow- ner), because from exact parallelism is so small, that it corre- sponds to a convergence of plumb-lines amounting to about 1 minute. The zenith and nadir are the poles of this horizon; it is to say, point 90° distant from each other. The horizon itself is therefore the vanishing line of a system of planes parallel to the sensible and rational horizon. *From Arabic words. Nadir corresponds evidently to the German nachdem.*
Decr. Def. Description
78. Decr. 2. The poles of the earth are points distant from the center of the earth. The North Pole is that nearest to Europe; the South pole that most remote from it.
79. Decr. 3. The sphere of the heavens, or the sphere of the universe, is that which comprehends all the stars, and having the centre of the earth, or, which comes to the very same thing, the eye of any spectator on earth, as its centre. This sphere may be regarded as the vanishing point of a system of lines parallel to that radius of the sphere which passes through it, seen in perspective from any point at a great distance from it. The vanishing line of a system of planes parallels to itself. This mode of conceiving such points and circles has great advantages in a variety of cases.
80. Decr. 4. The meridian is a plane passing through the sphere of the heavens, vertically over the specta- tor's head, and vertically under his feet; they are, there- fore, perpendicular to each other. They are also perpendi- cular to the direction of a plumb-line at his station. The plumb-line itself is, in every point of the earth, perpendi- cular to the horizon. Hence, if we consider two points be- fore can the actual directions of two plumb-lines be re- garded as mathematically parallel? They converge to- wards each other towards their respective vanishing points (as in the area of building--in one and the same tow- ner), because from exact parallelism is so small, that it corre- sponds to a convergence of plumb-lines amounting to about 1 minute. The zenith and nadir are the poles of this horizon; it is to say, point 90° distant from each other. The horizon itself is therefore the vanishing line of a system of planes parallel to the sensible and rational horizon.
58 A TREATISE ON ASTRONOMY. CHAP. I. (81.) Def. 5. Vertical circles of the sphere are great circles passing through the zenith and nadir, or great cir- cles perpendicular to the horizon. On these are mea- sured the angles of the celestial meridian and equator—the complements of which are their zenith distances. (82.) Def. 6. The poles of the heavens are the points at the extremities of the vertical circle passing through the zenith and nadir, or the vanishing points of all lines parallel thereto. (83.) Def. 7. The earth's equator is a circular line on the surface of the globe, dividing it into two hemispheres—a northern and a southern—in the midst of which is situated the respective poles of the celestial sphere. The pole of the earth's equator is, therefore, a plane perpendicular to the earth's axis, and passing through its centre. The celestial equator is a circle in this plane, making with it an infinite extension of the plane of the terrestrial, and is the vanish- ing line of all planes parallel to it. This circle is called the celestial equator. (84.) Def. 8. The terrestrial meridian of a station on the surface of the earth is that straight line passing through both the poles and through the place. When this line is prolonged to the sphere of the heavens, it marks the north and south poles of that sphere, and divides it into two equal parts. It is also called the celestial meridian, which is a vertical circle passing through both poles. The place of the meridian is the phase of this circle, and its intersection with the sensible horizon of the speci- tation is called its horizon line, and marks the north and south poles of that visible heavens is determined. For their simultane- ous measurement, a peculiar instrument has been im- p CHAP. I. LATITUDE AND LONGITUDE. gined, called an altitude and azimuth instrument, which was described in the preceding chapter. (S6.) DER. 10. The latitude of a place on the earth's surface is its angular distance from the equator, measured in degrees, minutes, and seconds, from 0 up to 90°, and northwards or southwards according to the hemisphere; the place lies at 51° 28' 40" north latitude. This definition of latitude; it will be observed, is to be considered as only temporary, because it does not give us the physical form of the figure of the earth, and a better acquaintance with the necessities of astronomy, will show that this definition is insufficient for all purposes. For instance, if we consider a point in such a circle by its latitude, then Green- wich would be said to be situated in the parallel of 51° 28' 40" (Q.E.D.) (77.) DER. 11. Parallels of latitude are small circles on the surface of the earth, and they are everywhere at right angles to each other. The inclination of these parallels to the surface is the inclination of their meridian to that of some fixed station referred to as a point to reckon from. Eng- lishmen call this inclination the Greenwich Meridian. Greenwich for this station; foreigners, the principal ob- servatories of their respective nations. Some geographers have been so much influenced by this name, that when we speak of longitude, we reckon from Greenwich. The longitude of a place is, therefore, measured by the arc of the great circle passing through that place and Greenwich; and that of Greenwich; or, which is the same thing, by the spherical angle at the pole included between these meridians. As latitude is reckoned north or south, so longitude is reckoned east or west; but both are reckoned in opposite directions, and greatly, however, to avoid confusion and ambiguity in computations, were this mode of expression abandoned, and longitudes reckoned from any given point instead of from Greenwich; and the whole circle from 0 to 360°. Then the longitude of London would be 51° 28' 40" east, or 357° 39' 38" west of Greenwich. In short, it is evident on which we shall henceforth use and recommend others
Lat. Long.
51° 28' 40" west
60 A TREATISE ON ASTROLOGY. CHAP. L to use the term, the latter is its proper designation. Longitude is the meridianal distance of a place from 24°; for 360°, or 15° per degree. In this system the longitude of Paris is 238h, 50m, 4s. (88.) The meridianal plane and latitude of a place, may be laid down on an artificial globe; and thus a map of the earth may be constructed. Maps of particu- lar countries are made by extending the meridians, or, simply, extended into places; or, rather, they are representations on planes of such portions, extended according to certain conventions, which are determined by the object of which it is intended to represent. Thus, the outlines of countries from what they are on the globe, to the extent of their limits, are drawn. In this specia- tion or graphical measurement, the latitudes and longi- tudes of places which occur in them, without referring to the sphere or to poles—or for other precise uses. See chap. III. (89.) A Globe, or general map of the heavens, as well as what is called a Celestial Sphere, when conceived, and the stars laid down in their proper situations rela- tive to each other, and to the poles of the heavens and the celestial equator, will exhibit a true appearance of those which are seen in succession to every spectator on the surface of the earth. This is because all points appear once by one at the centre of the globe. It is, therefore, in- dependent of all geographical localities. There will occur at any time two points in the heavens—the north neither—either east nor west points; and although great circles may be drawn on it from pole to pole, cor- responding with the meridians of longitude; these appear, in this point of view, regarded as the celestial meri- dians of fixed points on the earth's surface, since, in the course of time, they have been observed that they pass beneath each of them. It is on account of this change of conception, and with a view to establish a con- ception more conformable to nature than that in "Geog- raphy" and "Uranography," that astronomers have adopted different terms (viz. declination, and right) * For the earth: $x^{\prime}y^{\prime}$; to describe or represent: $x^{\prime}y^{\prime}$; the heavens: $x^{\prime}y^{\prime}$
CHAP. L.] LATITUDE AND LONGITUDE.
01
discussing) to represent those lines in the heavens which correspond to latitudes and longitudes on the earth. It is for this reason that they term the equator of the heaven the equinoctial; that what is meridians on the earth are called parallels of latitude, and that the angles they include between them at the poles are called hour angles. All this is convenient and intelligible; but it may be asked, why did not some other confusion could ever have arisen. Unluckily, the early astronomers have employed the word "equator" in two different senses, one of which was very misleading. In speaking of arcs of circles not corresponding to those meant by the names of the lines on the earth, but representing the apparent motions of the stars among the stars. It is now too late to remedy this confusion, which is ingrained into our language, and we must hope that it will not warn the reader of it, that he may be on his guard when, at a more advanced period of our work, we shall find ourselves employing the word "equator" in its celestial sense, at the same time urgently recommending to future writers the adoption of others in their places.
I
fixed meridian, or from a determinate point on the equator; so right ascensions in the heaven require some such point as a pole, and declinations are equinoctial, as the commencement of their reckoning, or their zero point. The hour circle passing through some fixed point on the meridian would have been no particular advantage in this ; and astronomers have adopted, in preference, a point in the plane of the ecliptic as a pole for their calculations. This is a great mistake, because it does not pose the hour circle to pass, from which all others are reckoned, and which point is then the zero point of all right ascensions and declinations.
The right ascensions of celestial objects are always reckoned eastward from the vernal equinox, or from 0° to 360°; and seconds, as in the case of terrestrial longitudes, from 0° to 360°, which composes the circle of degrees. In both cases, therefore, there are 24 hours (or 24 days). The apparent diurnal motion of the heavens being contrary to the real motion of the 02 A TREATISE ON ASTRONOMY. CERAF. earth, this is in conformity with the westward reckon- ing of longitude (Art. 87). (32). Sideral time is reckoned by the diurnal motion of the stars, or rather that point in the equinoctial from which right ascensions are reckoned. This point may lie anywhere between the meridian and the pole; but in fact, there; and moreover, the point itself is liable to a cer- tain small variation, so that, however, as not to affect, perpendicularly, the course of the celestial equinoctial returns to the meridian. This interval is called a sideral day, and is divided into sidereal hours. There are two again, first and second. A clock which marks sidereal time, i. e. which goes uniformly at such a rate as alternately to advance and retard, when it comes on the meridian, is called a sidereal clock, and is an indispensable piece of furniture in every observatory. (36). It remains to illustrate these descriptions by reference to a figure. Let C be the centre of the earth, NCS its axis; then N and S its poles; EQ its equa- tor ; AB the parallel of latitude of the station A on its surface; AP parallel to SCN, the direction in which an observer at A will see the elevated pole of the heavens; and AZ, the prolongation of the terrestrial radius CA, A diagram showing a celestial sphere with various lines and points labeled. The diagram includes a central point C representing the Earth's center, with lines extending outward to represent the Earth's surface. Lines from C to N and S represent the Earth's poles. Line AB represents a parallel of latitude through station A. Line AP represents a line parallel to SCN (the direction in which an observer at A would see the elevated pole of the heavens). Line AZ represents the prolongation of the terrestrial radius CA. Points N and S are labeled as North Pole and South Pole respectively. Point EQ is labeled as Equator. Point G is labeled as Greenwich Meridian. Point D is labeled as Declination Meridian. Point B is labeled as Right Ascension Meridian. Point Z is labeled as Zenith. CHAP. I. [DEFINITIONS EXEMPLIFIED.] 63 that of his zenith. NAES will be his meridian; NGS that of his nadir; and PZ, the plane through the earth's centre, and the spherical angle NGE, his longitude, and EA his latitude. Moreover, if we be a plane touching the surface of the earth at any point, and if we project this plane by its intersection with his meridian will be his meridian line, and a and the north and south points of his horizon. (94.) Again, neglecting the size of the earth, or con- ceiving him stationed at its centre, and referring every point on the surface to the same pole, we shall have to repre- sent the sphere of the heavens; C the spectator; N his zenith; and N his nadir; then will HA a great circle of the sphere, which we call ZN, be his hori- zontal horizon; PP the elevated and depressed zones of A diagram showing a celestial sphere with various lines and points labeled. The main elements include: - A large circle representing the Earth's surface. - A smaller circle around the Earth's center (C). - Points labeled D, E, F, G, H, I, J, K, L, M. - Lines connecting these points to represent different directions. - A vertical line from C to Z (the zenith) and another from C to Z' (the nadir). - A horizontal line from C to Z'' (the horizon). - Labels such as "P" for poles, "Z" for zenith, "N" for nadir, "H" for horizon. - Additional labels like "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M". - A small circle around C representing the Earth's radius. - A small triangle around C representing the Earth's circumference. - A small square around C representing the Earth's area. - A small circle around C representing the Earth's volume. - A small circle around C representing the Earth's mass. - A small circle around C representing the Earth's energy. - A small circle around C representing the Earth's temperature. - A small circle around C representing the Earth's pressure. - A small circle around C representing the Earth's density. - A small circle around C representing the Earth's velocity. - A small circle around C representing the Earth's acceleration. - A small circle around C representing the Earth's force. - A small circle around C representing the Earth's torque. - A small circle around C representing the Earth's moment of inertia. - A small circle around C representing the Earth's angular momentum. - A small circle around C representing the Earth's angular velocity. - A small circle around C representing the Earth's angular acceleration. - A small circle around C representing the Earth's angular momentum per unit mass. - A small circle around C representing the Earth's angular velocity per unit mass. - A small circle around C representing the Earth's angular acceleration per unit mass. - A small circle around C representing the Earth's angular momentum per unit time. - A small circle around C representing the Earth's angular velocity per unit time. - A small circle around C representing the Earth's angular acceleration per unit time. - A small circle around C representing the Earth's angular momentum per unit mass per unit time. - A small circle around C representing the Earth's angular velocity per unit mass per unit time. - A small circle around C representing the Earth's angular acceleration per unit mass per unit time. - A small circle around C representing the Earth's angular momentum per unit mass per unit time per unit mass. - A small circle around C representing the Earth's angular velocity per unit mass per unit time per unit mass. - A small circle around C representing the Earth's angular acceleration per unit mass per unit time per unit mass. - A small circle around C representing the Earth's angular momentum per unit mass per unit time per unit mass per unit mass. - A small circle around C representing the Earth's angular velocity per unit mass per unit time per unit mass per unit mass. - A small circle around C representing the Earth's angular acceleration per unit mass per unit time per unit mass per unit mass. - A small circle around C representing the Earth's angular momentum per unit mass per unit time per unit mass per unit mass per unit mass. - A small circle around C representing the Earth's angular velocity per unit mass per unit time per unit mass per unit mass per unit mass. - A small circle around C representing the Earth's angular acceleration per unit mass per unit time per unit mass per unit mass per unit mass. - A small circle around C representing the Earth's angular momentum per unit mass per unit time per unit mass per unit mass per unit mass per unit mass. - A small circle around C representing the Earth's angular velocity per unit mass per unit time per unit mass per unit mass per unit mass per unit time per unit mass per unit mass per unit mass per unit mass per unit time per unit mass per unit mass per unit mass per unit time per unit mass per unit mass per unit 64 A TREATISE ON ARITHMETIC. CURAP. I. or of the heavens. Moreover, if HA, Oo, be small cir- cles, or parallels of declination, touching the horizon in its near parts, and if the stars be divided into two per- petual apparitions, between which and the elevated pole the stars never set; so that of perpetual occultations, between which and the same pole they never rise. In all the zone of the heavens between HA and Oo, they rise and set, any one of them, on S, remaining above the horizon, while another is below it, as represented by ABA, and below it throughout all the part represented by ADa. It will exercise the reader to construct this figure with respect to any other star than the sun for a variety of positions of the star S in each. The follow- ing consequences result from these definitions, and are propositions which the reader will readily be in mind. (96.) The altitude of the elevated pole is equal to the intial of the same place on the horizon. For, comparing the figures of arcs 93 and 94, it appears that the naze PAZ, between the pole and zenith, in the one figure, is equal to the naze PABZ (the initial of the altitude) of the pole, is equal to the naze NCA in both; and APAC is parallel whose containing point is the centre of the earth. Hence, by definition, NCA = OAO. (96.) The same stars, in their diurnal revolution, come to the meridian successively, at every place on the globe once in twenty-four hours. Therefore, in sidereal time, which changes between the same star coming upon the meridian and rising or setting, is measured by the dif- ference of longitudes of the places. (97.) The difference of longitude between two different stars coming on the meridian of one land and the same place, expressed in sidereal time, is the measure of the difference of right ascension of the stars. This expression is called a mean division of the equator and equinoctial into degrees and hours. (98.) The equinoctial intersects the horizon in the east and west points. At any point on this line, the alu- tude is equal to the co-incline of the place. Thus, at **CHAP. L.** STARS VISIBLE BY DAY. Greevwich, the altitude of the intersection of the equi- meridian and meridian is 38° 31' 20". (90.) All the heavenly bodies caldulante (i. e. come to their nearest approach to the horizon) are visible. There- fore, the best situation to observe them, being least con- fused by the inequalities and vapours of the atmosphere, or by the light of the sun, is at the meridian. (100.) All celestial objects within the circle of perpe- tual apparition come twice upon the meridian, above the hori- zon, at equal distances from the pole, one above and one below the pole. These are called their upper and lower culminations. (110.) We shall conclude this chapter by calling the reader's attention to a fact, which, if he now learn for the first time, will not fail to surprise him, viz., that the stars continue to rise and set at equal intervals of time, though not as the night; and thus, in proportion to the power of the instrument, not only the largest and brightest of them, but also those of medium size, may be observed during the eye at night at all conspicious, are readily found and followed even at moonlight, amongst this part of the sky, which is most suitable for astronomical observations. The means of pointing a telescope accurately to the proper places. Indeed, from the bottoms of deep narrow pits, such as those in which we have our observatories, so that the zenith may even be discerned by the naked eye; and we have ourselves heard it stated that in some places, this was done with instruments which drew his attention to astronomy was the regular appearance, at a certain hour, for several successive days, of a considerable star, through the shaft of a chimney. r 2 66 A TREATISE ON ASTRONOMY. [CRAF. II CHAPTER II. Of the Nature of Astronomical Instruments and Observations in general— Of solar and solar time—Of the Measurement of Time-Clocks, Chronometers, and other Instruments for measuring Intervals—Application of the Telescope to Instruments devised to that end—Of the Quadrant and other Instruments for measuring angles—The Level—Plumb-Bob—Artificial Horizon—Collimation of Copernican Instruments—Of the Equatorial and Meridian Instruments—Of the Sextant and reducing Circle—Principles of Regulating Instruments. (106.) Our first chapter has been devoted to the acquisition chiefly of preliminary notions respecting the globe we inhabit, its relation to the celestial objects which surround us, and the nature of the observations by means of which all astronomical observations must be made, as well as to provide ourselves with a stock of technical words of most frequent use in astronomy. The second chapter will now proceed to a more exact and detailed statement of the facts and theories of astronomy; but in order to do this with accuracy, it is necessary that every reader shall be made acquainted with the principal means by which astrono- mists possess, of determining, with the degree of nicety their instruments can attain, and with the extent of their conclusions; in other words, of ascertainng by measure- ment the apparent and real magnitudes with which they are concerned. It is impossible to give any idea of this knowledge that he can fully appreciate either the truth of the theories themselves, or the degree of reliance to be placed upon them without having had some trial; since it is only by knowing what amount of error can certainly be perceived and distinctly measured, that he can judge whether his own observations are sufficiently near an approximation, in its numerical results, to actual pha- nomena, as will justify him in regarding it as a true repre- sentation. (103.) Astronomical instrument-making may be justly regarded as the most refined of the mechanical arts, and that in which the nearest approach to geometrical preci- sion is required, and has been attained. It may be thought **CAP. II.** **PRATHEAU DIFFICULTIES.** on every thing, by one unacquainted with the niceties re- quired, to turn a circle in metal, to divide its circumfe- rence into 360 equal parts, and these again into smaller sub- divisions, so that each part may be exactly equal to the pre- vious just in it a given position; but practically it is found to be one of the most difficult. Nor is this appear extraordina- ry, when we consider how few of our own instruments are adapted to the purposes of angular measurement, every impu- rity being rejected which does not come within the sphere of the whole optical power of that instrument; and that thus, not only direct errors of workmanship, arising from unskilful hands, but also those due to the unavoidable inaccuracies which originate in far more uncontrollable causes, such as the unequal expansion and contraction of ma- terials, the imperfect adjustment of screws, and other unavoidable flexure or bending by their own weight, be- come perceptible and measurable. An angle of one mi- nute subtended by a circle of 100 inches would require 100 inches in radius, only about $\frac{1}{4}$th part of an inch, a quan- tity too small to be certainly dealt with without the use of instruments of great precision. The same difficulty ap- plies in the astronomical measurement of an angle. Under the instruments now employed in observatories, a single sec- ond of arc can be measured with accuracy, though not ac- tually visible and appreciable quantity. Now, the arc of a circle, subtended by one second, is less than the ten-thousandth part of an inch; and therefore any object in diameter it would occupy no greater linear extent than $\frac{1}{10000}$th part of an inch; a quantity requiring a powerful microscope to measure accurately. It is evident then, to himself, therefore, the difficulty of placing on the circum- ference of a meridional circle of such dimensions (supposing the earth to be spherical) a point which shall be at right angles dots, or cognizable divisions, which shall be true to their places within such minute limits; to say nothing of the difficulty of measuring the arc itself with accuracy. And yet, of these again into seconds. Such a work has probably been billsfold, and will probably never be attempted until the summoning up of skill and industry nor, if occa- cused, could it endure. The ever varying fluctuations of heat and cold have a tendency to produce not merely tem- 68 A TREATISE ON ASTRONOMY. CHA. II. porary and transient, but permanent, unaccompanied changes of form in all considerable masses of those metals which alone are applicable to such uses, and their own weight, which is so great that the motions they lose unequally sustained, since it is impossible to apply the sustaining power to every part separately; even could this be done, the parts would not be able to move and to fix them ; which can never be done without producing temporary and fixed inequalities of motion. It is therefore, by the nature of things, on their centres, and in the libera- tive places they are destined to occupy, and by a thousand ingenious and delicate contrivances have been accomplished. The degree of perfection has been given, not merely to chefs d'œuvre, but to instruments of moderate price, and useful, and in certain cases, even of great consideration, most un- appear very surprising. But though we are entitled to look for wonders at the hands of art, yet we are not to expect miracles. The demands of the astronomer will always surpass the power of the artist; and it must be admitted that he who would make himself, no far as possible, independent of the imperfections incident to every work the later ence place in his hands. He must therefore observe his opportunities, and so to familiarize himself with all the causes which may pro- duce irregularities in the motions of the stars, and the pecu- liarities of structure and material of each instrument he possesses, as not to allow himself to be misled by their errors, nor to be deceived by any appearance of possi- bility, all that is true, and reject all that is erroneous. It is in this that the art of the practical astronomer consists, an art which is not only necessary for him at his first hand, of which we here can only notice some of the leading and general features. (104) The principal aim of the practical astronomer be- ing numerical correctness in the results of instrumental measurement, his constant care and vigilance must be directed to its detection and correction either by error, either by nullification, or by taking account of, and al- lowing for them. Now, if we examine the sources from **CHAP. IV.** **CLASSIFICATION OF SOURCES OF ERROR.** which errors may arise by any instrumental determina- tion, we shall find them chiefly reducible to three prin- cipal heads:— (165.) External or incidental causes of error, concomitantly such as depend on external, uncontrollable circumstances; such as, fluctuations of weather, whence disturbances of observations, or of the labora- tory conditions, and being reducible to no fixed law, inducing uncertainty to the extent of their own possible magni- tude; (2) accidental causes of error, which vary with vary also the form and position of the instruments used, by altering relative magnitudes and the tension of their parts; (160.) truly, Errors of observation: such as arise, for example, from inexpertness, defective vision, sloveness in making observations, etc., or from some unex- plored, or precipitancy in anticipating it, &c.; from at- mospheric indistinctness; insufficient optical power in the instrument; imperfect adjustment of the instrument; or be closed all errors arising from momentary instrumental deterioration,—this in clamping, looseness of screws, &c. (161.) Instrumental errors: such as arise from the classes of errors to which astronomical measurements are liable, arise from causes which may be deemed instru- mental errors, but which are not so in the ordinary sense of the word. The first comprehend those which arise from an instrument not being what it professes to be, which may be due to its being faulty in some respect. Thus a sternical of being, as it ought, exact cylindrical, be slightly flattened, or have a slight tapering towards one end. The se- cond class comprises with the circle it carries over, if this circle (as called) be in reality not exactly circular, but elliptical or oblong. These two classes are not always precisely equivalent, should be placed in reality at un- equal intervals,—and a hundred other things of the same sort. But these are only accidental errors, not fundamental ones, but practical anomalies, which every observer has to con- sult with. (162.) The other subdivision of instrumental errors comprehends such as arise from an instrument not being placed in the position it ought to have ; and from those 70 A TREATISE ON ASTRONOMY. [CHAP. IL] of tie parts, which are made purposely invariable, not being properly disposed to receive the motions of their adjuncts. Some are unavoidable, as they arise from a general indelicacy of the seal or building in which the instrument is placed, or from the want of a firm base to be noticed in any other way, become appreciable in delicate astronomical observations; others, again, are consequently so minute, that even when the instrument once well adjusted will not remain so, but keeps deviating and shifting. But the most important of this class is that of the errors arising from the force of natural inclinations, other than those offended by astrono- mical observations themselves, whether an instrament has or has not been well adjusted. In the first place, in the horizon and its cardinal points, the axis of the earth, or to other principal astronomical lines and circles, which is only one degree in latitude and longitude, and which (169.) Now, with respect to the first two classes of error, it must be observed, that in so far as they cannot be reduced to any known cause, they are not objects of calculation and due allowance, they actually vitiate, to their full extent, the results of any observations in which they are employed; but though they may be occasional and accidental, their effects necessarily lie sometimes one way, sometimes the other; sometimes diminishing, sometimes augmenting. Hence it is necessary to make, by greatly multiplying observations, under varied circum- stances, and taking the mean or average of their results this class of error. For instance, if we wish to destroy them to destroy one another, so no longer sensibly to vitiate any theoretical or practical conclusion. This is the greatest difficulty in astronomy; for it does not refer merely to the astronomer, but to the investigator of na- tural results in every department of physical research. (170.) It is therefore desirable that all instruments work universally, not only the possibility, but the certainty, of their existence, in every imaginable form, in all instru- ments; and that none ever shall be found where ma- chines never formed a circle, drew a straight line, or erected a perpendicular, nor ever placed an instrument in perfect adjustment, unless accidentally ; and then only **CHAP. II.** MUTUAL DETECTION OF EOBERS. During an instant of time. This does not prevent, how- ever, that a great proportion of all these decisions should be mistaken. But it is the peculiarity of astrono- mical observation to be the ultimate means of detection, and therefore it is impossible that any other mode of detection. What the eye can't discern, nor the touch perceive, a course of astrono- mical observations will detect. The imperfect products of man's hands are here tested by the most exacting standards of science; and the per- manence of man's nature; and there is none which will bear the trial. Now, it may seem like arguing in a vicious circle, to say that we have no right to make such observations, and then to turn round upon the instruments with which those observations were made, accuse them of error. But this is not so. We have no right to make errors by means of the very laws and theories which they have helped us to a knowledge of. A little consi- deration will show us that each course of procedure is perfectly legitimate. (II.) The steps by which we arrive at the laws of nature are necessarily successive. Those which are necessary for their verification on numerical determinations, are necessarily successive. Gross results and palpable laws are verified by experiments; but these are not neces- sary, or without any instruments at all; and these are corrected and refined upon by nicer scrutiny with more accurate instruments; and these again are verified by laws are brought into view, which modify both the verbal statement and numerical results of those which first op- erated. Thus we proceed step by step, from gross to full out, and reduced to certainty; others, again, subordinate to each other in order to form a complete system for further inquiry. Now, it is invariably happens (and the reason is evident) that the first glimpse we catch of such a subject is dimly seen through a veil; and this is dimly shadowed out to our minds—is that of errors. We perceive a discordance between what we expect and what we find; but we do not know whether to attribute it to accident or to some defect in our instruments. We 72 A TENTATIVE SYNONYMY. [CAP. II. them inquire, to what amount of error their determina- tions can, by possibility, be liable. If their limit of per- fect error exceed the observed deviation, we at once condemn the instrument, and set about improving its construction, or altering its mode of making observations occur, and so far from being palliated, are more marked and better defined than before. We are now sure that we are not mistaken in our first observation, and presume it till we have reduced it to a definite statement, and verified it by repeated observation, under every variety of circumstances. (112.) Now, in the course of this inquiry, it will not fail to happen that other discordances will strike us. Though we may suppose that they are accidental, or some natural law, here unknown; yet to falsitate (i.e. draw out in order) the results of our observations; or to pro- duce errors which do not appear distinctively indi- cations of a regular progression. Again we improve or vary our instruments, and find them still defective; or, suppose that the defect is in ourselves, altogether or in some other manner; but when we have tried all these ways, and found no cause of error in any part of our work, we are left with the conclusion that the error is what we have supposed it to be. We examine therefore, the theory of our instrument; we suppose defects in its struc- ture, and by direct observation ascertain their influ- ence in producing actual errors into its indications. These errors have their laws, which, so long as we have no means of correcting them, they must be con- founded with laws of nature, and are mixed up with them in their effect. They are not fortuitous, like errors of chance; they are inherent in the instrument, and unchangeable while it is used; and its adjustments remain unchanged; they are reduci- ble to one or more causes; and though one particular defect, whether of structure or adjustment, producing its own appropriate form of error. When these are thor- oughly investigated and corrected, the remaining one which coincides in its nature and progression with that of our observed discordance. The mystery is at once solved: we have detected, by direct observation, an in- strumental defect. A page from a book with text on it. **CHAP. III.] DETECTION OF INSTRUMENTAL ERRORS.** (113.) It is, therefore, a chief requisite for the practical astronomer to make himself completely familiar with the theory of his instruments, so as to be able at once to determine whether the construction of structure or adjustment will produce in any given circumstances under which an observation can be made, errors greater than those which may be considered as required that a circle should be exactly concordant with the axis of the instrument to be used. As this is a condition which no workman would fail to satisfy, it is only necessary to inquire into what errors will be produced in observations depending on the graduation of the limb by the very easy method of reading off the divisions on the scale, and then comparing them with those read by means of a vernier, or by any other means; for the effect of eccentricity is always to increase one such reading by just the same quantity by which the other is diminished. The object of this inquiry is to ascertain the proper use of the instrument required that this axis should be exactly parallel to that of the earth. As it never can be perfectly so, it follows that some amount of error will arise in its use from any assigned deviation, whether in a horizontal or vertical plane, from the true meridian or from the true zenith. This is one of the sources of instrumental errors; a theory of the utmost importance to practice, and one of which a complete knowledge is essential before any instrument can be properly employed. It is also necessary to know how far it is possible by means, to attain a degree of precision which might seem to belong only to the most refined and costly. In the first place, we must consider how far it is practicable to reduce all errors to zero. The few astronomical instruments we propose to describe in this chapter will be considered as perfect both in construction and adjustment. (114.) As the above remarks are very essential to a right understanding of the philosophy of our subject and 73 74 A TREATISE ON ASTRONOMY. [CHAP. II. the spirit of astronomical methods, we shall elucidate them by taking a case. Observant persons, before the invention of telescopes, had observed that the stars, when they appear to move, con- II sidered the apparent diurnal motions of the stars to be performed in circles about fixed poles in the heavens, as shown in fig. 10. But this conclusion was not con- II clusion, however, refraction was entirely overlooked, or, if forced on their notice by its great magnitude in the mundane motions of the sun and moon, it was neglected as being a local irregularity, and, as such, neglected or shunned over. As soon, however, as the diurnal paths of the stars were examined with the aid of a telescope, it became evident that the motion of exact circles described about one and the same pole would not represent the true course of any star. For if it were due to some cause or other, the apparent diurnal orbit of every star is distorted from a circular into an oval form, its every member being nearer to the horizon than it appears. The de- II viating being nearer the nearer the star approached the horizon, the effect being the same as if the circle had been squared off at its circumference, so that its parts II were more than the bisector. For such an effect, as it was soon found to arise from no casual or instrumental cause, it became necessary to seek some other explanation. This question was frequently recurred to solve the difficulty. In fact, it is a case precisely analogous to what we have already (art. II 7) pointed out concerning the apparent diurnal motion of the sun and moon around the horizon, only on a larger scale, and traced up to greater amplitudes. This new law once established, it became ne- II cessary to consider how far it could be applied. It can be re- II solved, by inserting in it a sura for the effect of refraction, or by making a distinction between the apparent diurnal orbit of each star and its true path through space, which is distinct from that of effect. (145) Again: The first impression produced by a view of the diurnal movement of the lunaeus is, that all the heavenly bodies perform this revolution in one com- mon period, viz. at dawn, or 24 hours. But no sooner do we come to examine this matter more closely than we find that it is not so simple as it seems to be. For instance, let us take a case, by acting, by timekeepers, their successive arrivals on the meridian, than we find differences which cannot be ac- II cepted without further inquiry. CHAP. II. LAWS TRACED BY OBSERVATION. 75 counted for by any error of observation. All the stars are in truth, except the same interval of time between their successive passages to the meridian, or to any vertical circle; but this is a very different one from that occupied by the sun, which passes through the meridian in 23° 53' 40", instead of 24 hours, such hours as our calendar is founded on. Hence, we have thereby lost nearly two days in every year; and, as the sun moves faster than the moon, we observe the moon, we find a third, much more rapid motion of the stars, which is called the sidereal year; and this is 23° 53' 40" of our ordinary time, which lasts is sidereal time, being of necessity conformable to the sun's succesive appearances, on which all the business of life de- (116.) Now, all the stars are found to be unanimous in their motions; and they all move with respect to each other in the sidereal day; which, therefore, cannot hesitate to receive as the period in which the earth makes one revolu- tion round its axis. But this is not true of the sun and moon as exceptions to the general law I as having a different motion, or at least a different relation to the earth's axis. The sun has no motion whatever; but the moon, apart from her own independent rotation of the earth on its axis. Thus a great and most important dis- tinction is made between them. (117.) To establish these facts, almost no apparatus is required. An observer need only station himself to the side of a building, and place his eyes exactly at a certain fixed point (such as a hole in a plate of metal mil- luminated by a lamp), and then watch for the disappearances of any star behind the building, by a careful eye with a dark-coloured smoky glass, and notice the moments when its western and eastern edges successively appear and disappear. This will be done with great ease and quickness; for it is evident that when any star appears behind which the eye is bright, or a planet/diameter shall be seen to pass over it, it must necessarily be behind it; and vice versa. And thus we can easily distinguish appearances from disappearances to a tenth, and discover the moment of their occurrence; this is easily secured, by making up a smooth edged board.
Equation: $\theta = \alpha + \beta$
78 A TREATISE ON ASTRONOMY. [CHAP. II. come up to the wall, from which, by taking half the inter- val he will ascertain (what he cannot directly observe) the mean solar day. (118.) When, in pursuing and establishing this gene- ral fact, we are led to attend more nearly to the times of the sun's daily motion, we shall find that its irregularities (so they first begin) seem to be observed. The inter- vals between two successive arrivals are not the same at all times, sometimes being less than 24 hours, sometimes greater, sometimes less than 24 hours, as shown by the clock ; that is to say, the solar day is not always of the same length. For instance, when the sun is at the meridian, it is a half-minute longer, and about the same day of Septem- ber nearly as much shorter, than its average duration. And thus, on account of these variations, we may deduce between the actual solar day, which is never two days in succession alike ; and the mean solar day of 24 hours, which is always supposed to be constant throughout the year. Hence, then, a new source of inquiry opens upon us. The sun's apparent motion is not only not the same with that of the earth, but also varies in different parts of the firmament. It is subject to fluctuations, whose laws become matter of investigation. But to pursue these laws, we require to know what instruments we have for measuring them. We have described, and are obliged to call into our aid an instru- ment called the transit-instrument, especially designed for such purposes. This instrument consists of a tube in all the cases of irregularity in the going of clocks and watches which may affect our reckoning of time. Thus we be- come involved in a great number of questions respecting in- stru-mental inquiries ; and we specify first that, in pro- portion as we ascertain the amount and law of one great or lesser irregularity in any part of the heavens, so that of the sun's diurnal motion, we bring into view others continu- ally smaller and smaller, which were before observed, or fixed by experience, but which are now found to be imperfect. In short, we may not simply compare the mean length of the solar day to the mean or average length of the terrestrial day ; or even to that of the sea unagitated by tide or waves. The great annual fluctua- tion noticed above may be compared to the daily varia- **CHAP. II.** OF TIME AND ITS MEASUREMENT. 77 ions of level produced by the tides, which are nothing but enormous waves extending over the whole ocean, and which, being so vast, are not perceptible to the eye, are limited to waves ordinarily so called, on which, when hazy, we perceive lesser undulations to take, and on these undulations we can perceive no more. (115.) With the causes of these irregularities in the surface of the sea, I shall not trouble myself further; but mention belongs to a more advanced part of our subject; but the distinction between the solid and sideral days, as well as the difference between the two periods of time introduced, and never lost sight of. It is, as already ob- served, the mean or average length of the solar day, that is, 24 hours 48 minutes and 45 seconds; and the peri- mences at midnight, as astronomers (at least those of this country), even when they use mean solar time, do not consider the sidereal day as equal to 24 hours; but to 23 hours 56 minutes and 4 seconds; and reckoning the hours from 0 round to 24. Thus, if a clock is the foreman of the second of June, it will strike 12 o'clock at noon on that day; and if it strikes 12 o'clock at noon on the first of July, it will strike 12 o'clock at noon on the second of July; and so on through all the months of the year. The mean solar day is 24 hours 20 minutes and 30 seconds longer than the sidereal day. (129.) Both astronomers and civilians, however, who inhabit different points of the earth's surface, differ from each other in their reckoning of time: as it is obvious that if any one place be considered as a fixed point, it is midnight at a place diametrically opposite: sunrise at another; and sunset, again, at a fourth. Hence it happens that in different parts of the world places differing very widely in situation, and which may even in some critical cases involve the mistake of a whole continent; it has been introduced a system of reckoning time by mean so- lar days and parts of a day counted from a fixed instant, common to all the world, and determined by no local cir- 78 A TREATISE ON ASTRONOMY. CHAP. II. circumstance, such as noon or midnight, but by the motion of the sun among the stars. Thus, so reckoned, it is called equinoctial motion, because it is observed at every instant, in every part of the globe. Its origin will be ex- plained hereafter, in a more advanced stage of our work. (121.) Time is thus seen to be a fundamental observation, in a twofold point of view—1st, As the representative of the duration of any motion; 2ndly, as the mechanical motion being uniform, every star describes its diurnal cir- cle uniformly; and the time elapsing between the pas- sage of the stars over any given point on the meridian of any observer becomes, therefore, a direct measure of their dif- ferences of zodiacal ascent. 2dly, As the fundamental principle of astronomy, it is necessary to have a knowledge of geometry in all dynamical theories. The great object of astronomy is the determination of the laws of the celestial motions, and this can only be effected by means of measurements. Now, the statement of the laws of any observed motion in a celestial object can be no other than a propor- tionate relation between two quantities which represent the real or apparent situation of that object at any time past, pre- sent, or future. To compare such laws, therefore, with observations requires that we should know both the observed situations of the object in question, and of the times when they were observed. (122.) The measurement of time is performed by clocks, chronometers, ephemerides, and hour-glasses: the two former are alone used in modern astronomy. The hour-glass is employed for measuring very short intervals, or rather coming out fixed portions of time, and is en- tirely dispensed with. The ephemeris, which measured time by the general course of the sun's motion through a definite ordinate or circle, is susceptible of considerable execu- tiveness, and was the only dependence of astronomers before the invention of clocks. But since clocks are now so much in abundance, owing to the greater convenience and exactness of the latter instruments. In one case only has the evidence been obtained by means of clocks—the accurate measurement of very small portions of time, by the flow- ing out of mercury from a small orifice in the bottom of a vessel, kept constantly full to a fixed height. The **chap. II.** **clocks—chronometers.** stream is intercepted at the moment of noting any event, and directed anew into a receiver, into which it continues to flow until the next interruption occurs. But when the intercepting sense is suddenly removed, the stream flows in its original course, and ceases to run into the receiver, unless it be again intercepted by some other sense, with the weight received in an interval of time observed by the clock, gives the interval between the events ob- served by the clock, and therefore, since all these intervals are known with all possible precision, a problem which has of late been much agitated, is due to Captain Kite. Captain Kite's chronometer was a very simple balance watch, with those improvements and refinements in its structure which constitute it emphatically a *chronometer.* e.g., that it is capable of being set to any given time, for his knowledge of the lapse of time. These instru- ments are now brought to such perfection, that an irregu- larity in their operation, which would have been unex- pected in twenty-four hours in two consecutive days, is not tolerated in one of good watches. The twenty-four hours may be certainly ascertained within a few tenths of a second, by their use. The same is true of the day, since we know as well as we can the amount of error risked, because greater, be- cause the incidental errors of many days may accumu- late together than could be detected in one day. We are in the rate of going may subsist unperceived. It is not safe, therefore, to trust the determination of time to clocks, or watch, but to observe them carefully during their use, and ascertain their errors by reference to natural events which we know to happen, day after day, at equal intervals of time. The errors of a clock or watch may be fixed with the same precision as the shortest; since, in fact, it is only the times intervening be- tween two observations which are subject to error, and such of those periodically recurring events adopted for our point of reckoning, as occur within twenty-four hours, are sufficient to fix the errors of a clock or watch for cer- tial means. The whole days are counted out for us by nature; the fractional parts only, at either end, are me- *scire,* *dare,* *acquire,* *to measure.* A diagram showing a balance wheel and pendulum in a watch. 80 A TREATISE ON ASTRONOMY. [CHAP. II. sured by our clocks. To keep the reckoning of the inter- day's correct, so that none shall be lost or counted twice, we have recourse to the stars, which mark out the order of succession of events, and refers them to their proper years and days ; while chronometry, grounding its calculations on the motions of the sun, fixes each regularly periodical event as can be conveniently and exactly subdivided, enables us to fix the moments in which phenomena occur, and thus to make the most pre- cision. (124.) In the cadences, or transit (i.e. the pas- sage across the meridian of an observer) of every star in the heavens, he is furnished with such a regularly peri- odical mutual event as we allude to. Accordingly, it is to this circumstance that we owe the astronomically situated fixed stars that astronomers resort to ascertain their exact time, or, which comes to the same thing, to determine the duration of a day or a clock's tick. (125.) The instrument with which the culmination of celestial objects is observed is called a quadrant or hori- zontal quadrant. It is a telescope firmly fastened on a hori- zontal axis directed to the east and west points of the horizon, or at right angles to the plane of the meridian of the place where it is used. The tube of the quadrant is formed into cylindrical pivots of exactly equal diameters, which rest in notches formed in metallic supports, besides which it is supported by two wooden pillars of stone, and susceptible of nice adjustment by screws, both in a vertical and horizontal direction. By the for- mer adjustment, the axis can be rendered precisely hori- zontal, by levelling it with a level made to rest on the **CAP. II.** **TRANSIT INSTRUMENT.**

81

pirote. By the latter adjustment the axis is brought, orien- tally into the east and west direction, the direction of meridian passage of the sun being that meridional plane with the instrument, or by a well-defined object called a meridian mark, originally determined by such observa- tions as have been made on the meridian. The axis is per- manently established at a great distance, exactly in a meridian line passing through the observer's position; but the exactness of this determination is evident, from the fact, that at the centre line of the telescope (in which which join the two axes) the object (such as a star) is seen to move which is called in astronomy its line of culmination), be one which is adjusted at right angles to the axis of the transit, it will nevertheless appear in the meridian when the instrument remains turned out on its axis.

(126.) In the focus of the eye-piece, and at right an- gles with it, there are placed two horizontal and four equilateral vertical threads or wires, as represented in the annexed figure, which always appear in the field of view, when properly illuminated,

A diagram showing a circular eyepiece with two horizontal and four vertical wires arranged around it.

by day by the light of the sky, by night by that of a lamp introduced by a contrivance not necessary here to explain. The place of this system of wires may be altered by ad- justing them so as to be parallel with each other; but it is this by means brought to such a position, that the middle one of the vertical wires shall intersect the line of conjunction of the sun and earth's axis, and be thus per- manently fastened. In this situation it is evident that the middle thread will be a visible representation of the meridian line, and that when any point in the tele- scope is pointed; and when a star is seen to cross this wire in the telescope, it is in the act of culminating, or passing the celestial meridian. The instantat this event is

82 A TREATISE ON ASTRONOMY. [CHAP. II. noted by the clock or chronometer, which forms an indis- dispensable accompaniment of the transit instrument. For greater precision, the moments of its crossing all the five vertical threads is noted, and a mean taken, when (excepting the cases of very small errors) the same result, were all the observations perfect, and will, course, tend to insidivide and destroy their errors in any system of observations. (127.) For the mode of executing the adjustments, and allowing for the errors unavoidable in the use of this simple instrument, we may say that all those who have done work especially devoted to this department of practical astronomy. 2 We shall here only mention one important point worthy of notice, viz., that of correcting in re- versing the ends of the axis, or turning it east for west. If this be done, and it continue to give the same results, and having observed that it does not vary much, we may say that the line of collimation of the telescope is truly at right angles to the axis, and describes strictly a plane perpendicular to the axis of rotation of the tube. In good transit observations, an error of two or three tenths of a second of time in the moment of a star's entrance is therefore negligible; but an error of one second in the error of the clock: in other words, a clock may be compared with the earth's diurnal motion by a single observation on each side of noon. By multiplying ob- servations, of course, a yet greater degree of pre- cision may be obtained. (128.) The mean intervals measured by means of the transit instrument and clock are arcs of the equino- xial, intercepted between circles of declination passing through the points where they intersect each other. In this case, is performed by no artificial graduation of circles, but by the help of the earth's circular motion, whereby every hour is divided into sixty minutes; thus, meridian, in equal times, at the rate of 15° per sidereal hour. In all other cases, when we would measure un- gular distances between stars or between two cir- cles, or portions of circles, constructed of metal or other See Dr. Poggia's Treatise on Practical Astronomy. Edoardo Banchi Sopra il Sistema del Pianeta. Edizione di Milano, 1834. CHAP. III. MEASUREMENT OF ANGLES. 83 firm and durable material, and mechanically subdivided into equal parts, such as degrees, minutes, etc. Let ABD be such a circle, divided into 360 degrees (num- A diagram showing a circular protractor with angles labeled from 0° to 360°. The center of the circle is marked as O, and the circumference is divided into 360 equal parts. bered in order from any point (0) in the circumference, round to the same point again), and connected with its centre by spokes or rays, xyz, firmly united to its cir- cumference or limb. At the centre let a circular hole be pierced through the axis ab, so that a tube may pass, carrying a tube, whose axis, ab, is exactly parallel to the plane of the circle, or perpendicular to the pivot ; and also let another circular hole be pierced through one piece with the tube and the axis ; so that the motion of the axis on the circle shall carry the tube and arms smoothly along it. This instrument is called a quadrant. When this point please, by a contrivance called a clamp. Sup- pose now, we would measure an angular interval be- tween two points on the limb of the STP. To do this, we must first be adjusted so as to pass through them both. This done, let the axis AB be turned until it coincides with one of these points, say A. Then will a mark on the arm at point either exactly to some one of the divisions on the circumference or else to some other part of it. In the former ease, the division must be noted, as the reading of the arm A. In the latter, the fractional part of one whole degree must be added to it. Thus measured by which the mark on x surpasses the last inferior division must be estimated or measured by some mechanical or optical means. The same process is repeated for each mea- sured point thus taken, and reduced into degrees, minutes, and seconds, to be set down as the reading of the limb. j 84 A TREATISE ON ASTRONOMY. [CHAP. II. corresponding to that position of the tube ab, where it points to the object S. The same must then be done for the other side of the circle, so that the telescope may "read off". It is manifest, then, that if the lesser of these readings be subtracted from the greater, their difference will represent the angle between the line of sight seen from the centre of the circle, at whatever point of the limb the commencement of the gradination on the point of being read is found. (129.) The very same result will be obtained, if, in- stead of making the tube moveable upon the circle, we connect it with a second circle, which shall revolve together on an axis concentric with the circle, and forming one piece with it, working in a hollow formed to receive it. This arrangement is shown in fig. 10. The combinaion is represented in section in the annexed sketch. T is the tube or sight, fastened, at pp, on the circle AB, A sketch showing two circles connected by a tube T, which can rotate around an axis AB. whose axis D, works in the solid metallic centring E, from which originates an arm F, carrying at its ex- tremity an index, or other proper mark, to point out and read off any desired angle. The index F will always point close to it. It is evident thus, as the telescope and circle revolve through any angle, the part of the limb of the latter, which is opposite to the index F, will measure the angle described. This is the most usual mode of applying divided circles in astronomy. (130.) Another mode of obtaining angles is by means of a vernier (fig. 11). In this manner, like a clock hand (fig. a); or a vernier (fig. b); or, A diagram showing a vernier scale attached to a telescope. **CHAP. II.** APPLICATION OF THE TELESCOPE. Lastly, a compound microscope (fig. $a$), represented in section (in fig. $b$), and furnished with a cross in the common focus, of its object and eye-glass, movable by a fine threaded screw, by which the intersection of the two glasses may be varied at will, is employed to observe the image of the nearest of the divisions of the circle; and by the turns and parts of a turn of the screw required for this purpose, the distance between any two adjacent points of zero or point of the microscope may be estimated. This instrument is capable of measuring the distance between a circle of a degree of accuracy only limited by the power of the microscope, and the perfection with which a screw can be turned. The same principle is applied to all the same footing of optical certainty which is introduced into their measurement by the use of the telescope. The following table shows how many degrees must descend, 1st, on the precision with which the tube $a b$ can be pointed to the objects; 2dly, on the accuracy of the division of the circle; and 3dly, on the number of which the subdivision of the intervals between any two consecutive graduations can be accomplished. The reason why this exactitude has been explained in the last article. With regard to the limitation of the limb, being merely an inch long, it is evident that no great degree can be further than this, that, in the present state of instrument making, the amount of error from this source of inaccuracy cannot exceed one minute. With regard to the first, it must be obvious that, if the sights $a b$ be nothing more than what they are represented in fig. $c$, they will not be able to point accurately at either end of a hollow tube, or an eye-hole at one end, and a cross at the other, no greater nicety in pointing can be expected than that which is given by means of a compass or quadrant. But if, in place of these simple but coarse conveniences, the tube itself be converted into a quadrant or sextant, so as to have a sight at each end at $a$ and $b$, and the motion of the tube on the limit of the circle be arrested when the object is brought just into the centre of the field at $a$, it is evident that a greater degree of exactness may be attained in pointing H 86 A TREATISE ON ASTROPHYS. [CHAP. IV. the tube than by the unassisted eye, in proportion to the magnifying power and distinctness of the telescope used. The last attainable degree of exactness is secured by stretching the tube so that the two extremities of the eyeglasses two delicate fibres, such as fine hairs or spider- lines, intersecting each other at right angles in the centre of the tube, may be brought into contact with each other, and form a permanent mark with which the image of the object can be brought to exact coincidence by a proper degree of curvature of the tube. The tube being thus adjusted, bringing the telescope to its final situation on the limb of the circle, and returning it then till the "reading off" is finished, (14) this instrument will be found to be con- sidered as completely abolishing that part of the error of observation which might otherwise arise from crosse- ous coincidences between the rays of light issuing from the observer's eyes, or from the centre of the im- strument. It is, in fact, the grand source of all the pre- cision which has been attained in astronomical re- finements in instrumental workmanship would be thrown away; the errors capable of being committed in point- ing the telescope towards any given star being greater than what could arise from any but the very nearest graduation." In fact, the telescope thus applied becomes, as Tycho Brahe observed, "a most perfect instru- ment deduced from Nature," and one which he en- joyed during his life time. In 1605, he wrote to Galilei, who was then living in Florence, "I have seen Cabe- tus and Hercules in my telescope's passage." The passage cited by Tycho Brahe is that of Galileo's first visit to Padua in 1605. Galileo had applied telescopes to his quadrant and sextant with great success, and had made many observations with them. He had also invented a telescope for use in illuminating the field of view by artificial light, which he found useful when observing stars at night. These inventions were "very convenient" for him, according to Tycho Brahe. Galileo's invention of the telescope was a major advance in astronomy because it allowed for more precise measurements in the art of observation. Galileo, however, patented the use of revolving mirrors in his telescope in 1607. This invention was not widely adopted until 1617, when Peculiar and Aumond (Lahmier, Astron. 20), after which it was adopted by others. In 1630, Kepler proposed to substitute the telescope for plane sights but it did not find much favour. In 1640, Huygens brought it to a culmination, which gave the telescope its importance in astronomy. See Lalande, loc. cit. A diagram showing a telescope with two eyeglasses intersecting at right angles. CHAP. II.] INTERVALS IN DECLINATION MEASURED. 57 with respect to angular, when the microscope is with respect to linear, by means of the telescope at its smallest point, and magnifying into palpable inter- tervals the minutest differences, it enables us not only to ascertain the exact position of any object in space, but it is pointed, to refer their apparent places, with all but geometrical precision, to the parts of any scale which will serve our purpose. (143.) The simplest mode in which the measurement of an angular interval can be executed, is what we have just described. But this method is applicable only to terrestrial angles, such as those occupied on the sensible horizon by the objects which surround our sin- gular station. For example, if we wish to measure the interval while the telescope is shifted on the limb from one object to the other. But the dextral motion of the telescope being perpendicular to the line of sight, the direct measurement of angular distance from object to object by this means is impossible. The same objection, however, arises whenever we seek to measure the angle between the interval between the diurnal circles described by any two celestial objects. Suppose every star in its diurnal revolution describes a circle round the pole of the heavens, a fine line of light, for instance--then a telescope brought to coincidence with the intersection of these wires would constantly remain pointed to some portion or other of the heavens. Now, if we suppose that each wire moves in its field as a luminous line, permanently intersecting the same point, till the star come round again. From this supposition it follows that no star can ever be at leisure, without error; and then the angular interval between the two diurnal circles, in the phase of the tele- scope's motion, must always be equal to zero. We cannot see the path of a star in the heavens, we could still till the star itself crosses the field of view, and seize the moment when it passes through it. But if we observe wires so that the star shall traverse it; by which, when the telescope is well changed, we equally well secure the position of its diurnal circle as if it continued to see it ever so long. The result is that if the limb may thus be 88 A TREATISE ON ASTRONOMY. [CHAP. II. performed at bisure; and when another star comes round into the plane of the circle, we may unclamp the telescope, and a similar observation will enable us to se- cure the position of this star with respect to the circle, and the observations may be repeated alternately, every day, as that star passes, we will be satisfied with their result. (134). Thus, by means of a circle of stars, which is nothing more than such a circle as we have described in art. 129, firmly supported on a horizontal instru- ment, on a level with the horizonal circular axis. This axis is let into a massive pier, or wall, of some (whence the name of the instrument), and so secured by screws as to be exactly horizontal, and to remain in that exact horizon- tal direction; so that like the axis of the transit, it can be maintained in the exact direction of the east and west points of the horizon, without any change being con- sequently truly meridional. (135). The observations made at right angles to all the diameters of the circle, marked by the stars, its arc intercepted between any two of them will measure the least distance between those diameters; and therefore will show the difference of the declinations, as also to the difference of the meri- dian altitudes of the objects—at least when corrected for refraction—by means of the differences of the angular intervals directly measured by the circular circle. But from these, supposing the law of refraction known, it is easy to deduce both quantities; but only, but the quantities themselves, we shall now explain. (136). The declination of a heavenly body is the com- plement of its altitude; and therefore if a star being a point in the meridian, might be directly observed at the limb of the circle, if any star stood exactly therein; and then observing its altitude at that place; and making reck- onations of all the rest, might be at once determined. But this not being the case, a bright star near the pole as can be seen by telescope, will appear lower and lower culminations; that is, when it passes the meridian above and below the pole. Now, as its distance from the pole is constant; and as it is always passing off the circle in the two cases is, of course (when corrected for refraction), equal to twice the polar distance of the **CHAP. II.** 59 MURAL CIRCLE. star; the are intercepted on the limb of the circle being, in this case, equal to the angular diameter of the star's meridional circle. In the mean meridian, at P the pole, BA, AQ, CD, the di- urnal circles of the stars which arrive on the meridian--at BA and C in their upper, and at RQD in their lower cul- tions, of which D happens above the horizon ITO, P is the pole; and if we suppose A p a to be the meri- dian circle, having S for its centre, b e p b will be the points on its circumference corresponding to BACPD in the mean meridian. The points A p a and b e b are immediately below each other; and since CP=PD, we have also c p = m p, and each of them are d e = d e, consequently the distance between them is constant; so that the circle of the circle becomes known, and the area p b p a p e, which represents on the circle the polar distances re- (387.) The rotation of the pole star, which is a very important one, is evidently necessary for this purpose, being only once in a day and a half (see page 10); it is, therefore, the star usually and almost solely chosen for this important purpose. It is situated in such a manner that both its culmination taking place at great and not very different altitudes, the refractions by which they are accomplished are nearly equal to each other, so that their correction is easily and safely applied. The brightness of the pole star, too, allows it to be easily observed in the daytime. In consequence 90 A TREATISE ON ASTRONOMY. [CHAP. II.] of these peculiarities, this star is one of constant resort with astronomers for its adjustment and verification of instruments. The transit of Venus across the face of the sun, for example, furnishes a ready means of ascertaining whether the plane of the telescope's motion is coincident with that of the earth's rotation. The latter plane bisects its circular disc, the eastern and western portion of it require equal times for their description. Let us suppose that we have a pole standing at right angles to the meridian, and below the pole be noted ; and if they are found to follow at equal intervals of 12 sidereal hours, we may conclude with certainty that the axis of the telescope's motion is meridional, or the position of its horizontal axis exactly east and west. But if it pass from one to the other ap- parently without any interval, then it must be true that it is equally certain that an extra-meridional error must exist, the deviation lying towards that side on which the least interval occurs. This is easily seen by referring to azimuth accordingly, till the difference in question dis- appears, when the axis will be found meridional. (183). The place of the pole point on the limb of the mural circle once determined, becomes an origin, or zero point, upon which all the distances of all objects, referred to other points on the same line of sight, is matters not whether the actual commencement 0° of the graduated circle be taken as a starting point; still only by the difference of the readings in the area round this limb are determined; and hence a great advantage is obtained by employing a large number of observations, in which a different part of the circum- ference of the circle shall be employed, and different graduations used; so that no single point of division may be detected and neutralized. This is accom- plished properly by detaching the telescope from its old attachment, and setting it affixing on a different part of the circumference. (184). A point on the limb of the mural circle, not less important than that just mentioned, is called a "mean point," which being once known, becomes in like man- ner an origin, or zero point, from which altitudes are reckoned. The principle of its determination is uti- **CHAP. II.** POLAR AND HORIZONTAL POINTS. nately merely the same with that of the polar point. As no star exists in the celestial horizon, the observer must seek to determine two points on the line, the one of which is called the polar point, and the other the point at which the star is above it. For this purpose, a star is observed at its culmination on one night, by pointing the telescope towards it, and then again on another night by looking through the image of the same star reflected in the still, unmirrred surface of a fluid at perfect rest. Mercury, or the most distant star from the earth, is usually employed for this purpose. As the surface of a fluid at rest is necessarily horizontal, and as all the reflections, by the laws of optics, are equal in height, that of immersion being always just as much depressed below the horizon, as the star itself is above it (if we neglect any difference in elevation of the observer's position), these images are inter-cepted on the limits of the circle between the star and its point of intersection with the horizon. The first image, re-lected for refraction, is the double altitude of the star and its point of intersection with the horizontal point. The re-lection of this image is called "the artificial horizon." The limit of the altitudes of objects is called an artificial horizon. (140.) The mental circle is, in fact, at the same time, a transit instrument. A transit may be constructed by a sys-tem of vertical wires in the focus of its telescope, may be used as such. As the axis, however, is only support-ed by a single wire, it cannot be made perfectly level; it is neces-sary for the more delicate purposes of a transit; nor can it be verified, as a transit may, by the reversal of the instrument; for if it be turned round so that one end pre-vents a divided circle being permanently fastened on the axis of a transit instrument, near to one of its exter-nal edges, and if this circle be examined under magnification formed by a microscope fixed on one of its piers. Such an instrument is called a telæstic circle, or a meridian-circle. (141.) The determination of the horizontal point on the right ascensions and polar distances of objects ob- served with it; at the time of their culmination by clocks; and also their declinations by the lateral mirrors. (141.) The determination of the horizontal point on the limit of an instrument of such essential importance in astronomy, that the student should be made acquainted 92 A TREATISE ON ASTRONOMY. [CHAP. II. ed with every means employed for this purpose. These are the artificial horizon, the plumb-line, and the floating bubble. The artificial horizon has been al- ready explained. The plumb-line is a fine thread or wire, to which is suspended a weight. When the line is at imperfectly horizontal, reduced to rest by placing it on the water, the direction uniformly assumed by such line, admitting its perjctlity, is that of the true meridian, or per- pendicular to the plane of still water. Its application to the purposes of astronomy is, however, so delicate, and difficult, and liable to error, that it is seldom used. The accu- racy attained in its use, dit it is present almost uni- versally shamselne, for the most convenient and equally exact instrument. (142.) The level * is nothing more than a glass tube nearly filled with a liquid (spirit of wine) being that now generally used, on account of its extreme mobility, and not being liable to freeze), the bubble in which, when the A diagram showing a bubble in a tube labeled "level" with arrows indicating directions of movement. tube is placed horizontally, would rest indefinitely in any part if the tube could be mathematically straight. But this being impossible, we must suppose the tube having some slight curvature, if the convex side be placed up- wards, the bubble will come the higher part, as in the figure; but if the concave side be placed upwards. Suppose such a tube as AB firmly fastened on a straight bar, CD; and marked at ab two points distant by the length of the tube; then if the bubble be placed so as to that the bubble shall occupy this interval, it is clear that CD can have no other than one definite inclination to the horizon; and therefore that whatever may happen to way or other, the bubble would shift its place, and run towards the elevated side. Suppose, now that we would necer- tain whether any given line PQ be horizontal; let the base of the level CD be set upon it and note the points CHAP. II.] OF THE LEVEL. 93 a b, between which the bubble is exactly contained; thus turn the level end for end, so that C shall rest on Q, and D on P. If then the bubble continue to occupy the same position, it will be seen that it must be horizontal, otherwise it would be inclined. If not, the side towards which the bubble runs is highest, and must be lowered. Astro- nomical instruments are constructed in such a manner, which the places of the ends of the bubble can be nicely marked; and it is said that they can be executed with such exactness, that a single second of angular deviation from exact horizontality. (143.) The mode in which a level may be applied to find the height of any point, or to measure the circle may be thus explained: Let AB be a telescope firmly fixed to such a circle, DEF, and moveable in one A diagram showing a telescope (AB) mounted on a circular base (DEF). The telescope is pointed at a point A on the circle. with it on a horizontal axis C, which must be like that of a transit, susceptible of reversal (see art. 127), and with which the circle is inseparably connected. Direct the telescope at some point A on the circle, and see it by its horizontal wire, and in this position clamp it fast. Let L be a level fastened at right angles to an axis parallel to C, and let it be turned until it touches and, if we please, another E. Let this arm be fitted by grinding on the axis C, but capable of moving smoothly on it. Then take up the telescope, and while it is still fast on it, so as to prevent it from moving until required. While the telescope is kept fixed on the object S, let the 94 A TREATISE ON ASTRONOMY. [CHAP.I.LT level be set so as to bring its bubble to the marks $a$ & $b$, and clamp it there. Then will the arm LCF have some cer- tain determinate inclination (so mucheter what) to the horizon, in which position it may be left. Now let the whole apparatus be recurred by turning it horizontal axis end for end, without inclining the level arm from its former position. The bubble will then remain in the whole instrument (level and all) on its axis, restore the level to its original position with the bubble at $a$ & $b$. Then we are sure that the level has been placed at such inclination to the horizon the other way, that it had when pointed to $a$ & $b$. But if the level P if will not have been changed. Now turn round the circle on the axis, so as to enar- gy, back through the zenith to $B$, and in that position clamp the circle so as to be horizontal. It is evident that an angle equal to twice the zenith distance of $h$ has been turned through by the telescope from its last position. Lastly, without unclamping the telescope and circle, let the level be once more rectified. Then we shall find that the telescope and circle are de- finite position with respect to the horizon ; and, conse- quently, if the circle be again read off, the difference be- tween this reading and that made when the telescope was at the arc of its circumference which has passed under the point F, which may be considered as having all the while remained constant, will be equal to half of this difference, then will be the double zenith distance of $S_1$ and its half the zenith distance simply, the complement of which is its altitude. Hence, if we make use of this method of reading of the limb becomes known, or, in other words, the horizontal point on the limb is ascertained. Circuitu- nary as this method is, yet it is one of those methods of employing the level for this purpose which does not in the end come to the same thing. Most commonly, however, it is employed in conjunction with another process, to preserve a horizontal point once well determined by other means, which is done by adjusting so as to stand level while making observations. This is very useful in thus keeping depending on the permanence of its adjustment. (144.) The last, but probably not the least exact, as it CHAP. II. THE FLOATING COLLIMATOR. 05 Certainly, in immense cases, the most convenient means of ascertaining the horizontal point, is that ad- vocated by the floating collimator, a recent invention of Captain Krier. This elegant instrument is nothing more than a glass sphere, with a hole bored through its center, to receive a wire, which may be made to focus, and fastened horizontally, or as nearly so as may be, on a flat iron float, which is suspended by a string from the top of the sphere. The wire will, when left to itself, ac- sume always one and the same invariable inclination to the horizon. If the cross-wires of the collimator be illu- minated by a lamp, being in the focus of its object-glass, the rays from them will issue parallel, and will therefore be in a state to be brought to a focus by the object- glass, and thus form an image of the lamp. This im- age as it may be observed as it were a star, and that, however near the two tele scopes are to each other. By transferring then, one of these lenses from side to side, we shall see that the one side to the other of a circle, we are furnished with two quasi-identical objects, at precisely equal altitudes, and at equal distances from the observer. Proceeding in succession with the telescope of the circle, bringing its cross to bisect the image of the crown of the collimator (for example), we shall find that this line is perpendicular to the plane of the horizon. If now we turn our telescope upwards or downwards, we shall find that it is inclined at an angle equal to that between the horizon and the object-glass of our instrument. In this manner we have determined both the altitude and azimuth of any point. Another method is also very useful for determining latitude, in which the telescope is vertical and whereby the zenith point at desired latitude, is described in the Phil. Trans. 1849 p. 327 for this same purpose. A diagram showing a floating collimator with a wire suspended from its center and illuminated by a lamp. A diagram showing two telescopes with their cross-wires aligned with each other. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still and tilted further still and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still and tilted further still and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tilted further still and tilted further still and tilted further still and tilted further still and tilted further still. A diagram showing two telescopes with their cross-wires aligned with each other but slightly offset and tilted and tilted further and tiled 56 A TREATISE ON ASTRONOMY. [CHAP. II. (145.) The transit and mural circle are essentially me- ridian instruments, being used only to observe the stars at the meridian, and at the same passage. Independent of this being the most favourable moment for making observations, it is that in which their diurnal motion is parallel to the horizon, and therefore, at this time, they can be set at any other, to place the telescope exactly on their direct true direction; since their apparent course in the line of view between the observer and the stars, when observed at different times of the day, by means of wires therein, they may, by giving a fine motion to the telescope, be brought to exact coincidence with it, and thus ascertain whether the stars have made this co- incidence, if not it must presently halt, which is impossible in no other situation. Generally speaking, all angular magnitudes are either increasing or decreasing; but ex- actly, should it, possible, be observed at their mean ex- minima of increase or diminution; because at these points the stars appear to move with a uniform motion for a time long enough to complete, and even in many cases to re- peat and verify our observations in a careful and honestly manner. This uniformity of motion of the stars, is in this preclusion, in the altitude of the star, which measures its maximum or minimum on the meridian, and which is measured by the transit circle. (146.) The purposes of astronomy, however, require that an observer should possess the means of observing any object whatever at any point of his meridian circle or, wherever it may present itself in the heavens. Now, a point in the sphere is determined by referring it to two right angles to each other; or of two circles one of which passes through the pole of the other. These, in the language of geometry, we call parallels and meridians. Thus, if we suppose, for instance, on the earth, a place known if we know its longitude and latitude --in the stary heavens, if we know its declination and right ascension-- we can find any visible hemisphere, if we know its azimuth and altitude. (147.) To observe an object at any point of its diurnal course, we must use some means of directing a tele- scope to it; which, therefore, must be placed on a stand in two planes at right angles to each other; and this CHAP. II.] CO-ORDINATE CIRCLES. 97 amount of its angular motion in each must be measured on two circles co-ordinate to each other, whose planes must be parallel to those in which the telescope moves, and which are so placed that the axis of one of them coincid- ed by making the axis of one of the circles perpendicular to the other at right angles. The pierced axis turns on these circles, and is supported by a fixed support, which is either by any external support, but is sustained entirely by that, when it penetrates, which is strengthened and enlarged by a ring or frame. This figure exhibits the simplest form of such a combination, and shows how it is in point of mechanism. The two circles are readjusted until they are in their proper position, and then the circle attached to the fixed support which carries the telescope is turned through 90° about the axis of the principal axis. Both circles also are susceptible of being moved with respect to each other. (148.) It is manifest that such a combination, however its principal axis be pointed (provided that its direction be invariably with respect to the observer's station), will always pass through all great circles in the visible hemisphere, one of which passes through the poles, and the longitudes of the principal axis or the vanishing points of the two circles coincide with those of this line; and the other passes through all lines parallel to this line, and the other poles; and finally, it is the vanishing line of all planes parallel to the circle GH ; and these two planes being, by the constructi- on of the instrument, at right angles, the great circles, A diagram showing a combination of two circles used for measuring angular motion. The main axes are labeled K and L, with a fixed support labeled F. The circles are labeled A and B. 08 A THEATRE ON ASTRONOMY. CHAP. II. which are their vanishing lines, must be so too. Now, if two great circles of a sphere be at right angles to each other, the one will always pass through the other's poles. (445.) There are, however, but two exceptions in which such an equality may not hold, as to be of any practical utility in astronomy. The first is, when the principal axis CD is parallel to the earth's axis, and therefore passes through the pole of the horizon. In this case the vanishing points of all lines in his system of parallels ; and when, of course, the principal circle AB is parallel to the equator, and therefore passes through the pole of the meridian. This is necessary for its vanishing lines, and measures, by its arcs read off, how much the observer has risen or fallen in ascension. In this case, great circles in the heavens belonging to various positions, which the circle GH can be made to represent, will have no vanishing points on its perp. line axis CD, are all hour-circles ; and the arc read off on this circle will be declinations, or polar distances, or their differences. (180.) In this position the apparatus assumes the name of an equatorial, or, as it was formerly called, a parallactic instrument. It is evident that all instruments designed for all such observations as require an object to be kept long in view, because, being once set upon the object, it can be left undisturbed until it is removed again ; i. e., by merely turning the whole apparatus round on its polar axis. For since, when the telescope is set on a star, the axis of the telescope coincides with the star's polar axis is equal to the polar distance of the star, it follows, that when turned about its axis, without altering the posi- tion of the telescope itself, it will always point towards it if directed will always lie in the same circle of the heavens coincident with the star's diurnal path. In many observations it is necessary to know also what part of which belongs to no other instrument. The equatorial is also used for determining the place of an unknown body compared with another known body. This subject cannot be described in the fourth chapter. The adjustments of the equatorial are somewhat complicated and difficult. They are best performed by following the pole-star round **CHAP. II. AZURITE AND ALUMINUM INSTRUMENT.** The entire diurnal circle, and by observing, at proper inter- tervals, other considerable stars whose places are well ascertained. The other position in which such a compound aperture as we have described in art. 147 may be advan- tageously mounted, is that in which the principal axis of the instrument is perpendicular to the horizon, and consequently corresponds to the celestial horizon, and the azimuthal adjustment of the transit being performed by angles measured on the former are therefore azimuthal, or, differences of azimuth, and those on the latter zenith dis- tances from the upper point of its limb, or from one 90° distinct from it. It is therefore known by the name of the Zenith transit. The adjustment of this instru- ment of its principal axis is secured either by a plumb- line suspended from the upper end, which, however, it is not always convenient to use, or by a level fixed to it, and the same filamental mark near its lower extremity, or, by a level fixed directly sense it, whose bubble ought to be placed in the middle of the vertical circle when the mouth. The north or south point on the horizontal cir- cle is ascertainment by bringing the vertical circle to com- plete coincidence with the meridian plane, and then by which the azimuthal adjustment of the transit is per- formed (art. 137), and noting, in this position, the read- ing of the vertical circle. (182). Let a bright star be observed at a considerable distance to the east of the meridian, by bringing it on the vertical circle, and then describing a semicircle in course, let it be followed by moving the whole instrumen- tum round to the west, without, however, unshading the meridian plane. This is done by means of a small plate, by continuing the horizontal motion, the star, and the circle, will appear to move nearer to each other. In this position is evident the star must have the same latitude. See Linnæus on the Adjustment of the Equatorial.—Mem. Astron. Soc., vol. ii. p. 45. A diagram showing a Zenith Transit instrument with a plumb line suspended from the upper end. 100 A TREATISE ON ASTRONOMY. [CHAP. II.] attitude about the meridion, that it had no mo- ment of the first observation above the horizon. At this point both the zenith and nadir will be on the same circle, and may again fall. The difference of the readings will be the azimuthal as described in the interval. Now, it is evident that the difference between the two observations must be either side of the meridian, its azimuthal, whether reckon- ed both from the north or both from the south point of the horizon, or whether reckoned from one point of the south south point of the horizon must bisect the azimuthal arc thus determined, and will therefore become known. (153.) The difference between the zenith and south points of a horizontal circle (by which, when known, we may draw a meridian line called the "methodical meridian") is a great convenience in useful astronomy. If we note, at the moments of the two observations, the time, by a clock or chrono- meter, and also the altitude of the sun at each moment of the star's meridian passage, which may thus be determined without a transit, and, vice versa, the error of any star's declination may be soon discovered. For this last purpose, it is not necessary that our instruments stand in such a position as to show horizontals circles of equal length by which altitudes can be mea- sured will enable us to determine the moments when the same star arrives at its highest point in its diurnal course and lowest point in its diurnal course; and then, once known, the instant of meridian passage and the error of the clock are easily found. (154.) One of the chief purposes to which the altitude and azimuth circle is applicable is the investigation of the moon and planets. For instance, if we know following with it some star whose places pass the zenith and another which grazes the horizon, through their whole diurnal course they will appear to move in different orbits, or the oval into which their circles are distorted by refraction, can be traced; and their deviation from circles, or ellipses, will give us information as to the observation in the direction in which the refraction itself takes place (i. e. in altitude), is made a matter of direct observation. **CHAP. II.** HALEY'S SEXTANT. (155.) The zenith sector and the theodolite are pecu- liar modifications of the altitude and azimuth instrument. The former is adapted for the very exact observation of the zenith, by means of a telescope, which is fixed upon the vertical axis, and suppressing all the circumference of the vertical circle, except a few degrees of its lower part, so that the line of sight may be directed to any proportional enlargement of the divisions of its arc, is ob- tained. The latter is especially devoted to the mea- surement of horizontal angles, and in this respect the telescope never requires to be elevated more than a few degrees, and in which, therefore, the vertical circle is suppressed entirely, and only one quadrant is left, scale, and with less delicacy; while, on the other hand, great care has been taken to exclude every ob- stacle to the plane of the telescope's motion, by resting its horizontal axis on two supports like the pieces of a quadrant, so that it may be turned about freely on the spokes of the horizontal circle, and turn with it. (156.) The last instrument we shall describe is one which belongs to a class of instruments which pro- jects may be measured, or the altitude of a single one determined, either by measuring (its distance from the horizon) by means of a quadrant (by its angle of dip), or from its own reflection on the surface of mercury. It is the extant, or quadrant, commonly called Halley's, and was invented by Sir Isaac Newton, who himself belongs undoubtedly to Newton, whose claims to the gratitude of the navigator are thus doubled, by his having invented this instrument. It is constructed so that it can be securely guided, and the only instrument which has ever been found to avail in applying that theory to practice. (157.) The principle of this instrument is the optical property of reflected rays, thus announced:---*The *Newton communicated it to Dr. Halley, who suppressed it.* The same principle was afterwards applied by Halley himself in among his papers, in Newton's own handwriting, by his executor, who published them in 1742. In these papers are contained many details respecting Newton's death, and eleven other publications of Halley's invention, showing how he had made use of our knowledge of Newton's, though Halley minimizes the contrary. *Newton communicated it to Dr. Halley, who suppressed it.* The same principle was afterwards applied by Halley himself in among his papers, in Newton's own handwriting, by his executor, who published them in 1742. In these papers are contained many details respecting Newton's death, and eleven other publications of Halley's invention, showing how he had made use of our knowledge of Newton's, though Halley minimizes the contrary. 13 102 A TREATISE ON ASTRONOMY. [CHAP. IL angle between the first and last directions of a ray which has suffered two reflections in one plane is equal to twice the inclination of the reflecting surfaces to each other." Let AB be the limb, or graduated arc, of a portion of a circle 60° in extent, but divided into 120 equal parts. On the radius BC let a silvered glass D be fixed, at right angles to the plane of the circle; on the meridional radius CE let another such silvered glass, C, be fixed. The glass D is perfectly parallel fixed to AC, and the glass C is silvered with a thin film allowing objects to be seen through it. The glass C is wholly silvered, and its surface is polished to the height of the perpendicular line AE, of the extremity E, of which a vernier is placed to read off the divisions of the limb. On the radius AC let a telescope F, through which any object Q may be seen, be fixed. The rays will pass through the universal portion of the glass D, while another object, P, may be seen through the telescope by rays reflected from reflection C. It has been shown upon the silvered part of D, and are thence directed by a second reflection through C. Thus two distinct images so formed will be both seen in the field of view together; and by moving the radius CE will (if the reflectors be truly perpendicular) the place of their meeting until pass over each other's path; each thus being thus however, is arrested when they meet, and at this point the angle between them is found to be 60°. One of these objects, and FG of the other, is twice the angle included between the fixed and movable radii CB, CE. Now the graduations of the limb being purposely made A diagram showing a telescope (F) looking through a silvered glass (D) onto an object (Q), with another object (P) visible through a similar glass (C). The diagram also shows a vernier scale on the limb (AB) and a line AE indicating the height of the extremity E of one of the glasses. **CHAP. II.** **PRINCIPLE OF REPEITION.** only half as distant as would correspond to degrees, the arc BE, when read off, as if the graduations were whole degrees, will express only half of the angle ABE, and therefore the numbers to read off will express not the angle EBC, but its double, the angle subtended by the arc BE. (158.) To determine the exact distances between the stars by direct observation is comparatively of little service; for it is impossible to observe with accuracy their distances from the moon, and of their altitudes, is of essential importance; and as the sextant requires no focus, and can be used on land and sea, and even on ship-board, the utility of the instrument becomes at once obvious. For altitudes at sea, as no level, plumb-line, or horizon can be obtained, the sextant is the only resource; and the image of the star observed, seen by reflection, is brought to coincide with the boundary of a circle drawn upon a card placed at a distance above the sea-line; and this corrected for the dip of the horizon (art. 24) gives the true altitude of the star. The same method may be applied to measure distances by the consideration of dip is rendered unnecessary. (159.) The reflecting circle is an instrument destined for measuring angles greater than 90°; it consists of two circles being entire, and the divisions carried all round. It is usually furnished with three verniers, so as to admit of very minute gradations; and by this means the error of graduation and of reading is reduced. This is altogether a very refined and elegant instrument. (160.) The question arises whether without mention of the "principle of repetition"? an invention of Horace, by which the error of graduation may be diminished? Let PQ be two objects which we may suppose fixed, for purposes of explanation, and let KL be a plane surface perpendicular to PQ. On this surface let us draw two circles, AML and AB'C', of which the former, AML, is absolutely fixed in position; while B'C' may move freely about a point on the axis. The telescope is attached permanently to the latter circle, and moves with it. An arm OA carries the index, or A diagram showing two circles AML and AB'C', with an arm OA carrying an index. 104 A TREATISE ON ASTRONOMY. CHAP. II. vernier, which reads off the graduated limb of the fixed circle. This arm is provided with two clamps, by which it can be temporarily connected with either circle, and detached at pleasure. Suppose, now, the telescope di- rected to P. Clamp the index arm OA to the inner circle, and unclamp it from the outer, and read off. Then carry the index arm OB to the object Q. In so doing the inner circle, and the index-arm AB, which is changed to it, will also be carried round, over an arc AB, along the graduated limb of the outer circle, through the angle PQO. Now clamp the index to the outer circle again, and unclamp the inner, and read off: the difference of readings will be equal to that of the angles POQ and PQO. The result will be liable to two sources of error: that of gradation, and that of observation, both which it is our object to get rid of. To do this we must first change P into P', without unclamping the arm from the outer circle; then, having made the bisector of P'P', clamp the arm to b', and mark off on the graduated limb of the outer circle, from Q, by which the arm will now be carried with it to C, over a second arc, BC, equal to the angle PQO. Now again read off at B'. We have thus obtained two measures of reading and the original one measures twice the angle PQO, affected with both errors of observation, but only with those of gradation. If we now repeat this process (the pro- cess be repeated often as we please (suppose ten times)); then will the final arc ABCD read off on the circle be ten times the required angle, affected by the A diagram showing a telescope with a vernier scale attached to its index arm. The diagram includes labels for various points such as P, P', Q, O, A, B, C, D. **CHAPTER III.** ## OF GEOGRAPHY. Of the Figure of the Earth—Its Exact Determination—Its Form that of Equi- lateral Spheroid—The Geographical Position of the North Pole—The Meridian Surface—Spherical and Dynamical Measures of Gravity—The Funda- mental Principles of Geodesy—The Determination of the Geographical Positions of Winds—Determination of geographical Positions of Latitudes—Of the Measure of the Angular Distance between the Meridians—Of the Mea- surement of the Sphere—the Measurement of Heights by the Barometer. (161.) GEOGRAPHY is not only the most important of the sciences, but also the most difficult. It is not merely a branch of natural science, but also, in its turn, a science of science, and therefore, as well as a part of the whole science, a part of the whole science. The earth being the ge- neral object of all our observations, we have to make use of our knowledge of the local situation of particular stations on its surface is of great consequence, when we come to inquire into the relations which exist between them. This has been concluded from observations of their parallax as well as on all other occasions, where a difference of locality can be observed. But this conclusion is not sufficient; for, how- ever, in this chapter, to explain the principles by which astronomical observation is applied to geo- graphical determinations, and to give at the same time 105 joint errors of all the two observations, but only by the same constant error of graduation, which depends on the initial and final readings of each instrument. For if one instrument be found to be defective, it may be corrected by another; and so that, if sufficiently multiplied, their in- fluence will be entirely removed. But in this case we shall find then, only the constant error of graduation, which comes to be divided in the final result by the number of obser- vations made with it. Hence it is evident that we cannot attain to one truth at its possible amount or, to less if need be. The abstract beauty and advantage of this principle seems to be confirmed in practice by some unknown errors which probably must be sought for in imperfect clamping. --- **CHAPTER IV.** ## OF GEOMETRY. Geometry is a branch of mathematics which treats of figures and their properties. It is divided into two parts— (162.) THE ELEMENTARY PRINCIPLES OF GEOMETRY. I. The Elements (Euclid's Elements) are divided into five books. In Book I., Euclid gives a definition of a point, line, plane, solid, etc., and then proceeds to define angles and straight lines. He then proves that two straight lines cannot meet in more than one point; that two straight lines which meet in one point cannot meet again in any other point; that two straight lines which do not meet cannot be parallel; that two straight lines which do not meet can never be equidistant; that two straight lines which do not meet can never be perpendicular; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a third straight line; that two straight lines which do not meet can never be bisected by a thirdstraight 106 A THEATRE ON ASTRONOMY. [CHAP. III. an outline of geography so far as is to be considered a part of astronomy. (163.) Geography, as the word imports, is a delineation or description of the earth. In its widest sense, this comprehends not only the definition of the form of its continents, islands, rivers, mountains, seas, and their physical condition, climates, and products, and their apprehension by communities of men. With physical and natural history it has much to do; but it concerns here Astronomical geography has for its objects the exact knowledge of the form of the earth, and the position of all points on it by means of latitude and longitude, and the configuration of the surface of the latter, regarded as pro- tuberant above the level of the sea, or below such a surface formed by the level of the table land, unless neither the form of the bed of the ocean, regarded as a continua- tion of the surface of the earth, nor that of any other body of water, be left out of consideration; we know it is very very little of it; but this is no reason hence to be incomplete, and, if possible, to be omitted; for it would be impossible to have an accurate knowledge of any branches of inquiry which would be greatly advanced by a better acquaintance with it. (164.) With regard to the figure of the earth as a sphere, it is generally supposed that it is perfectly round; but it may be regarded as spherical; and the reader who has duly appreciated this remark (§ 28) will see that it is a less than perfect sphere. This result, concluded from our observa- tions not susceptible of much exactness, and embracing very small portions of the surface at once, may be regarded as an approximation, and may require to be materially modified by entering into minute before neg- lected, or by increasing our future extent larger areas of its surface. For instance, if it should turn out (as it will), on minister inquiry, that the true shape somewhat chalipical or flattened towards an orange-shaped dimen- sion which coincides with the axis about which perturber than the earth revolves (§ 29), then we shall have so radial deviation from the spherical form that if a mea- sured such proportions were turned in wood and laid before us on a table, the nicest eye or hand would not **CHAP. III.** **FIGURE OF THE EARTH.** 107 detect the flattening, since the difference of diameters, in a globe of sixteen inches would amount only to $\frac{1}{54}$th of an inch. In all common parlance, and for all ordinary purposes, this difference may be considered as nothing; nevertheless, by careful measurement, the difference would not fail to be perceived, speaking strictly, it would be found that the globe is not perfectly spheroidal, which is the name appropriated by geometers to such figures. (16.) The sections of such a figure by a plane are not circles, but ellipses; so that, on such a shaped earth, the horizon appears to be elliptical. This is easily seen; it is easy to demonstrate, however, that its deviation from the circular form is very slight. A sphere of 16 inches in diameter, as above supposed, would be quite imperceptible, not only to our eyesight, but to the test of the dioptris; so that we might suppose it to be perfectly spherical. But it is easy to notice so small a deviation from perfect sphericity. We are led to this conclusion, as a practical result, by applying the same principles which we have employed in determining with accuracy the dimensions of the whole, or any part of the earth. (17.) It is evident that gross the earth, nor recede from it far enough to view it at once as a whole, and compare it with a known standard of measure in any degree con- sistent with our powers of observation. We must therefore use it, and apply our diminutive measures to comparatively small parts of its vast surface in succession, it becomes necessary to employ means more accurate than those of our physical powers; and from a delicate and careful measurement of such small parts to conclude the form of the immense whole. It will be observed that this is a very difficult task. Little difficulty, if we were sure the earth were strictly a sphere, for the proportionate size of its parts would be known. But as we know that it is not (viz., that of $3\cdot1415952$ to $1\cdot000000$), we have only to ascertain the length of the entire circumference of any great circle, such as a meridi- an line in latitude; and then divide this length into equal parts, each part being equal to one-eighth of the diameter in units of the same kind. Now the cir- cumference of the whole circle is known as soon as we 108 A TREATISE ON ASTRONOMY. [CHAP. III. know the exact length of any abridged part of it, such as 1° or $\frac{1}{3}$rd part; and this being not more than about several hundred miles, we may measure it with very exact measurement, and could in fact, be measured (if we knew its exact termination at each extremity) within a very small degree, indeed, inches, by methods precisely to be particularized. (16.) Supposing then, we were to begin measuring with the quadrant, we would find that the true direction of a meridianal, and go measuring on, till by some indication we were informed that we had accomplished an exact distance of one degree. The next question would then be at once resolved. It only remains, therefore, to inquire by what indications we can be sure, 14., that we have reached the desired point. We have hitherto been measuring in the exact directions of great circles. (167.) New, the earth has no landmarks on it to indi- cate the direction of a meridianal. We must seek guide us in such a course. The compass, though it affords a tolerable guide to the mariner or the traveller, is far too uncertain for our purpose. We must depend upon the stars in its laws, to be of any use in such an operation. We must, therefore, look outwards and refer our station on the surface of the earth to the stars which belong to it, and which are of equal permanence and stability with the earth itself. Such marks are afforded by the stars. By observing their positions at different stations on any survey station, and from their known polar distances, we conclude the height of the pole; and since the altitude of the pole is known, we can determine the latitude. Thus, by the same observations give the latitudes of any stations where we may establish the requisite instruments. When our latitude is thus determined, and our longitude known, we know that provided we have kept to the meridianal, we have described one three hundred and sixtieth part of the earth's circumference. (168.) The direction of the meridian may be secured at every instant by the observations described in art. 157., and also by those described in art. 166. But since in our measurement from this exact direction, yet if we keep a strict account of the amount of this deviation, a **CHAP. III.] LENGTH OF A DEGREE OF LATITUDE.** very simple calculation will enable us to reduce our ob- served measure to its meridional value. The next operation which we must important geographical operation, the measurement of an arc of the meridian. In its detail, however, a somewhat modi- fied method is employed, by which the arc is first mounted and dismounted at every step ; so that we can not identify and measure an exact degree neither more nor less than one minute. This is a very difficult thing, we know with equal precision how much, more or less, we have measured. In place, then, of measuring this pre- cise degree of latitude, we may take any other arc of measuring from one good observing station to another, about a degree, or two or three degrees, as the case may require. We shall then have no difficulty in determining the precise difference of latitudes between the stations. (170.) Again, it is of great consequence to avoid in our observations all possible errors. The least error committed in the length of a single degree will be multiplied 360 times in the circumference, and nearly indefinitely multiplied in the meridian circle. Any error which may affect the astronomical determination of a star's altitude will be especially dangerous. Now the amount of refraction at moderate altitudes, not to make it exactly zero, may vary from 15 to 20 seconds, and even more. It is therefore wise to take care to select observatories at the extreme stations, some star which passes through or near the zenith being observed at each station. But when a few degrees of the zenith is very small, and its fluctua- tions and uncertainty, in point of quantity, so excessively large as to render it impossible to determine accurately the same thing whether we observe the pole to be raised or depressed a degree, or the zenith distance of a star when it passes through the zenith. If at one station we observe any star to pass through the zenith, and at the other to pass one degree south or north, then we know that the difference of geographical latitude, or the altitude of the pole at the two stations, must dif- fer by the same amount. (171.) Granting that the terminal point of one degree K 110 A TREATISE ON ASTRONOMY. [CHAP. III. can be ascertained, its length may be measured by the methods which will be presently described, so we have before remarked, to within a very few feet. Now, the error which may arise from this cause, when the terminal points cannot exceed that which may be committed in the observation of the zenith distance of a star, properly observed with the most exact instruments, and errors with proper care, can hardly exceed a single second. Supposing we grant the possibility of ten feet of error in the measurement of the distance between two stars, each of the zenith distances of one star, observed at the northern and southern stations, and, firstly, suppose all these errors to be equal, then, since the circumference is a result greater or less than the truth, it will appear, by a very easy proportion, that the whole amount of error which may arise from this cause would not exceed earth's diameter, as concluded from such a measure, would not exceed 544 yards, or about the third part of a mile, and therefore could not affect our hypothesis. (172.) This, however, supposes that the form of the earth is that of a perfect sphere; nor, in consequence, the length of its meridians is uniform throughout. But when we come to compare the measures of meridians made in various parts of the globe, the results ob- tained, although not always accurate enough to show that the supposition of a spherical figure is not very remote from the truth, yet exhibit discrepancies for greater lengths than what we have hitherto supposed; and these discrepancies are so great, and render it evident that the hypothesis, in strictness of its wording, is untenable. The following table exhibits the differences between the actual measures (arithmetically determined as above described), expressed in British standard feet, as resulting from actual observations made by Messrs. Horsley and Hutton; by com- missioners of various nations, men of the first eminence, supplied by their respective governments with the best instruments and materials; and by persons who had no other object than to ascertain a successful result of their important labours. *The first four columns of this table are extracted from among the data given in Professor Airy's excellent paper "On the Figure of the Earth," in the Encyclopaedia Metropolitana." A page from a book with text on it. CHAP. III. DEGREES IN DIFFERENT LATITUDES.
Country. Latitude Angle Length of the Arc Observers.
of the Arc of the Arc of the Arc of the Arc of the Arc
Bavaria. 50° 37' 18" N. 19° 57' 36284 Schweinfurt.
Russia. 50° 17' 32" N. 13° 52' 36284 Leningrad.
Saxony. 49° 20' 30" N. 12° 58' 36284 Kassel.
France. 48° 21' 30" N. 9° 58' 36284 Lorraine, Châlons.
Austria. 47° 19' 30" N. 8° 56' 36284 Lorraine, Metz.
Austria, U.S. 47° 19' 30" N. 8° 56' 36284 Munich, Brixen.
Holland. 46° 19' 30" N. 7° 54' 36284 London, Eversen.
India. 45° 19' 30" N. 7° 54' 36284 London, Eversen.
Persia.
It is evident from a mere inspection of the first and fourth columns of this table that the measured length of a degree increases with the latitude, being greatest near the poles, and least near the equator. Let us now con- sider whether this fact agrees with our previous assump- tions as regards the form of the earth. (II.) Suppose we were to make a model of the earth, and place it on a flat wood, it would be, as already observed, so nearly spherical, that neither by the eye nor by any other means could we detect any considerable deviation from that form. Suppose, too, we were debar- red from measuring directly across from surface to surface in all directions, but only had access to one point at a time, might at once ascertain whether one diameter were longer than another; how then, we may ask, are we to ascer- tain whether it is a true sphere or not? It is clear that we have no resource, but to endeavour to discover, by some nicer means than simple inspection or feeling, whether the equality of its surface is the same in every part; and if not, where it is greatest, and where least. Suppose, then, within plate of metal to be cut into A diagram showing a circular plate with a central hole and two smaller holes near the edge. The plate is labeled "A." A line drawn from the center of the plate to one of the smaller holes indicates a measurement. Another line drawn from the center of the plate to the edge of the plate shows a different measurement. The text around the diagram reads: "some nicer means than simple inspection or feeling, whether the equality of its surface is the same in every part; and if not, where it is greatest, and where least." The text also mentions that "Suppose... within plate of metal to be cut into..." This suggests that the diagram represents a method for determining whether a sphere is truly spherical or not." 111 112 A TREATISE ON ASTRONOMY. JCHAP. IIL a con vexity at its edges, so as exactly to fit the surface at A; let this now be removed from A, and applied successively to every other part of the surface, taking care to keep its convexity always in the same direction as that here represented. If, then, we find any position B, in which the light can enter in the middle between the globe and plane, and produce a visible effect by reason of the pressure, or admit the light under its edges, we are sure that the curvature of the surface at B is less, and at greater times than at A. (174.) What we here do by the application of a metal plate of determinate length and curvature, we do on the earth by means of a circle of given radius, drawn in the altitude of the pole. Curvature of a surface is nothing but the continual deflection of its tangent from one fixed direction to another. By measuring with some measured distance of admeasure, we find the tangent (which answers to our horizon) to have shifted its posi- tion with respect to the axis of the earth, or with respect to the axis of the heavens, or the line joining the earth's centre and some given star; more in one part of the earth's surface than in another. It is necessary, therefore, that the curvature of the surface at the former place is greater than at the latter; and, vice versa, when, in order to reach a given star, we must travel with respect to the pole (suppose 1°), we require to travel over a longer measured space at one point than at an- other, in order to arrive at it. From these facts we conclude that the curvature of a meridional section of the earth is smaller great at the equator than to wards the poles. The curvature is not spherical, but flattened at the poles, or, which comes to the same thing, produced at the equinoxes. (175.) Let NADIBER be a meridional section of the earth, C its centre, and NA, BD, GE, arcs of a meridian, each corresponding to one degree of difference of latitude. Let us suppose that NA represents a certain altitude of a star, as referred to the horizon of a spectator travelling along the meridian. Let nN = NA, bB = DB, gG = GE; NA being the required measure of the planimeter for the sections NA, NB, BD, GE; of which we will suppose N **CHAP. III.** **MERIDIONAL SECTION OF THE EARTH.** 113























































































<
n a b d e
N A NA NA NA NA
z y x y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x
z y x z y x z y x z y x z y x z y x z y x z y x
to be at the pole and E at the equator; then will the meri- gents to these points at these points respectively be per- pendicular to these lines; consequently, if each pair, viz. nN and aA, bB and dD, gG and eE, be pro- longed to meet one another, the angles which they make with the angles NA, ByD, GZE, will each be one degree each, and therefore, all equal; so that the small curvilinear are between any two of them will be equal to the sum of one degree each, described about $x$, $y$, $z$, as centres. These are what in geometry are called centres of curva- ture; and the perpendiculars drawn from any point on present radii of curvature, by which the curvatures at those points are determined and measured. Now, as the areas of the curvilinear figures are proportional to their respective centres, are in the direct proportion of their radii, and as the arc NA is greater than BD, and the angle NA is greater than ByD, it follows that the area must be greater by By, and By greater by Ez. Thus it appears that the mutual intersections of the plumb-lines will not, as was supposed before, be at right angles to each other; but will be arranged along a certain curve, xyz (which will be rendered more evident by considering a number of such curves constructed upon different bases), and this curve is given the name of the evolute of the curve NABDGF, from whose centres of curvature it is constructed. k2 114 A TREATISE ON ASTRONOMY. CHAP. III. (176.) In the flattening of a round figure at two op- posite points, and its protractiveness at points regularly circular, we have a very remarkable and interesting feature of the elliptic form. Accordingly, the next and simplest supposition that we can make respecting the nature of this figure, is that it is a circle. But to be a circle, is, that it is an ellipse, or nearly so, having NS. the axis of the earth for its shorter, and ET, the equa- torial diameter for its longer axis. The form of the earth's surface is that which would arise from making such a curve revolve about its shorter axis NS. This figure would be a circle, but with a certain degree of the degree in going from the equator to the pole. In the ellipse, the radius of curvature at E, is the extremity of the tangent to the curve at E; and at N, it is zero; so that the greatest it admits, and the form of its evolute agrees with that here represented. Assuming, then, that it is an ellipse, we may proceed to see how we can make use of it to assign the proportion between the lengths of its axes which shall correspond to any proposed rate of ve- locity. For this purpose, let us take any given length of arc length, corresponding to my assigned length of the degree in a given latitude. Without troubling the reader with any more than what I have already said (as well as any work on the conic sections), it will be sufficient to state that the lengths which agree on the whole best with the ratio of velocity which I have supposed have been satisfactorily measured, are as follow:—
Length of arc Length of arc
100° 100°
80° 80°
60° 60°
45° 45°
30° 30°
20° 20°
15° 15°
12° 12°
10° 10°
8° 8°
6° 6°
5° 5°
4° 4°
3° 3°
2° 2°
1° 1°
The proportion of the diameters is very nearly that of 800:299, and their difference $\frac{2}{299}$ of the greater, or a very little less than one hundredth part. (177.) Thus we see that the rough diameter of 8000 miles we have hitherto used is rather too great, the ex- cess being about one mile. And if we consider it extremely improbable that an error to the extent of *The dotted lines are the portions of the evolute belonging to the other quadrant.* † See Proclus' Airy's Essay before cited. A diagram showing an ellipse with axes labeled NS and ET. **Greatest or symmetrical diameter** **Lesser or asymmetrical diameter** **Difference of diameters, or plane curve** **Proportions** \[ \text{Diameter} = \frac{8000}{299} \approx \frac{8000}{300} = \frac{80}{3} \] \[ \text{Difference} = \frac{2}{299} \approx \frac{2}{300} = \frac{1}{150} \] **CHAP. III.]** **EXACT DIMENSIONS OF THE EARTH.** 115 five miles can subsist in the diameters, or an uncertainty to that of a tenth of its whole quantity in the circumferences just stated. As we have seen, this is a very great degree of precision; but, thus far, our mind, that in our intuitions there are just as many thousands of feet in a degree of the meridian as there are in a degree of latitude, is satisfied. But, speaking loosely, a degree is about 70 British statute miles, and a second about 100 feet; and that the equatorial diameter of the earth is a little less than 25,000 miles (34.89). (178.) The supposition of an elliptic form of the earth has been made by some philosophers, on account of its simplicity, and confirmed by comparing the numerical results we have just set down with those of actual measurements. But, though these results may be considered as accuracies, it is true, as observed, which, although still too great to be referred to error of measurement, are yet so near to the truth as to render it impossible to suppose the spherical hypothesis, as completely to justify our regarding the earth as an ellipsoid, and refuting the observations which have been made respecting its comparatively small causes. (179.) Now, it is highly satisfactory to find that the greatest possible errors which can practically proceed to error, is precisely what ought theoretically to result from the rotation of the earth on its axis. For, let us suppose the earth to be perfectly homogeneous, and perfectly round, and externally covered with an ocean of equal depth in every part. Under such circumstances it would obviously be impossible for any part of the surface to move more than one revolution per day; for if any part moved more than one revolution per day, it would necessarily move around the equator, so as to produce that difference of the polar and equatorial diameters of 26 miles which we have observed. Now, if any part of the surface moved on a ridge or equatorial continent, only, would be thus formed, from which the water would roll down the valleys formed by it; and this would be impossible. However solid might be the ground rest where it was placed, the liquid purl, at last, would not remain there any more than if it were thrown on the side of a hill. The consequence, therefore, would 110 A TREATISE ON ASTRONOMY. CHAP. III. be the formation of two great polar seas, hemmed in all round by equatorial seas, and separated from each other by some immense lake case in the North. The ocean occupies, indifferently, all latitudes, with no more partiality to the polar than to the equatorial regions. The polar seas, therefore, occu- pies an elevation above the centre no less than 13 miles greater at the equator than at the poles, and yet manifestly do not sink below the level of the sea towards wards the latter, it is evident that it must be retained in that situation by some adequate power. No such power, however, can be found in the earth itself, which is a sphere, which is therefore not conformable to nature. In other words, the spherical form is not the figure of equili- brium : but this is not to say that the earth is not so internally constituted as to attract the water to its equatorial regions, and retain it there. For the latter supposition would lead us to expect that we should find any analogy to lead us to such an idea. The former is in accordance with all the phenomena of the apparent fluctuation of the tides ; and if we will consider how we will furnish us with the answer in question, we can have no hesitation in adopting as true the one. (180.) Now, every body knows that when a sphere is turned round, it re- quires thereby a tendency to recede from the centre of its motion ; which is easily understood by supposing a string whirled round in a sling is a common illustration : but a better, for our pre- sent purpose, is a sphere hung up and sus- pended by a cord, and made to spin round, while the cord hangs perpendicu- larly downwards. At first sight, the instead of remaining horizontal, will be- come concave, as is the figure. But this is only owing to the tendency of all the water to leave the axis, and press towards the circumference : it is, therefore, only a temporary state, and forced up its sides, till the excess of height, and consequent increase of pres- sure downwards, just counteracts its **CHAP. III.] ACTION OF THE SEA ON THE LAND.** centrifugal force, and a state of equilibrium is attained. The experiment is a very easy and instructive one, and is abundantly calculated to show how the forces of equili- brium act on the surface of the earth. Let us suppose that, if, for example, we allow the rotation to cease by degrees, as it becomes slower we shall see the convergence of the water as it approaches the axis, and the depression of the water be- neath, and the depressed central zone, while all the time a perfectly smooth surface is maintained, till the rotation is exhausted, and then the water begins to flow away. (181.) Suppose, then, a globe, of the size of the earth, at rest, and covered with a uniform ocean, were to be set in motion by a centrifugal force, which would cause it to move by degrees more rapidly, till it turned round once in twenty-four hours; a centrifugal force would thus be gen- erated at every point of its surface, and would cause the water at every point of the surface to recede from the axis. A rotation might indeed, be conceived so swift as to *first* throw off all the water from the earth's surface; but this could not be done without a greater velocity than what we now speak of. In the case supposed, the weight of the water being equalized by the tendency to recede from the axis could only be satisfied, therefore, by the water leaving the poles, and flowing away towards the equator. But this cannot take place in reality, just as the water in our pails accumulates against the side; and being retained in opposition to its weight, or natural tendency to fall into the pail, it must remain there until such time as it can escape by some other means. This, however, could not take place without laying dry the polar portions of the land in the form of immovable rivers. In fact, if any such polar seas were formed; or if any cases, therefore, that is thus—in the former, a great equa- lization of weight would occur; or in the latter, a great con- centration of weight would occur at some part of the zone of ocean be disposed around the equator. This would be the first or immediate effect. Let us now see what will happen when this happens. The rivers which have been allowed to take their natural course. (182.) The sea is constantly beating on the land, gradually wearing down its surface; and throwing off particles and fragments, in the state of mud and pebbles, under its bed, 117 118 A TREATISE ON ASTRONOMY. [CHAP. III. Geological facts afford abundant proof that the existing continents have all of them undergone this process, even more than once, and been entirely torn in fragments, or reduced to a state of mere mud, as is the celebrated Land, in this view of the subject, loses its attribute of fixity. As a mass it might hold together in opposition to forces which would tend to disperse it, but at the stage of successive or simultaneous degradation, when dissemi- nated through the water, in the state of sand or mud, it is subjected to the action of the waves, by which, in their lapse of time, then the perpendiculair land in both cases would be destroyed, and spread over the bottom of the ocean, filling up the depressions left by the former. It will re- model the surface of the solid medium, in correspondence with the form of equilibrium in both cases. Thus, after a sufficient lapse of time, the earth would assume the equatorial continent, thus forcibly constructed, would again be levelled and transferred to the polar excursions, and the other parts would be similarly treated. In that of an earth in rotation, the polar protuberances would gradually be cut down and disappear, being trans- ferred to the poles. In this case also, after a long time, the earth would assume by degrees the form we observe to have—lost of a flutened or eliptic shape. (183.) The following is a general account of the pro- cess by which the earth really assumed its actual form; all we intend is to show that this is the form to which, under circumstances similar to those supposed above, it was originally formed; and which it would attain, even if originally and (so to speak) perforce constituted otherwise. (184.) The first question is what is the form of the earth and its time of rotation being known, it is easy thence to calculate the exact amount of the centripetal force, which must act on every part of it; for instance, if the force or weight by which all bodies, whether solid or liquid, tend to fall towards the earth. By thin friction of its surface, they are prevented from falling directly, and thereby rendered susceptible of being supported at a higher level, or more remote from the centre than at the poles, where no such counteracting force exists; and See Cab. Cps. Mechanicae, c. viii. **CHAP. III. LOCAL VARIATION OF GRAVITY.** where, in consequence, the water may be considered as **specifically heavier**. Taking this principle as a guide, and combining it with the laws of gravity (as developed by Sir Isaac Newton), we find that, in all parts of the earth, mathematicians have been capable to investigate, a pri- ori, what would be the figure of equilibrium of such a body as the earth itself, revolving about its axis, and keeping the earth to be covered wholly or partially with a fluid, and revolving uniformly in twenty-four hours; and the result has been found to agree exactly with experiment, with what experience shows to be the case. From their investigations it appears that the form of equilibrium is, in all parts of the earth, nearly spherical; and that the ellipticity very nearly identical with what is observed, and which would be double accurately so, did we know the whole surface of the earth. (185.) The confirmation thus incidentally furnished, of the hypothesis of the earth's rotation on its axis, cannot fail to give rise to some reflections upon the nature of a sphere was not contemplated among the original astronomers. It is evident that any one who considers solely on account of the apparent diurnal motion of the heavens, and who sees that, once more, a direct proof is given, as a necessary con- sequence of this other remarkable phenomenon of nature, no other satisfactory account could be rendered. Indeed, so long as it was supposed that the earth was flat, and that the earth's figure was discovered and demonstrated by New- ton to be a consequence of his rotation, and its amount attended to only as a circumstance; but when my observations had suggested such a conclusion. As it will appear from our subject, we shall find the same simple principles brought into view in connection with other phenomena. In consequence of these considerations, some obvious enough, others which at first seem curiously unconnected with it, and which, until they are examined more closely than they have been, had ranked among the most inscrutable areas of astronomy; as well as among its grandest phenomena. Of these phenomena I propose to mention two which we may here mention one which falls in naturally with our present subject. If the earth really revolve on its axis, this rota- 120 A TREATISE ON ASTRONOMY. [CHAP. III.] tions must generate a centrifugal force (see art. 18), the effect of which must of course be to counteract a certain portion of the attraction of the earth upon the equator, as compared with its weight at the poles, and in any intermediate latitudes. Now, this is fully confirmed by experience, and it is evident that it can exist in differ- ence in the gravity, or downward tendency, of the body and the same body, when conveyed successively to stations at different latitudes, and that this difference is great- est near the poles, and in every accessible part of the globe, have fully demonstrated the fact of a regular and progressive increase of gravity towards the poles, corresponding to the increase of latitude, and fixed according to the law of its progression. From these it appears, that the extreme amount of this difference between the weights of bodies be- tween the equatorial and polar weights of one and the same mass of matter, is one part in 104 of its whole weight, and that this increase in travelling from the equa- tor to the pole being at the square of the size of the lati- tude. (187.) The cause why we speak of what is meant by speaking of the same body as having different weights at different stations ; and how such a fact, if true, can be explained without contradiction to a balance or a steelyard we do not counteract its weight by the equal weight of mother body under the very same circumstances; but if we suppose that all parts of its counterpoise be removed to another station, their gravity, if changed at all, will be changed equally so, that they will still remain equal to each other's. A dif- ference in the intensity of gravity could therefore never be detected by these means ; nor is it in this sense that we ascertain that all parts of our planet have equal weight will weigh 54 at the pole. It commerchanlly in a scale or steelyard at the former station, an additional pound would be added on either scale at the latter would inevitably sink the beam. (188.) The meaning of the proposition may thus ex- plained. Conceive a body suspended by a string from an equator by a string whose weight passing over a pulley A, and conducted (supposing such a thing possible) over other **CHAP. III.** **STATICAL MEASURE OF GRAVITY.** pulleys, such as B, round the earth's convexity, till the other end hang down at the pole, and there sustained the weight A by means of a string passing over a pulley C, and y were such as, at any one station, equatorial or polar, would ex- actly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by side over a single pulley, they would exactly balance or when suspended side by size 122 A TREATISE ON ASTRONOMY. [CHAP. III. secured, from travelling, from rest, strain, or disturbance, and the whole apparatus conveyed to a station in a lower latitude. The weight of the pendulum will then be less than that, though although loaded with the same additional weights as be- fore, the weight F will no longer have power enough to steer the pendulum through its orbit, but will only be sufficient to a similar extent. More weights will require to be add- ed; and the additional quantity necessary will be evi- dently more than that which was required for two stations, as exerted on the whole quantity of pendent matter, i.e., the sum of the weight of F and half that of the earth's attraction. Generally speaking, one spring can be constructed of such strength and dimensions that a weight of 10,000 grains, including its own, shall produce a deflection equal to that produced by a spring straining it; one additional grain will produce a further extension of $\frac{1}{100}$th of an inch, a quantity which cannot possibly be detected by the eye. Thus we should be provided with the means of mea- suring the power of gravity at any station to within $\frac{1}{100}$th of an inch. (190.) The other, or dynamical process, by which the force urging any given weight to the earth may be de- termined, is by measuring its velocity when released, by it to the weight when sufficed to fall freely in a given time, as one second. This velocity causes, indeed, by directly applying it to a spring, to produce a motion; and this motion furnishes an easy and certain means of deducing it, and, consequently, the intensity of gravity, by observing the oscillations of the pendulum. In this respect, the physi- cians (see Cah. Cyc., Mechanics, 216), that is, if one and the same pendulum be made to oscillate for different times, of different lengths of arc, and if these times and numbers of oscillations made in the same time in each *Whether the process above described could ever be so perfecltly and without error performed as to give results agreeing in magnitude depend on the degree of permanence and security of settings, etc., and on the constancy of the motions of the pendulum; but even supposing all these conditions to be perfect, on the possibility of transmitting them, absolutely unaltered, from one place to another; still it would not follow that an apparatus and mode of observation would necessarily prove accurate if conve- niently applied. The great difficulty attending upon such a proce- tedious and expensive process, render the attempt very much inad- III 193 case he contended, the inertias of the forces will be too great to counteract other influences, and the excesses of the numbers of oscillations made, and thus their proportion becomes known. For instance, it is found that, under the equator, 60,535 vibrations occur in a mean day solar ; and that, when transported to London, the same pendulum only has 86,535 vibrations in the same time. This difference arises from the intensity of the force urging the pendulum downwards at the equator is less than at London as 86400 to 86535. Now, if we suppose that this difference is due to a mass of matter at the equator weighing 10,000 pounds exerting the same force on the pendulum as does 86400 pounds placed below it, then 10,031 of these same pounds, transported to London, would exert here (191). The experiments show that this is so. Hence, by means of accurate measure and minutest precaution to insure exercises in all accessible latitudes ; and their general application throughout the world, we shall obtain a true expression of the difference of gravity at the equator and poles. Now, it will not fail to be noticed by the reader that this experiment is not a direct experi- tion against the explanation here given of the fact by the earth's rotation, that this difference materially exceeds the fraction which may be accounted for by its motion. The difference by which this former material exceeds the latter is small in magnitude, but still far too large to be accounted for by any motion whatever. It is distinctly accounted for, and not to prove that this explanation is not valid, but to give a strict account of it. Of course it must be admitted that many persons are fond of a curious and instructive example of the indirect influence which mechanical causes often exercise, and of which they are not aware. The rotation of the earth gives rise to the conical figure of the centrifugal force produced in every body revolving about its axis. This force tends to modify its power of attraction on bodies placed at its surface, and thus gives rise to the difference in question. Here then we have the same cause exercising its effect in a direction not directly in question. The amount of the former CHAP. IV.] GRAVITY ON A SPHEROID. 124 A TREATISE ON ASTRONOMY. [CHAP. TH] is easily calculated, that of the latter with far more diffi- culty, by an intricate and profound application of geo- metry, whose steps we cannot proceed to trace in a work like this, but which may be found in the treatise of Sir (193). The weight of a body (considered as uni- methylated by a centrifugal force) is the effect of the earth's attractive power on its motion. This attractive power, more or less, consists, not in a tendency of all matter to any one particular point, but in a dispersion of every par- ticle of matter into space, so that no particle is at a dis- tance from any other particle equal to the radius of the sphere of which it is the centre, and not opposed to approach to, every other. The attraction of the earth, then, on any body placed on its surface, is not a simple action towards one point, but a series of attractions of all its parts. Now, it is evident, that if the earth were a perfect sphere, the situation excited by it on a body would be such that the body would move either in its equator or poles must be exactly alike, for the same reason of exact symmetry of the sphere in every di- rection. But since the earth is not perfectly spherical, and this symmetry or similitude of all its parts is not existing, the same result does not occur everywhere. A body placed on the equator will be exposed to a greater than a flattened ellipsoid, stand in a different geometrical rela- tion to the mass as a whole. This difference, without entering into the question whether it can be proved or not, draws with it a difference in its force of attraction on the two bodies. Cavaliere confronos this idea. It is a question which has been long debated and has never been treated with perfect clearness and precision by New- ton, Machanu, Clairaut, and many other eminent geome- ters; and it appears that they have all agreed in showing that owing to the elliptic form of the earth alone, and in depression of the centre of gravity, the attraction ought to increase in proportion as a body is going from the equator to the poles by almost exactly $\frac{1}{2}$th part ; which, toge- ther with $\frac{1}{2}$th due to the centrifugal force, make up the whole quantity required. (194) Another great geographical phenomenon, which owes its existence to the earth's rotation, is that of the tides. This subject requires our attention; on which we shall enter in a part of our argument. A diagram illustrating Newton's theory of tides. **CHAP. III.** THE TROG-STRIPS. rise from, 1st, the unequal exposure of the earth's sur- face to the sun's rays, by which it is unequally heated in different latitudes ; and, 2ndly, from that general law in the constitution of all fluids, in virtue of which they are always in motion, and consequently in a state of motion when not than when calm. These causes, combined with the earth's rotation from west to east, afford an easy and complete explanation of the phenomena under discussion. (195.) It is a matter of observed fact, of which we have no other explanation farther on, that the sun is con- sistently vertical over some one or other part of the surface between two parallels of latitude, at the same time re- gardless of the length of the equinoxes, and that the whole of that zone or belt of the earth's sur- face included between the tropics, at any given moment, is always in the same degree of altitude. The great altitude attained by the sun in its diurnal course, maintained at a much higher temperature than that of the poles. Now, the heat thus acquired by the earth's surface is communicated to the inundable air, which is continually being drawn up from the sea by the sun's warmth, and so keeps the air insensible on the rest of the globe. It is therefore, in obedience to the general laws of hydraulics, displaced towards the poles, being cooled by colder, and therefore heavier air, which glides in, on both sides, along the equator. This air being lighter than that which it displaces, thus raised above its due level, and unnas- tained by any lateral pressure, flows over as it were, from pole to pole, and is carried down into the ocean, towards the poles; which, being cooled in its course, and also sucked down to supply the deficiency in the extra- polar regions (186.) (186.) Since the earth revolves about an axis passing through the poles, the equatorial portion of its surface being more exposed to the sun's rays than any other part, therefore it receives more heat than any other part; and this is shown less in the proportion of the radius of the circles of latitude to which they correspond. But as the air, when relatively and apparently rest on any part of the earth's surface, is only so because reality it participates in its 2 126 A TREATISE ON ASTRONOMY. CHAP. III. motion of rotation proper to that part, it follows that when a mass of air near the poles is transferred to the regions near the equator by any impulses urging it direct- ly towards the latter, and being thus carried with it to- wards its new situation it must be found deficient in ro- tatory velocity, and therefore unable to keep up with the speed of the earth's motion at that latitude, and consequently Hence, the currents of air which set in towards the equator from the north and south must, as they glide along the surface of the earth, be continually drawn back and drag upon it in the direction opposite to the earth's rotation, i.e. from east to west. Thus these currents, which lie between the equator and the poles, and are nor- thely and southerly winds, acquire, from this cause, a relative direction towards the west, and assume the character of permanently westward currents (see fig. 33). (187.) Were any considerable masses of air to be inol- derly transferred from beyond the tropics to the equator, the difference of their velocities would produce a tempest of situations would be so great as to produce merely a wind, but a tempest of the most destructive violence. But this difference of velocity would only occur on both north and south is gradual, and all the while the earth is continually acting on, and by the friction of its surface accelerating every particle of air which approaches towards the equator to cease at any point; this cause would almost immediately communicate to it the defi- cient rotary velocity which it has acquired gradually with quited with the earth, and be at relative rest. We have only to call to mind the comparatively thinness of the conti- nent (see fig. 34), and the immense mass of the latter, compared with the former (which it exceeds at least 100,000,000 times), to appreciate how little space there is left for an exten- sive territory of the earth over the atmosphere immedi- ately incumbent on it, in point of motion. (188.) It is evident that when two currents of wind on both sides approach the equator, their easterly tendency must diminish. The lengths of the diurnal circles in- Ssee Coriolis, "La Mécanique de l'Air," "Voyage et Processe," p. 56; see also, vol. i., p. 162, where this is very distinctly marked out at an imme- diate distance from the equator. CHAPTER III CONCENTRATION OF THE TRADE-WINDS. 127 creases very slowly in the immediate vicinity of the equator, and for some distance on either side of it hardly change at all. Thus the friction of the surface has more time to act in accelerating the velocity of the air, bringing it up to its maximum value, than it has to retard it, whereby the relative size of the currents from east to west, which, on the other hand, is feeble, and, at length, no longer increases with latitude, is diminished by this cause. Arrived then, at the equator, the trades must be expected to lose their already considerable strength. But they will not do so uniformly throughout; some will meet and opposing, will mutually destroy each other, leaving only such portions of them as have been acted upon by the friction of the earth's surface. The remainder will continue to move in their former direction, but with less velocity than before. This is what actually happens (180). The result then, must be the production of two great tropical belts, in the northern of which a constant current flows from east to west; and in the southern one a similar current from west to east. These currents must prevail, while the winds in the equatorial belt, which separates the two former, should be comparatively feeble. They will therefore be produced by a greater friction in that belt than in any other part of the earth. All these consequences are agreeable to observed facts, and the system of aerial currents above described is capable of explaining exactly what is understood by the regular trade-winds. (208). The constant friction thus produced between the atmosphere and the earth's surface produces a rotation of mass (it may be objected) by degrees reduced and at length destroys the rotation of the whole mass. The circular motion of the earth is therefore generally impossible; and it is easy to see, in the present case, where and how the compensation takes place. The air which moves towards the north pole, owing to its greater velocity towards the poles, carries with it the rotatory velocity due to its equatorial situation into a higher latitude, where it becomes stationary; and when it moves southward or towards the equator, it travels northward or southward, it will gain continuously more and more on the surface of the earth in its diurnal motion, and assume consequently more and more a See for work not cited. 128 A TREATISE ON ASTRONOMY. [CHAP. III] exactly relative direction; and when at length $r$ returns to the surface, in its circulation, which it must do more or less in all cases, it will have traversed the whole circuit of the globe, and will have cut on it by its friction a powerful south-west wind in the northern hemisphere, and a north-west in the southern, and both winds will have been generated from it by the sun's rotation. We have here the origin of the south-west and westery gales so prevalent in our lati- tudes, and of the northerly gales in those of the North Atlantic, which are, in fact, nothing else than a part of the general system of the reaction of the trades, and of the general circulation of the atmosphere of the earth's surface. This is maintained under their actual (201.) In order to construct a map or model of the earth, such as may represent its true form, and land over its surface, the forms of the outlines of its continents and islands, the courses of its rivers and mountains, and other features of nature, with respect to each other, of those points which chiefly interest us, as centres of human habitation, or from other causes, it is necessary to know their distances from one another; but this is not sufficient to determine the situation of any proposed station on its surface. For this, two elements require to be known, the latitude and longitude of every point on the earth's surface; the poles or the equator, the latter, the meridians on which that distance is to be reckoned. To these, in strictness, should be added, his height above the sea level; but the * * * it is unnecessary to consider this last circumstance.* convenience alone requires that we should know how much elevation does the atmosphere on the great scale, we call its conden- sation. It seems worth inquiry whether hurricanes in tropical climates may ever occur without being accompanied by some other phenomenon? It is evident that they cannot be produced by any change in the weather weather before their relative velocity has been sufficiently reduced by de- cay; for if they could be produced by any change in the air-pressure the earth with that tremendous velocity which given them their despra- tive character, it would be impossible that they should ever have been given. Their course, generally speaking, is in opposition to the regular course which hurricanes usually take; and it is only because they are in Lociola's (504.) book that I have ventured to say anything on this subject. But by no means follows that this must always be so. The hurricane may arise from a sudden change in the atmos- phere of any local which is frequently cause might carry over it some violent disturbance. But this is not likely to happen very often; for if such a case should ever occur, at such a time as hurricanes are most intense on record might easily result from their condensation.—Author consideration of this had better be deferred, to avoid complicating the subject. (302.) The latitude of a station on a sphere would be merely the length of an arc of the meridian, intercepted between two parallels of latitude, which would have been reduced to degrees. (See art. 86.) But as the earth is elliptic, this mode of conceiving latitudes becomes inadequate; and we must therefore adopt some other defi- nition of latitude as a generalization of that property (art. 95), which affords the resultant mean of determining the inclination of any line drawn through the center of being independent of the figure of the earth, which, however, is not always neglected in practical applications. The latitude of a station, then, is the altitude of the elevated pole, and is, therefore, astronomical. It is thus seen how great is the necessity for ascertaining that important element. In consequence, it will be remembered that, to make a perfectly correct determination of latitude, it is necessary to ascertain equal differences of latitude are not represented by ex- actly equal intervals of surface. The latitude of a point on the equator of a sphere, then, is unity. It is otherwise with its longitudinal, whose exact de- termination is a matter of more difficulty. The reason why it is so difficult to determine accurately the longitude of any point on the surface of the earth, may be easily understood. For instance, suppose we are obliged in this case, as in the ease of the latitude, to resort to observations at different stations situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif- ference in the two cases--to observers stationed at sta- tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in the two cases--to observers stationed at sta. tions situated at different distances from each other; and let us consider what are the objects for our measurement; but with this dif. ference in 130 A TREATISE ON ASTRONOMY. [CHAP. III. by their horizons, and attain the same altitude. In the former case there is, in the latter there is not, any thing in the appearance of the heavens, which through a whole circle of stars, which are at different altitudes, shall appear to have the same locality in the observer. (204.) But no two observers, at different points of the earth's surface, can see at the same instant the same celestial hemisphere visible. Suppose, to fix our ideas, an observer stationed at a given point of the equator, and that he sees a star at his zenith. This star being a bright star to be in his zenith, and therefore on his meridian, he should be suddenly transported, in an instant of time, round one hundred and eighty degrees of longitude. It is evident that he will no longer have the same star ver- tically above him: it will now appear to him to be just rising or setting. And if this star rises or sets again comes to his zenith, z.c., before the earth's rotation from west to east carries him back again to the line joining the star with himself, he will not see it at his zenith. (205.) The difference of the cases, then, may be thus summed up: so long as we refer all observations to stations differing only in latitude, the same star comes to the meridian at the same time, but a different altitudes. In that of station B, for instance, it comes to the meridian at the same altitude, but at different times. Supposing, then, that an observer is in possession of any means by which he can determine accurately the time of known stars' transit across his meridian, he knows his longitude; or if he knows the difference between the times of transit of two stars having different latitudes, that of any other station, he knows their difference of longitudes. For instance, if A be a place at a certain mean moonrise, and that of B exactly one hour of sidereal period, or one twenty-fourth part of the earth's diurnal period, later, then the difference of longi- tudes between A and B is one half of a degree or less; if B is so much west of A. (206.) In order to a perfectly clear understanding of the principle on which the problem of finding the longi- tude by astronomical observations is resolved, the reader **CHAP. III.** **DETERMINATION OF LONGITUDES.** must learn to distinguish between time, in the abstract, as common to the whole universe, and therefore reckoned by the same clock throughout the world, and local time, which reckons at each particular place, from an epoch, or initial instant, determined by local convenience, and which varies with every locality. We have an example in what we have before defined as equinoctial time, which dates from an epoch determined by the equinoxes, and which varies with latitude. In reckoning, we have instances in every sidereal clock in an observatory, and in every town clock for common use, of a difference between the mean time and the sidereal clock, so that it shall indicate 0° 0' 0", when a certain point in the heavens, called the equinox, is on the meridian of the observer's place; but this is only a mean real time ; which is, therefore, entirely a local reckoning. It gives no information to say that an event happened at any particular moment of time; it does not even charac- terize the station to which the sidereal time meant appertains. Just so is it with mean or common time, whether it be civil or ecclesiastical. The mean noon, or the average of all the times throughout the day, when the sun is on the meridian of that particular place, is a mean real time; but it is not a true mean time, nor when we date any event by mean time, it is necessary to name the place, or particularize what mean time is meant to apply to. This is because mean time is absolute, and requires no such explanatory ad- dition. (37.) The astronomer sets and regulates his sidereal clock by observing the meridian passages of the more conspicuous and well known stars. Every one of these has its own period of passage through the heavens with respect to that imaginary point called the equinox, and by noting those times of passage he can ascertain when he knows that the equinox passed. At that moment his clock ought to have marked 0° 0' 0", and if it did not, he knows and can determine by the difference between that star and the assigned mean time how much his clock was behind or ahead. By this means he can ascertain whether his clock is correctly regu- lated to go twenty-four hours in one diurnal period, and 132 A TREATISE ON ASTRONOMY. [CHAP. III] if not, can ascertain and allow for its rate. Thus, although his clock may not, and indeed cannot, either be set cor- rectly, or be kept so long as he continues to observe (as they are technically termed), he can correct its inaccuracies, and ascertain the exact sidereal times corresponding to them, by observing the meridian passages of stars. This operation is called getting his local time. For simplicity of explanation, however, we shall suppose the clock a perfect one, and that it is always correctly set. But this is its error and rate applied at every moment it is consulted, and included in its indications. (208.) The observer, therefore, at distant sta- tions, A and B, each independently of the other, set out and regulate his clock to the true solar time of his station. When he has thus regulated it, let him go to take up without deranging its going, and set down by the side of the other, they would be found, on compar- ison, to differ only in their rates. This is because the time is, by the law occupied by the equinox, or by any star, in passing from the meridian of A to that of B; in other words, in passing from one meridian passage to another in sidereal hours, minutes, and seconds. (209.) A pendulum clock cannot be thus taken up and transposed without losing its proper arrangement, but a chronometer may. Suppose then, the observer at B to use a chronometer instead of a clock, say, by bodily transferring it from A to B; he will find no difference, direct comparison of sidereal times, and thus obtain his longitude from A. And even if he employ a clock, yet by comparing with the chronometer at B; for when transferring the latter instrument for comparison with the other clock, the same end will be accomplished, provided the group of stars be observed at both stations. (210.) Were chronometers perfect, nothing more com- plete and convenient than this mode of ascertaining dif- ferences of longitude could be devised. It is now very provided with such an instrument, and with a portable transit, or some equivalent method of determining the local time at each station; and by making observations from place to place, and observing the meridian passages of stars at each (taking care not to alter his chronome- CHAP. IIL.] LONGITUDES FOUND BY CHRONOMETERS. 133 ter, or let it run down), ascertain their differences of longi- tude with any required precision. In this case, the same time-keeper being used at every station, at one place only will be affected by the error of the chronometer, and it will be just so much顺德ial time in error as the dif- ference of longitudes of A and B is equivalent to: in other words, the difference of longitude between A and B is equal to the error of the time-keeper on the local time of B. If he travel westwards, then his chronometer will appear con- stantly too fast, and if he travel eastwards, then it will appear con- stantly too slow. For instance, he set out from A, when the equinox was on the meridian, or his chronometer at 0°, and in the latitude of 45° N., and arrived at B in 1 hour. At the moment of arrival there, his chronometer will again point to 0°, but the equinox will be, not on the meridian, but at 45° N., and therefore he has lost one hour more for its arrival at that of B. When it does arrive there, then his chronometer will point not to 0°, but to 45° N., and therefore he has gained one hour for its arrival at B. If he travel eastwards, the reverse will happen. In order to understand this proposition more clearly, attention is called to the following circumstances. The circum- nutation as above described, and constantly travelling westward to make the tour of the globe, and return eastward to make the same tour again. This is what we will happen: he will have lost a day in his reckoning of time. He will enter the day of his arrival in his chronometer at A, and leave it in his chronometer at B the next day. The reason is obvious. Days and nights are caused by the alternate appearance of the sun and star, and by the alternation of light and darkness which they bring to view them in succession. So many turns as he makes round the centre, so many days and nights will be passed. But if he travels westward from A to B, in the direction of its motion, he will, on his arrival, have really made one turn more round its centre; and if in that case he had been stationary at one point of its sur- face (as in the former case), then he would have witnessed one alteration of day and night; but since he has travelled westward he had trusted to the rotation of the earth alone to carry him round. M 134 A THEATRE ON ASTRONOMY. [CHAP. III. follows that a westward direction of his journey, by which he counteracts its rotation, will cause him to lose a day, and thus to arrive at the same place with the sun, with it to gain one. In the former case, all his days will be longer; in the latter, shorter than those of a stationary observer. This difference has been observed among circumnavigators. Hence, also, it must neces- sarily happen that distant settlements, on the same meri- dian, admit of different times of day, according as they have been civilized by settlers arriving in an eastward or in a westward direction,—circum- stances which may be very important when they come to communicate with each other. The only mode of correcting the ambiguity, and settling the disputes which arise from it, is by means of instruments having recourse to the equinoctial date, which can never be ambiguous. (215.) Fortunately for geography and navigation, the chronometer, though greatly and indeed wonderfully improved by the skill of modern artists, is yet far too imperfect for any practical purpose in this respect. Here even such an instrument may preserve its uniformity of rate for a few hours, or even days, yet in long absences from home it is liable to become so much more multiplied as to destroy all security of reliance on even the best. To a certain extent this may, indeed, be reme- died by keeping two chronometers together, but there is no such other method; but besides the expense and trouble, this is only a palliation of the evil—the great and fatal mental confusion which arises from the absence of longitude by time-keepers is liable. It becomes ne- cessary, therefore, to resort to other means of communi- cation from one place to another for determining the local time, or of propagating some principle situated, as a centre, its local time as a universal standard with which the time of every place may be compared; nor must it be at once compared, and thus the longitudes of all places be referred to the meridians of such central point. (216.) The most convenient method by which this object can be accomplished, when circum- stances admit of its adoption, is that by telegraphic signal- **CHAP. III. LONGITUDES DETERMINED BY SIGNALS.** Let A and B be two observatories, or other stations, pro- vided with clocks, and let them be situated at respective local times, and let us first suppose them visible from each other. Their clocks being regulated, and their errors known, we may consider them as at A, of some sudden and definite kind, such as the flash of gunpowder, the explosion of a rocket, the sudden ex- pansion of a balloon, or any other signal which may cause no mistake, and can be seen at great distances. The moment of the signal being made must be noted by each observer, and the time of its appearance observed by observing the transit of a star, or any astronomical phenomenon, and the error rate of the clock at each station being known, the difference between the local times will be found. Consequently, when the observers communicate their observations of the signal to each other, stating (owing to the nature of the signal) that it was seen at lightest they have been seen at the same absolute instant both by them, the difference of their local times will be found by adding their longitude to each other's. For example: At A a signal is observed to happen at 5° 0' 0" sid. time at A, as observed by applying the clock at A to the time shown by B. At B the same signal was seen at 7° 0' 0" sid. time at B, similarly observed from A. The difference between these times is 2° 0', by applying the clock at B to the time shown by A. (214.) The accuracy of the final determination may be increased by making and observing several signals at stations distant from each other, and taking means of all times, and the mean of all which is, of course, more to be depended on than the result of any single comparison. By this method it is possible to destroy almost all errors of clocks may be regarded as altogether destroyed. (215.) The distances at which signals are rendered visible are limited by atmospheric conditions and by the upposed country. Over sea the explosion of rockets may easily be seen at fifty or sixty miles; and in moun- tainous countries the flash of gunpowder in an open spot may be seen if a proper station be chosen for th
Let A and B be two observatories, or other stations, provided with clocks, and let them be situated at respective local times, and let us first suppose them visible from each other. Their clocks being regulated, and their errors known, we may consider them as at A, of some sudden and definite kind, such as the flash of gunpowder, the explosion of a rocket, the sudden expansion of a balloon, or any other signal which may cause no mistake, and can be seen at great distances.
The moment of the signal being made must be noted by each observer, and the time of its appearance observed by observing the transit of a star, or any astronomical phenomenon,
and the error rate of the clock at each station being known, the difference between the local times will be found.
Consequently, when the observers communicate their observations of the signal to each other, stating (owing to the nature of the signal) that it was seen at lightest they have been seen at the same absolute instant both by them,
the difference of their local times will be found by adding their longitude to each other's.
For example: At A a signal is observed to happen at 5° 0' 0" sid. time at A, as observed by applying the clock at A to the time shown by B.
At B the same signal was seen at 7° 0' 0" sid. time at B,
similarly observed from A. The difference between these times is 2° 0', by applying the clock at B to the time shown by A.
(214.) The accuracy of the final determination may be increased by making and observing several signals at stations distant from each other,
and taking means of all times,
and the mean of all which is,
of course,
more to be depended on than the result of any single comparison.
By this method it is possible to destroy almost all errors of clocks may be regarded as altogether destroyed.
(215.) The distances at which signals are rendered visible are limited by atmospheric conditions and by the upposed country.
Over sea the explosion of rockets may easily be seen at fifty or sixty miles;
and in mountainous countries the flash of gunpowder in an open spot may be seen if a proper station be chosen for th
A table describing how to determine longitude using signals from two observatories. 136 A TREATISE ON ASTRONOMY. [CHAP. III. exhibition, at much greater distances. The interval be- tween the stations of observation may also be increased by connecting them with intermediate points between them, but at an intermediate point, i. e., provided they are so se- parately placed, it is a matter of indifference where they are exactly situated. But if the distance between them be increased, the time required to make observations at each would be very limited, and the method is con- sequence of little use, but for the following ingenious contrivance, which has been successfully adopted and carried over any tract of country however difficult. (216.) This contrivance consists in establishing, be- tween the stations of observation, a line of stations whose longi- tude is to be ascertained, and at which the local time is observed, a chain of intermediate stations, alternately destined for observation and signal station, at A and Z to be the extreme stations. At B let a signal station be established, at which rockets, &c., are fired at stated in- tervals, and let C and D be other signal stations, one with a chronometer; at D another signal station; at E, an- other observer and chronometer; and so on till the whole line is occupied by stations so arranged, that the signals at B can be seen from A and C; those at D from B and C; and those at E from D. By this arrangement, and by the errors and rates of the clocks at A and Z ascertained by astronomical observation, let a signal be made at B, and observers at C and D observe it. Then subtracting from the difference between A's clock and C's chronometer be- comes known. After a short interval (five minutes for instance) another signal is made at B, and observed by C and E. Then will the difference between their respec- tive chronometers be determined; and the difference between the clocks at A and C becomes known. When this is as- certained, the difference between the clock A and chro- nometer E is therefore known. This, however, supposes A B C D E F Z line is occupied by stations so arranged, that the signals at B can be seen from A and C; those at D from B and C; and those at E from D. By this arrangement, and by the errors and rates of the clocks at A and Z ascertained by astronomical observation, let a signal be made at B, and observers at C and D observe it. Then subtracting from the difference between A's clock and C's chronometer be- **CHAP. III.** NATURAL SIGNALS. 197 that the intermediate character C has kept true scale real time or at least a known ratio to the interval between the signals. Now this interval is purposely made so very short, that no instrument of any pretension to cha- racteristic accuracy can detect any error in its lapse. Thus the time propagated from A to B may be considered as handled over, without gain or loss, by the signal sent from B to E, and then received, by the signal made at E, and observed at E and Z, the time so transmitted to E is forwarded on to Z; and thus all subsequent times are similarly calculated. But when the process may be repeated as often as is necessary to destroy error by a mean of results; and when the line of observation is extended over a great distance, with many points of signals, so as to allow each observer to note al- ternately those on either side, which is easily pre- vented by the use of a single line of observation, and to take the line at once, by which time is saved, and other ad- vantages obtained." In important cases the process is usually repeated three or four times. (217.) In place of artificial signals, natural ones, when they occur sufficiently definite for observation, may be equally useful. Thus we have seen that the passage of a singular meteor, called shooting stars, which may be observed, is usually very great; and as they are visible in the sky only for a few seconds, it is impossible to fix their great height at which they have been acertained to take place are visible over extensive regions of the earth's surface. The same difficulty arises in observing eclipses, with advantage, by previous consent and agreement be- tween distant observers to watch and note them. The eclipse of the sun (which is the most common) is of still greater extent and universality (being visible at once over a whole terrestrial hemisphere), as afforded by the eclipse of Jupiter, which is visible over all parts of the earth at one and the same time, when we come to treat of those bodies. Every such eclipse is an event which possesses one great advantage * * * The eclipse of the moon (which is less common than that of the sun) is also of great importance arising from a combination of all the observations, but it does not possess any advantage over that of the sun in respect to its duration. See Père de Laplace's "Traité de la Terre," by the author of this work. This idea was first suggested by Mr. H. de Molyneux. M 2 138 A TREATISE ON ASTRONOMY. [CHAP. III] in its applicability to the purpose in question, viz. that the time of its happening, at any fixed station, such as Greenwich, can be predicted from a long course of pre- vious observations, and that this prediction is sufficiently precise and certain, to stand in the place of a corresponding obser- vation. Now, it is impossible to say whether, however, who shall have observed one or more of these collected, and made use of them, will ever find occasion for a confirmation with Greenwich, to inform him at what moment the eclipse took place there, may use the predicted Greenwich time instead, and thereby at once, and on the spot, ascertain the truth of it. The need of ascertaining longitudes is, however, as we will presently appear, not susceptible of great exactness, and should only be sought after by means of the geographer. The nature of the observation also is such that it cannot be made at sea; so that, however useful to the geographer, it is of no use to him at sea. (210.) But such phenomena as these are of only occa- sional occurrence; and they are those which when cut off from all communication with any fixed station are inad- pensable to possess some means of determining longi- tudes, on which not only the geographer may rely for a knowledge of his own position, but also for that of one on land in remote regions, but on which the navigator can securely strike, at every instant of his adventurous course, the lives and fortunes of himself and his countrymen. Such a mode is afforded by LUNAR OBSERVATIONS. Though we have no means of predicting the time of the moon's motion, this will not prevent us from giving her the expository character of the lunary calendar; on the contrary, it will be highly convenient to do so, since by this course we shall have to deal with the naked principles, apart from all the peculiar sources of difficulty which attend their application to particular cases; but which are, in fact, completely extraneous to the principle of its application to the problem of the longi- tudes, which is quite elementary. (220.) If there were in the heavens a clock furnished **CHAP. III.] LUNAR METHOD OF LONGITUDES.** with a dish-pale and hands, which always marked Greenwich time, the longitude of any station would be at once known, by comparing it with this clock. Now, the offices of the dish-pale and hands of a clock are two points on the surface of the earth, whose position is known; the latter, by passing over all among those marks, moves in one direction, and the former in another; so that their motion is uniform, or what time has elapsed since a certain moment when it stood at one particular spot. (21.) In a similar manner, we may find the longitude of any point on the earth's surface, by observing the sun's equinoctial altitude at different times of the day, and finding its mean value; for it will be found that the sun's equinoctial altitude varies uniformly with the latitude of the place observed. This method is very useful in navigation, because it enables us to ascertain the longitude of any place without having recourse to any other means than the sun's altitude. (22.) The visible surface of the sterna heavens is the dish-pale of our clock; the stars are the fixed marks disposed upon it; and the hands are the hands of our clock. Now, let us suppose that we have a dish-pale and hands, which, with a motion that is superficially considered, seem uniform, but which, when carefully examined, exhibit a most remarkable peculiarity. We shall observe laws of astonishing complexity and intricacy in results, presenting beautifully simple in principle and design, proceeding from causes which are not only unknown to us, but over and hinging, or as it is called, oscillating, some, and gliding beside and between others; and whose position among them can, at any moment when it is visible, be 140 A TREATISE ON ASTRONOMY. [CHAP. III] exactly measured by the help of a sextant, just as we might measure the place of our clock-hand among the marks on its dial-plate with a pair of compasses, and hence, by the same method, we may measure the moon's motion, deduce the time. That the moon does so among the stars, while the latter hold constantly, with respect to each other, at a given distance, is the mo- nument of a few nights, or even hours, will satisfy the com- menting student, and this is all that at present we require. (283.) The next point which I propose to make clear is to make our analogy complete. Suppose the hands of our clock, instead of moving quite close to the dial-plate, were constantly at some distance from it, and yet always of it. Unless, then, in viewing it, we kept our eye just in the line of our centre, we should not see them exactly between the lines of the marks upon the dial-plate. And if we were either unaware of this cause of optical change of place, this parallel--or negligent in not taking it into account--we should be very much mistaken in reading the time, by referring the hand to wrong mark, or incorrectly appreciating its distance from the right. But this is not so difficult as it appears; for in every case, when we had occasion to observe the time, the exact position of the eye, there would be no difficulty in ascertaining whether or not this was a case of neglect of this cause of apparent displacement. Now, this is in just what obtains with the apparent motion of the moon among the stars. For though she is always near us (com- paratively near to the earth)--the latter immensely dis- tant); and in consequence of our not occupying the cen- tre of the earth's sphere--which is always changing and constantly changing place, there arises a parallelism, which displaces the moon apparently among the stars, and must always be considered as such until the true place she would occupy if seen from the centre. (284.) Such a clock as we have described might, no doubt, be made to move with any degree of accuracy one only one, and if incredible estimates were at stake on a perfect knowledge of time, we should judicious regard it as most precious, and think no pains ill bestowed in stu- dying the laws of its movements, or in furnishing the CHAP. III.] LUNAR METHOD OF LONGITUDES. 141 means of reading it correctly. Such is the parallel we are drawing, is the lunar theory, whose object is to reduce to regularity the indications of this strangely irregular body. The moon, which is always seen on one hand, and with absolutely certainly, revolves about among the stars, at every hour, minute, and second, in every direction, and in every place, so that its whole surface would be seen from the earth's centre, and still be seen from every accessible point of its surface; and such is the case with the sun also. But the moon has no angular distances from all these principal and consequent usures which lie in its course, as seen from the earth's centre, but only those which are given by the most exact and precision in almanacs published under national control. No sooner does an observer, in any part of the world, see the moon rise than he can determine from any one of those standard stars (whose places in the heavens have been ascertained for the purpose with great accuracy) whether he is in longitude east or west, or informed that comparison of his local time with the local times of every observatory in the world, which enables him to ascertain the difference of latitude between himself and all of them. (225.) The latitude by means of number of degrees of longitude of the earth's surface may be ascertained by the methods above described; and by thus laying down a sufficient number of principal points, and filling in the intermediate ones by interpolation, maps or plans of counties can be constructed, the outlines of continents and oceans ascertained, the outlines of countries and towns referred to their proper localities. In practice, however, it is found simpler, and more accurate, to use triangles. By means of great triangles, the angles of which are stations conspicuously visible from each other. Of these triangles, the sides are measured by means of a quadrant or doltie, with the exception of one side only of one triangle, which is called a base, and which is measured with even greater care than any other line in this operation common. This base is of moderate extent, rarely exceeding six or seven miles, and purposely selected in a 143 A TREATISE ON ASTRONOMY. [CHAP. III. perfectly horizontal plane, otherwise conveniently adapt- ed for purposes of measurement. Its length between its two extremities (which may be either mountains or plains let into massive blocks of stone, and which are, or at least ought to be, in all cases preserved with almost religious care) is measured, and its position with respect to the parallels of latitude and meridians of longitude is deter- mined, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- mined, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate, is then measured, with every precaution to insure precision, and its position with respect to the parallels of latitude and meridians of longitude is deter- minate. The annexed figure represents such a chain of triangles. AB is the base; O1C1 stations visible from both its extremities (one of which. O1 we will suppose to be a national observatory), within which it has a principal object (the other extremity being connected by a line com- pletely connected as possible); D1E1F1G1H1K1 other stations; remarkable points in the country; by whose connections we shall determine their positions; these points were arranged in a network of triangles. Now it is evident that the angles of the triangle A1B1C1 being observed; one or two sides being known; or else one angle being known; BC may be calculated by the rules of trigonometry; but when each side or each angle AC or BC becomes in turn a base capable by itself or by means only by itself alone; it follows that all angles. For instance; the angles of the triangles ACQ1 BCF1 being known by observation; their sides AC1BC1 being known; or else one angle being known; CQ1BF1 being known; CG1CF1 being known; and the included angle GCF1 may be calculated; so that The greatest mistake can be in the fork-bone between arcs real and fictitious ones. See [Notebook], p. 580. *The greatest mistake can be in the fork-bone between arcs real CORRECTION FOR THE EARTH'S SPHERICITY. 143 On this may all the stations be accurately determined and laid down, and as this process may be carried on to any extent, a map of the whole country may be thus con- structed, which will give a very accurate idea of the country (227). Now, on this process there are two important remarks to be made. The first is, that it is necessary to take into account the inequalities of the earth's surface, triangles formed from any very great inequality in their an- gles. For instance, the triangle K'WF would be a very imperfect one, because the angle W is so great, owing to its rotation about the axis of the earth. The angles at B and K, because the angle F being very acute, a small error in the angle K would produce a great one in the angle B. Hence, it is evident that such triangles, therefore, must be avoided. But if this be at- tended to, the accuracy of the determination of the octa- hedral pyramid would be greatly increased. This could be obtained by actual measurement (were it practicable); and, therefore, as we recede from the base on all sides we shall find that the angles become smaller and bases the sides of much larger triangles, such as GF, GH, IK', &c.; by which means the next step of the operation can be easily made. On this plan, with a small scale, and embrace far greater intervals, than it would have been safe to do (for the above reason) in the imme- diate neighbourhood of London. It is now easy to divide the whole face of a country into great trian- gles of from 30 to 100 miles in their sides (according to the latitude), and when once they are well deter- mined, may be afterwards, by a second series of subdivi- sions operations, broken up into smaller triangles of equal size. In this order, till the final formu- lating in is brought within the limits of personal survey and actual measurement. A map is constructed, with any required degree of detail. (228.) The next remark we have to make is, that all the triangles formed from any great inequalities of the surface place a "spiral" existing on the surface of a sphere; or rather, to speak correctly, of an ellipsoid. In very small triangles, of six inches or less in their sides, this may be neglected; but differences are imperceptible; but in no other case it must be taken into consideration. 144 A TREATISE ON ASTRONOMY. [CHAP. III] It is evident that, as every object used for pointing the telescope of a theodolite has some certain elevation, not only above the horizon, but also above the earth's surface; and moreover, these elevations differ in every instance, a re- duction to the horizons of all the measured angles would appear to be necessary, which is not only inconvenient, of the theodolite (art. 150), which is nothing more than an azimuth and zenithal instrument, this reduction is made in the very act of reading. Let E be the centre of the earth; A, B, C, the points on its spheri- cal surface, at which are placed the two stations P, Q, in a country referred to radii E, A, EBD, EBC. The point P will be stationed at A, the axis of its horizontal circle will point to E the horizon, and the vertical circle will point to N, will be a tangent to the sphere at M, intersecting the ra- dius EA at N. This line MN is always perpendicular to the spherical surface. The telescope of the theodolite is directed towards P, and Q; but the readings off its azimuth circle give-and the sagittae PAG between the directions of the two points P and Q are equal to each other-are seen from A; but the azimuthal angle MAN, which is the measure of the angle A of the spherical triangle ABC. Hence it appears that the sum of three angles of any one of the three observed angles of any of the great triangles in geodesical observations is always found to be rather more than 180°; and this excess is called by astronomers "the spherical excess," because it is supposed that this excess be exactly 180°; and this excess, which is called the spherical excess, is so far from being a proof of incorrect- ness in our observations that it offers us at once another palpable proof of the earth's sphericity. (art. 151) In this way, then, of conceiving the subject of a trigonometrical survey, when the spherical form of the earth is taken into consideration, is to regard the net- CHAP. III.] PROJECTIONS OF THE SPHERE. 143 work of triangles with which the country is covered, as the triangles of a net, and by which we can measure the curvature of the earth. The theodolite gives us the true measures of the angles included by the planes of these pyramids, and by adding to each other all the angles at the level of the sea intersects them in an assembly of spherical triangles, above whose angles, in the ratio pro- longed to infinity, we have always a right angle, by superficial inequalities of mountain and valley. The ope- rare calculations of spherical trigonometry which this con- struction affords, and which are necessary for the de- ductions of a survey, are dispensed with in practice by a very simple and easy rule, called the rule for the spheri- cal triangle, or "the law of sines," which is very useful in geometry.* If we would take into account the ellip- ticity of the earth, it may also be done by approximate processes of calculation, but they are too laborious to dwell upon in a work like the present. (280.) Whatever process of calculation we adopt, the result will be that we shall find two triangles, one for each hemisphere, and the consequent determination of the geo- graphical latitude and longitude of every station observed. Thus we shall have to consider three countries or four continents; to lay down the outlines of continents and islands; the courses of rivers; the direction of mountain ridges; and so on. But it is impossible to give all those details which, as they belong to physical and statistical geography, are not necessary for our purpose. We need not here dilate on it. A few words, however, will be necessary respecting maps, which are used as well in astronomy as in geography. (291.) A map is nothing more than a representation upon a plane, of some portion of the surface of a sphere, and it is only when this portion is sufficiently large to be re- pressed, whether they be continuous outlines or points. Now, as a spherical surfacel can by no contrivance be extended or projected into a plane, without unlimi- *Laurens's Trigonometry, p. 94. Woodhouse's Atlas, p. 168. Ed. t N t We here neglect the ellipticity of the earth, which, for such pur- pose as imagining, is so trifling as has any material influence. 140 A TREATISE ON ASTRONOMY. CHAP. III. enlargement or contraction of some parts in proportion to others; and as the system adopted in so extending or projecting it will decide what part shall be enlarged or relatively contracted, we may suppose that when large portions of the sphere are to be mapped down, a great difference in their representations may subsist, which would not be properly represented (232). The projections chiefly used in maps are the orthographic, stereographic, and Mercator's. In the orthographic projection, the whole surface of the sphere is retraced on a horizontal plane of base, by a perpendicular let fall on it, so that the representation of the hemisphere is made as if it were a flat plate, and as it would actually appear to an eye placed at an infinite distance from it. This is seen from the annexed figure, that in this projection only the meridians are represented, and all other portions of their true form, while all the exterior is more and more distorted and crowded together as we approach the edges of the globe. The stereographic projection, though very good for small portions of the globe, is of little service for large ones. (233.) The stereographic projection is in great men- sure free from this defect. To understand this projection, A diagram showing a stereographic projection of a sphere. The sphere is divided into four quadrants, each with a central point labeled "C". The central points are connected to the edge of the sphere by lines labeled "A", "B", "D", and "E". The lines are drawn at equal intervals around the circumference of the sphere. A diagram showing a Mercator's projection of a sphere. The sphere is divided into four quadrants, each with a central point labeled "C". The central points are connected to the edge of the sphere by lines labeled "A", "B", "D", and "E". The lines are drawn at equal intervals around the circumference of the sphere. **CHAP. III.** **MERCATOR'S PROJECTION.** 147 We must conceive an eye to be placed at E, one extremity of a diameter, EUB, of the sphere, and to view the circumference of the sphere, which is represented by P, is referred to the diametral plane ADF, perpendicular to EB by the visual line PME. The stereographic projection represents the surface of the sphere by a repre- sentation of its concavity on a diametral plane; and, as such, it possesses some singularly elegant geometrical properties, which we shall now examine more particularly. (281.) And first, then, all circles on the sphere are represented by circles in the projection. Thus the circle X1 projected into z. Only great circles passing through the vertex B are projected into straight lines; inverting the direction of the BP will invert them into CA. Silly. Every very small triangle, GHK, on the sphere, is represented by a very small triangle, gkl, in the projec- tion. This is a very valuable property; for it insures a general similarity of appearance in the map to the reality in nature. For example, if we take any portion of the sphere in a single map, without any violent distortion of the configurations on the surface from their real forms. As we have seen before, when we project a part of a hemisphere are unduly crowded together; in the stereo- graphic, their projected dimensions are, on the contrary, somewhat reduced. (235.) Both these projections may be considered na- tural ones, inasmuch as they are really perspective re- A diagram showing a sphere with a diameter AB and a point E on it. A circle is drawn around E and intersects AB at points F and G. The center of this circle is labeled P. A line segment PE connects E to P. Another line segment PF connects P to F. A line segment PG connects P to G. A line segment PE' connects E' to P'. A line segment PF' connects P' to F'. A line segment PG' connects P' to G'. A line segment PE'' connects E'' to P''. A line segment PF'' connects P'' to F''. A line segment PG'' connects P'' to G''. A line segment PE''' connects E''' to P'''. A line segment PF''' connects P''' to F'''. A line segment PG''' connects P''' to G'''. A line segment PE'''' connects E'''' to P''''. A line segment PF'''' connects P'''' to F''''. A line segment PG'''' connects P'''' to G''''. A line segment PE'''', connecting E'''', to P'''', connects P'''', to F'''', and P'''', to G'''', respectively. presentations of the surface on a plane. Mercator's is entirely an artificial one, representing the sphere as it 142 A TREATISE ON ASTRONOMY. LURAF. III. cannot be seen from any one point, but as it might be seen by an eye at that place, and not by another. In it, the degrees of longitude, and those of latitude, bear always to each other their due proportion: the equator being a straight line, and the meridians straight lines at right angles to it, as in the figure. Altogether, the general character of maps is such, that they represent the whole globe, as what would be produced by referring every point in the globe to a circumferencing cylinder, by lines drawn from the centre of the globe to its surface, and parallel to it. Like the stereographic projection, it gives a true repre- sentation, so far as, for any particular small part, but greater portions of the globe are represented with- out the polar portions in particular being extremely en- larged; and the whole map, even of a single hemisphere, are better than any other known. (236.) We shall not, of course, enter here into any geographical detail; but one result of maritime discovery on the subject of the shape of the earth will be very fit for mention as an astronomical feature. When the con- tinent and seas are laid down on a globe (and since the discoveries of Captain Cook and others) we find that in- sects of land remain unknown, except perhaps at the south pole); we find that it is possible so to divide the globe that all parts of it may be equally distant from all the land; and the other being almost entirely sea. It is a fact, not a little interesting to Englishmen, and com- bined with this fact is another which is of great im- portance; the Atlantic, not a little explanatory of our com- mercial eminence, that London occupies nearly the centre of the circumference of the globe. This is a remarkable thing; the fact of this divisibility of the globe into an ocean and a terrestrial hemisphere is important, as demonstra- tive of the equality of density between all parts of the solid material of the two hemispheres. Considering the whole mass of land and water as in a state of equili- brium, let us suppose that we could separate them in- necessity be brought; not, of course, that we mean to assert it to be lighter than water; but, as compared with the whole globe, to a less degree heavier than CHAP. III.] DETERMINATION OF HEIGHTS. 149 that fluid. We have to deduce to draw from these premises their own conclusions (and we think them ob- vious enough) as to the internal constitution of the globe, and the manner in which the mountains and the continents at their actual elevation; but in any future investigations which may have for their object to explain the causes of the phenomena of the earth's surface, what the hypothesis of an exact elliptic figure would require, this, as a general fact, ought not to be lost sight of. (1.) The height of every point on the surface of the earth is not equal to its distance from the centre of the earth. This is evident from the following considerations: The latter object is attainable (with whatever difficulty and however slowly) by direct sounding; the former by two methods, viz., by observing the differences of level at all the stations of a survey; the other, by the use of the baro- meter, which measures the difference between the pressure at that of the sounding line. In both cases we measure the distance of the point whose level we would know from the sea-level, and then subtracting this distance from our case it is an ocean of water; in the other, of air. In the one case our sounding line is real and tangible ; in the other it is imaginary. But in both cases we must consider that the column of quid-silver or the superincumbent air is ca- pable of considering itself as a solid body; instead of air, the earth and ocean were covered with oil, and that human life could subsist under such circumstances. Let ABCDE be a A diagram showing points A, B, C, D, E connected by lines. continent, of which the portion ABC projects above the water, but is covered by the oil, which also floats at an S 2 150 A TREATISE ON ASTRONOMY. [CHAP. III.] uniform depth on the whole ocean. Then if we would know the depth of my point D below the sea level, we let down a plummet from F. But if we would know the height of my point B above the sea level, we must set up a float from B to the surface of the oil; and having done the same at C, point at the sea level, the difference of the two heights will be the depth of the oil. (239.) Now, though the atmosphere differs from oil in not having a positive surface equally definite, and in not being capable of being reduced to a fluid substance by such a use, yet it possesses all the properties of a fluid really essential to the purpose in view, and this is per- petual; that is, its surface is always equal to that of a strata of equal density are parallel to the surface of equi- lirium, or to what would be the surface of the sea, if prolonged to infinity. This is evident from the fact that any of them has all the characters of a definite surface to measure from, provided it can be ascertained and identifi- ed. Now, when we consider that mercury in a barometer is supported, informs us at once how much of the atmosphere is incumbent on B, or, in other words, how high above the level of the earth's atmosphere (indicated by its density) B is situated; whence we are enabled finally to conclude, by mechanical reasoning alone, that the whole globe is covered with a degree of density so to be found over the whole surface of the globe. Such is the principle of the application of the barometer to astronomy. For details, see Table 1. For de- tails, the reader is referred to other works.** (240.) Possessed of a knowledge of the heights of stations above sea-level, and knowing also their depths at the same latitude by level lines, the lowest of which will be the outline of the sea-coast; and the rest will mark out the successions of mountains and valleys. Thus we learn by this method to rise by regular and equal ascensions of level over the whole world, till the highest mountains were subsumed under seas; and then to descend through series of depressions in their Annamite; and Mr. Bully's Collection of Astrono- mical Tables on Formulas. * See Cal. Cyc., Partitum I. † Ros. Astronomic Physique, vol. II. ‡ For tables, see the work of Blagdon on "The Level Lines," &c.; also Mr. Bully's Collection of Astronomical Tables on Formulas. **CHAIR. IV.** **CRANIOGRAPHY.** 151 of hills are determined by their property of intersecting all these level lines at right angles, and being, subject to dust condition, the shortest and longest courses respec- tively parallel to the horizon and perpendicular to it. The former constitute the water-courses of a country ; the latter divide it into drainage basins : and thus origi- nates the division of the land into watersheds and basins, on which the distribution, limits, and peculiarities of hu- man communities are in great measure dependent. CHAPTER IV. --- **OF ELLINOGRAPHY.** Construction of celestial Maps and Globes by Observations of right As- sociations of Objects in the heavens, and by the use of the Equinoctial and Vernal Points, and ephemeris-Of the Constellations-Natural Regions in the Heavens and on the Earth-Of the Equinoctial and Vernal Points-Of the Equinoxes and Longitudes-Precession of the Equinoxes-Nonionation-Abbreviation of Names of Planets (241). The determination of the relative situations of objects in the heavens, and the construction of maps and globes which shall truly represent their mutual configu- rations, may be effected with great accuracy, when we have a more precise numerical record of the positions of each, as it is a task at once simpler and less laborious than that by which we have hitherto been occupied. Every star in the great constellation which appears to revolve above us, constitutes, so to speak, a celestial sta- tionary point, from which we can describe every part of the earth, triangle, by measuring with proper instruments their angular distances from each other, which, deleted on paper, will form a map of the country. We may lay down on charts, as we would the towns and villages of a country; and this without moving from our place, at least for a considerable time. (242). Great exactness might, no doubt, be attained by this means, and excellent celestial charts constructed ; but there is no for simpler matter, and at the same time infinitely more accurate course had open to us, if 152 A TREATISE ON ASTRONOMY. [CHAP. IV.] we take advantage of the earth's rotation on its axis, and by observing each celestial object as it passes our meridi- an, refer it separately and independently to the celesta- l equator, we shall have a perfect knowledge of the effect of an imaginary sphere, which may be conceived to re- volve with it, and on which it may be considered as pro- jected. (243.) The right ascension and declination of a point in the heavens conspicious to the longitude and latitude of a station, when observed at the same time that the point on the celestial sphere is determined, when the former elements are known, is such as that of a map on a map, by knowing the latter. The right ascension of any star, or other body of meridional observation possesses over that of incomming- from star to star, nor, then, first in every star is observed, but only in those stars which are seen at the best seen and least displaced by reflection. 244., that the instruments required (the transit and mural circle) are the same as those used in determining the right ascension of any used by astronomers. 245., that all the observa- tions can be made systematically, in regular succession, and will equal advances in the progress of astronomy, by ques- tion about advantageous or disadvantageous triangles, etc. And, lastly, that, by adopting this course, the very quantity of observations required will be so small as to be calculable by long and tedious operations of spherical trigonometry, and which are essential to the formation of a catalogue, you need not make more than one hundred thousand. It is almost needless to state, then, that this is the course adop- ted by astronomers. (246.) To determine the right ascension of a celestial object, all that is necessary to observe the moment of its meridian passage with a transit instrument, by a clock regulated by the sun's shadow, and to measure by ap- plying its known error and rate. The rate may be ob- tained by repeated observations of the same star at its successive passages through the meridian. This method re- quires a knowledge of the equinoxes, or initial point from which all right ascensions in the heavens reckon, as lon- gitudes do on the earth from a fixed meridian. (247.) The nature of this point will be explained pre **CHAP. IV.** RIGHT ASCENSIONS AND DECLINATIONS. scindly; but for the purposes of uranography, in so far as they concern only the actual configurations of the stars inter se, a knowledge of the equinox is not necessary. The right ascensions of the stars, being their longitu- densions, is purely artificial, and a matter of convenience; but as on the earth, any station (as a national observa- tory) may be selected as the point of reference, in uranography, any conspicuous star may be selected as an initial point from which all other stars may be de- termined. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be de- duced. In practice, these observations are made by ob- serving differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, these observations are made by observing differences at tercera of time, the situation of all others may be deduced. In practice, 153 the right ascensions and declinations have been determined with great accuracy; and it has been found that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one another; and that they vary very little from one other 154 A TREATISE ON ASTRONOMY. CHAP. IV. carrying sun, moon, and stars along in its diurnal mo- tion. If not, we must dismiss all such notions, and inquire into the nature of the phenomena which occur, with a view to discovering the laws of its peculiar mo- tions, and whether any and what other connexion subsists between them. (248.) So far is this, however, from being the case, that observation, even of the most curious nature, are sufficiently confirmed by experience to show that the bodies, and those the most conspicuous, are in a state of continual change of place among the rest. In the case of the sun and moon, this is very evident; but it is remarkable, that its alteration of situation with respect to such bright stars as may happen to be near it, may be noticed only at certain times of the year. For instance, two successive nights, cannot fail to strike the most curi- ous observer. With the sun, too, the change of place among the stars is so slow, that it is not easy to perceive the invisibility of stars to the naked eye in the day-time; it is not so readily recognised, and requires either the use of telescopes or a long series of observations. But there is a longer continuance of observation to be struck with it. Nevertheless, it is only necessary to call to mind its greatest effects on our daily life, to see how remarkable it is. The fact that the stars which come into view at night vary with the season of the year, to perceive that a great change occurs in their situation with respect to us is an immediate stimulus with respect to all the stars. Besides the sun and moon, too, there are several other bodies, called planets; and these also have their places among the stars. Only one of these planets can be seen at once by the naked eye only as the largest and most brilliant stars, and which offer the same phenomenon of a constant change of place among them. These are Mercury and Venus. They are two bodies from which, each of them as we may refer them to as mercurial, and some in longer, some in shorter periods, making, like the sun and moon, a complete revolution every twenty-four hours. (249.) These, however, are exceptions to the general rule. The immense multitude of the stars which are distributed through space do not undergo any appreciable motion, which preserves, not only to the eye of the casual observer, but to the nice examination of the astronomer **CHAP. IV.]** FIXED AND ECLATANT STARS. 155 a uniformity of aspect which, when contrasted with the perpetual change in the configurations of the sun, moon, and stars, appears to be a peculiarity of nature. It is not, indeed, that, by the refinement of exact meas- urements prosecuted from age to age, some small change has been detected in the aspect of the stars; and no to terrestrial cause, cannot be detected in some of them—such as are called, in astronomy, the proper mutual motions of the planets; but that these motions, that their accumulated amount (even in those stars for which they are greatest) has been insufficient, in the course of ages, to produce any perceptible change in any obvious or material alteration in the appearance of the stars. (250.) This circumstance, then, establishes a broad distinction of the heavenly bodies into two great classes; and although this distinction may have been observed (such observations continued for many years) no change of mutual situation can be detected; and the errant, or wandering (as they are called), stars, though they appear to move sun, moon, and planets, as well as the singular class of bodies termed comets, in whose apparent places among the stars they appear to move at different times of the day, or even hours, is sufficient to establish an indisputa- ble alternation. (251.) Photography, then, as it concerns the fixed celestial bodies (or, as they are usually called, the fixed stars), is reduced to a simple marking down of their re- spective positions on a plate. The reason why this is so, that in this globe, its due place in the great constellations of the stars, of the pole of the heavens, or the vanishing point of all lines drawn from it to any other point in the horizon and place of the equinox; points and circles there, which though artificial, and having reference entirely to the observer's position on earth; yet being such that which the earth's axis may be liable, are yet so con- venient in practice, that they have obtained an admission (viz., that other than artificial points and lines exist) in all globes and plumbines. The reader, however, will take care to keep them separate in his mind, and to REVERE & WANDERER 156 A TREATISE ON ASTRONOMY. [CHAP. IV.] familiarize himself with the ideas rendered of stars or more celestial globes, supposed and fitting on each other, on one of which - a real one - are inscribed the stars; on the others those imaginary points, lines, and circles which, according to his own judgment, he may invent, to aid their calculations; and to accustom himself to conceive in the latter, or artificial, spheres a capability of being made to represent all the stars that exist in the universe; other so; thus, should experience demonstrate (as it does) that these artificial points and lines are brought, by a sort of coincidence, into such and such particular variations (as they are called), to coincide, at very dis- tant intervals of time, with different stars, he may not be imperturbed by this change, but have reason to correct in his notions. (23d.) Of course no great shock of those en- counters will ensue between men and monsters, which are usually scrawled over celestial globes and maps, and serve, in a rude and barbarous way, to enable us to talk of groups of stars. For instance, the constellation which, though absurd or pernicious in its origin, have obtained a certainty from which it would be difficult, and perhaps impossible, to remove them. The figures have really (as some have) no slight resemblance to the figures called up by the mind by a sort of the most splendid imagination; they are a sort of con- sistence; but as they are otherwise entirely arbitrary, and correspond to no natural combinations or groupings of the stars themselves; therefore they light up our thoughts and disregard them; except for briefly naming remarkable stars, as a Louis XIV., &c., &c., or for making use of Greek names for certain constellations. The reader will find them on any celestial chart or globe, and may compare them with the heavens, and there learn for himself their position. *This diagram is neither apparent nor concealed. The constella- tions seem to have been drawn purposely named and delineated in some such manner as to make them appear as if they were real objects seen twice through bad and confused state of the heavens where no me- ans can be found to distinguish them from the stars themselves. I am aware that some persons consider this a mistake; but I think it is not so. A better system of con- stellations might have been a material help as an artificial history.* A diagram showing various constellations on a celestial globe. **CHAP. IV.** THE MILKY WAY.—THE ZODIAC. 157 (255.) There are not wanting, however, natural dis- tracts in the heavens, which offer great peculiarities of character, and strike every observer; such is the silky sway of the Milky Way, which appears to be spread over evening, all across the sky, from horizon to horizon, and which, when traced with diligence, and mapped out on paper, forms a very beautiful figure, resembling the whole sphere, almost in a great circle, which is neither an hour circle, nor coincident with any other of our astronomical circles. This is a very remarkable object of course, sending off a kind of branch, which unites again with the main body, after remaining distinct for about 100 degrees of arc. The Milky Way is not observed, from the earliest ages, the same relative situation among the stars ; and, when examined through powerful tele- scopes, it is found to be composed of a multitude of stars scattered by turbulence, like glistening dust, on the black ground of the general heavens. (256.) It is evident that the course of the zodiac is not from any thing peculiar in its own com- position, but from its being the axis within which the apparent motion of the planets takes place; and per- planets are connected. To trace the path of any one of these, it is only necessary to ascertain, by continued observa- tions, whether it be moving northward or southward; upon our map or sphere in sufficient manner to form a series, not too far displaced, to connect them by lines from one point to another; and then to observe their posi- tion at sea by mapping down its place from day to day. Now, this apparent motion is not uniform; it is an equi- circular path, or track, of the sun on the surface of the heu- mens, is no other than an exact great circle of the sphere whereof the earth is a part; and this great circle is equatorial at an angle of about 23° 27', intersecting it at two opposite points, called the equinoctial points, or equinoxes; and passing through those points are marked by the epiphysal vernal and autumnal; the vernal being that at which the sun crosses the equatorial from south to north; and the autumnal that at which it passes into and enters the southern hemisphere. Secondly, that the moon and all the planets pursue paths which, in like Q 158 A TREATISE ON ASTRONOMY. CHAP. IV. manner, encircle the whole heavens, but are not, like that of the sun, great circles exactly returning into their selves at the same time, but are composed of many parts, of much complexity, and described with very unequal velocities in their different parts. They have all, how- ever, the same period of revolution, and therefore their motions is the same with that of the sun, viz. from west to east, that is to say, the contrary to that in which both they move. The earth also moves in this manner, motion of the heavens; and moreover, that they never deviate far from the ecliptic on either side, crossing and recrossing it at equal distances from each other, and confining themselves within a zone, or belt (the zodiac already spoken of), extending 6° on either side of the ecliptic. (255.) It would manifestly be useless to map down on gloves or charts the apparent paths of any two bodies which do not cross one another's path; for those which do, demonstrably, must occupy at some one moment or other of their history, every point in the area of that zone of the heavens where their paths are thus pre- scribed. The apparent complication of their movements stares (that of the moon excepted) from our viewing them from below; but if we could see them from above, disappear, we could shift our point of view and observe them from the side. On the other hand, the apparent motion of the earth is so reduced to us under its in- volved form, and is stalled, from the station we occupy, to the greatest advantage by being removed out of the importance of luminosity to us in other respect; so by the investigation of the laws of its motions in the first instance we may hope to rise to a knowledge of those of all the other bodies out of it. (256.) The ecliptic, which is its apparent path among the stars, is traversed by the sun once in a year; and the side root angle between it and a circle consisting of 360° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° 0° **CHAP. IV.] THE ECLIPTIC.—SINEEZEAL YEAR.** trary direction to the apparent diurnal motion of both sun and stars, it comes to the same thing as if the diur- nal motion of the sun were so much slower than that of the stars, that he would have time to make one circuit of his daily course. Where this has gone on for a whole year, the sun will have fallen behind the stars by a whole sidereal revolution; but where it has gone on for only half a year, the sun will have made fewer diurnal revolutions, by one, than the stars. So that the same interval of time, which is called a solar year, is really a sidereal year, if reckoned in mean solar days, hours, &c., will be called 365$\frac{1}{4}$, &c., times, then, is the proportion between these two periods. But since the diurnal motion of the sun, reduced into a decimal fraction, is that of $0.002739$, the measurement of time by these different circu- latory motions of the sun and stars is always subject to error, or oftis of two different nations ; the proportion of which, once acted, can never become a source of error. (See p. 18.) The errors arising from this cause may, for our present purpose, be regarded as invincible. It is true that this is not strictly the case and on com- paring the motions of the sun with those of the stars, it held at the most distant epoch at which we possess observations, we find evidence of a small change, which though very slight, yet appears to be constantly increasing; explained; but that change is so excessively slow, that for all practical purposes, during several years, or even for whole centuries, this circle makes no difference in having the same position in the sidereal heavens. Yet it must be observed, that like those of any other great circle of the sphere, are opposite points on its surface, equidistant from the ecliptic in every direc- tion. These points are called poles of the ecliptic; they are the equinoctial, and removed from it by an angular in- ternal equal to the inclination of the ecliptic to the equi- niontal plane. They are denoted by $\mathrm{N}$ and $\mathrm{S}$ for $\mathrm{ecliptic}$. In the annexed figure, if $\mathrm{Pp}$ represent the north and south poles (by which, when used without qualifica- tions, they are understood to denote any two points on the sphere), then $\mathrm{NQ}$ represents $\mathrm{N}$ pole and $\mathrm{SQ}$ $\mathrm{S}$ pole; and $\mathrm{QAQ'}$ the equinoctial. VSAV the ecliptic; and Kk, its poles—the spherical angle QVS is the obliquity of 160 A TREATISE ON ASTRONOMY. [CHAP. IV. ecipital, and is equal in angular measure to PR or SQ. If we suppose the sun to move uniformly in the direction VSAW, V will be the vernal and A the autumnal equinox. S and W, the two points at which the ecliptic intersects the horizon, are called the solstitial solitudes, because, when arrived there, the sun ceases to recede from the equator, and (in that sense, so far as it is possible to speak of such a thing) it stands still in the heavens. S, the point where the sun has the greatest northern declination, is called the summer solitude, and W, the point where it has the greatest southern declination. These obliquities obviously have their origin in the depen- dence of the seasons on the sun's declination, which will be explained hereafter. The plane of the ecliptic (SQ), which passes through the poles of the ecliptic and equinoctial, is called the solstitial colure; and a meridian drawn through this colure is called a solstitial meridian. (250.) Since the ecliptic has a determinate situation in the stary heavens, it may be employed, like the equi- natorial circle, as a line of reference; and all circles drawn through them from its poles, and therefore per- pendicular to it. Such circles are termed, in astronomy, circles of latitude; and those which pass through any ecliptic, reckoned on the circle of latitude passing through it, is called the latitude of the star--and the arc of the A diagram showing various celestial elements including an equatorial circle labeled "E", an ecliptic labeled "Z", a meridian labeled "M", and other lines and labels indicating different celestial positions. ecliptic intercepted between the vernal equinox and this circle, its longitude. In the figure X is a star, PXR a **CHAP. IV. CELESTIAL LONGITUDES AND LATITUDES.** circle of declination drawn through it, by which it is referred to the equatorial, and K.V.T. circle of altitude referring it to the ecliptic—then, as VR is the right ascension of the object, V.R. is its longitude, and VT its latitude, and TX its inclination. The use of the terms longitude and latitude, in this sense, seems to have originated with the ancients, who considered the terrestrial equator as the base-line, and the celestial equator as the horizon, and thus measured all distances on the earth—the former holding an invariable position with respect to the stars, while the latter varies with respect to stations on the earth's surface. The force of this observation will presently become apparent. (26.) The angle between the plane of rotation of an object, we may find its longitude and latitude, and vice versa. This is a problem of great use in physical astronomy. For example, let us suppose that we wish to find EK.FQ, the solstitial colure is of course 90° distant from V, the veral equinoxes, which is one of its poles; so that if we know any two points on the ecliptic plane, say V.E., the ver E.R., and its measure, the spherical angle EPR. or FKP, is known. In the spherical triangle VEPF (fig. 3), VP is equal to VR, being the distance of the pole of the ecliptic and equinoctial, is equal to the obliquity of the ecliptic; 2d, the side EP is equal to VX, being half of the difference between V.R. and V.L.; 3d, the included angle K.PV; and therefore, by spherical trigonometry, it is easy to find the other sides and angles of this triangle. Thus we have the complement of the required latitude X.T., and the angle P.KX being known, P.KY being a right angle, Y.KX can be found; and consequently X.T. is known. Now this is no other than the measure of the longitude V.T. of the object. The inverse process is readily made when triangles are given whose sides are similar. (26.) The same mode of observations by which the pull of the sun among the fixed stars is traced, and the ecliptic marked out among them, determines, of course, the place of the equinox V upon the sphere stellate, at that time—point of greatest depression for perihelion—now as it is the origin or zero point of right ascension. o2 162 A TREATISE ON ASTRONOMY. [CHAP. IV.] Now, when this process is repeated at considerably dis- tant intervals of time, a very remarkable phenomenon is observed. The sun appears to move in a circle, in a con- stant place among the stars, but shifts its position, involv- ing continually and regularly, although with extreme slowness, from east to west, and from west to east. This motion of the sun appears to move in that circle. The equinoctial point thus moving through the heavens, and being always in the same annual round, the sun arrives at the equinoctial point sooner; that is, the time of the equinox happens sooner than it would have happened had the earth been stationary. The equi- noctial point changes a precession in the time of the equinox. The amount of this motion by which the equinoxes incline both ways is 0° 50' 0" per annum, an extremely minute quan- tity, but which, by its continual accumulation from year to year, produces a considerable change. This motion is in a way highly inconvenient to practical astronomers, by destroying, in the lapse of a moderate number of years, the uniformity of the apparent motions of the stars, making it necessary to reconstruct them. Since the formation of the earliest catalogue on record, the place of the equi- nox has changed about 30 minutes of arc; during which it performs a complete tour of the ecliptic, in 25,808 years. (38.) The immense astronomical effect of the precession of the equinoxes is to produce a uniform in- crease of longitude in all the heavenly bodies, whether fixed or moving. For instance, let us suppose that at any point of longitude, as well as of right ascension, a re- sent of this point on the ecliptic tells upon the longi- tudes of all other planets and stars. In this case, these pro- duces, so far as its amount extends, the appearance of a motion in longitude common to all, as if the whole hea- ven had one common centre. This motion will continue in the long period above mentioned, similar to what they have in twenty-four hours round those of the equinoctial. (39.) To understand this remarkable astronomi- cal phenomenon, however, we must abandon for a time, the consideration of the ecliptic, as tending to produce **CHAP. IV.** PRECESSION OF THE EQUINOXES. 165 emphasis on our idea; for this reason, that the stability of the ecliptic itself among the stars is (as already hinted, art. 357) only approximate, and that in consequence its interaction with the equinoxes is subject to a fluctuation, which mixes itself with what is due to the principal unarmo- gnesical causes of precession; and that, consequently, we cannot consider one cause alone, if, instead of regarding the equino- nox, we fix our attention on the pole of the equino- xial plane, we shall find that it is not stationary but moves (384). This place of this point among the stars is easily determined, at any epoch, by the most direct of all astro- nomical observations. For instance, when we observe this instrument we are enabled to ascertain at every mo- ment the exact distance of the pohar point from my own meridian; and by means of this instrument we can triangulate from these stars, with uttering precision, on a chart or globe, without the least reference to the actual position of the pole of the ecliptic, which is always really connected with it. Now, when this is done with proper diligence and exactness, it results thus, although the pole of the earth may be regarded as not sensibly variable, yet in reality it is in a state of constant, although extremely slow motion. The earth's rotation about its axis is a motion is not uniform, but composed of one principal, uniform, or nearly uniform, parts, and other smaller and more irregular parts. These latter parts give rise to the phenomenon of precession; the latter to another distinct phenomenon called nutation. These two phe- nomena are connected together in such a manner that they and the same general head, and are intimately connected together, forming part of a great and complicated chain. The first part of this chain is formed by the motion of its axis; but it will be of advantage to present clearness to consider them separately. It will be seen at once that in virtue of the uniform part of the motion of the pole, it describes a circle in the heavens around the pole of the ecliptic as a centre, keep- ing constantly at the same distance of 28° 8' from it, in a direction from east to west, and with such a velocity, 165 164 A TREATISE ON ASTRONOMY. [CHAP. IV. that the annual angle described by it, in this its imaginary orbis, is 50° 10′; so that the whole circle would be de- scribed by it in the above-mentioned period of 35,838 years. But, since the axis of the earth being at the pole will give rise to the retrograde motion of the equi- noxes ; for in the figure, art. 239, suppose the pole P in the position of the sun, then, when the equinox K comes K to come to O, then, as the situation of the equinoxial EVTQ is determined by that of the pole, thus, it is evi- dent, that when the pole is at E, then the equinox K will will take a new situation, EUQ 97° distant in every part from the new position Q of the pole. The point U, therefore, will describe a circle with center at E, and intersect the ecliptic, i.e., the displaced equinox, will lie on that side V of its original position, towards which the motion of the pole is directed. (265.) The precession of the equinoxes thus conceived, consists then, in a real but very short motion of the pole of the heavens, about a point situated between the pole of the ecliptic. Now this cannot happen without any corresponding changes in the apparent directions made by the stars in their courses through the heavens must proceed at very remote periods of history. The pole is moving more than the vanishing point of the earth's axis. As regards all these phenomena as they have been described, it necessarily follows that the earth's axis must have a conical motion, in virtue of which it points inci- sively into space at different times during its revolution. We may form the best idea of such a motion by noticing a child's peepcock, when it spins not upright or flat annu- larly but on one side or other. This motion being well and nicely balanced, becomes an elegant philosophical instrument for exhibiting, in as beautiful a manner, the whole phenomena of astronomy. For we see here, once a clear conception of it as a fact, and a considerable insight into its physical cause as a dynamical effect. The reader will easily perceive how this motion accounts for position of the earth's axis in space with a mere shifting of the imaginary line about which it revolves, as in its inte- rior. The same thing happens in our bodies, and goes along with the axis as if it were made of iron. **CHAP. IV.]** **NUTATON.** 165 driven through it. That such is the case is proved by the two great facts: 1st, that the latitudes of places on the earth, or their geographical situation with respect to the poles, vary very little during the whole period of time from the earliest ages. 2dly, that the sea maintains its level which could not be the case if the motion of the axis were accompanied with a motion of the whole mass of the earth. (267.) The visible effect of precession on the aspect of the stars is so slight that it can only be observed in some stars and constellations to the pole and recess of others. The bright star of the Lesser Bear, which we call Ursa Minor, will serve us for this purpose. This star will continue to be our cynosure: at the time of the construction of the earliest cabalistic it was 12° from the pole, and will remain so until within half a degree, after which it will again recede, and slowly give place to others, which will succeed it in order of magnitude. In 10,000 years, in 18,000 years, in 23,000 years, in 19,000 years, in 16,000 years, in 12,000 years, each star a Lyre, the brightest in the northern hemisphere, will have passed into the recess of a pole star, approaching within about 5° of the pole. (268.) The nutation of the earth's axis is a small and almost imperceptible change in its direction. As we are standing alone, the pole would describe among the stars, in a period of about nineteen years, a minute ellipse, whose long diameter would be about 13'24"; the longer being directed towards the pole of the ecliptic, and the shorter, of course, at right angles to it. But this is but an apparent approach and recession of all the stars in the heavens to the pole in the same period. Since, also, the sun describes an ellipse around the earth in about eighteen months (which is nearly equal to one year), and since he is always in his place when he passes over any place on our globe; therefore, while he describes his ellipse round us, we are describing an ellipse round him; and consequently, while he advances or recedes from any place on our globe, we are advancing or receding from that place. In consequence of this mutual action between us and him, we shall appear to advance or recede from any place on our globe according as he advances or recedes from it; and consequently, while he advances or recedes from any place on our globe, we shall appear to advance or recede from that place. In consequence of this mutual action between us and him, we shall appear to advance or recede from any place on our globe according as he advances or recedes from it; and consequently, while he advances or recedes from any place on our globe, we shall appear to advance or recede from that place. In consequence of this mutual action between us and him, we shall appear to advance or recede from any place on our globe according as he advances or recedes from it; and consequently, while he advances or recedes from any place on our globe, we shall appear to advance or recede from that place. In consequence of this mutual action between us and him, we shall appear to advance or recede from any place on our globe according as he advances or recedes from it; and consequently, while he advances or recedes from any place on our globe, we shall appear to advance or recede from that place. Since both these motions are considered separately they do not affect each other; but since they are considered together they do affect each other; because while one is increasing another is decreasing; and vice versa. Hence it happens that although these two motions are considered separately they do not affect each other; but since they are considered together they do affect each other; because while one is increasing another is decreasing; and vice versa. Hence it happens that although these two motions are considered separately they do not affect each other; but since they are considered together they do affect each other; because while one is increasing another is decreasing; and vice versa. Hence it happens that although these two motions are considered separately they do not affect each other; but since they are considered together they do affect each other; because while one is increasing another is decreasing; and vice versa. In virtue of this mixture, the pole is describing its little 166 A TREATISE ON ASTRONOMY. [CHAP. IV.] ellipse of 18°50" in diameter, it is carried by the greater and regularly progressive motion of precession over so much of its circle round the pole of ecliptic as cor- responds to the difference between the mean motions of nineteen times 50° round the centre (which in a small circle of 23° 25' in diameter, corresponds to 3° 59'), at each revolution of the earth about the sun, which it will pursue in virtue of the two motions, subsisting jointly, will be neither in eclipse nor an exact circle, but a greatly elongated ellipse. The eccentricity of this ellipse, however, the undulations are much exaggerated). (See fig. to art. 272). (270.) These movements of precession and nutation are common to all the celestial bodies both fixed and er- ratic; and this circumstance makes it impossible to attri- bute these phenomena to any one particular axis of the earth's axis, such as we have described. Did they only affect the stars, they might, with equal plausibility, be urged to be due either to a rotation on an axis passing through the poles of the ecliptic, or 25,808 years, and a real elliptical syzygy of that axis with the sun. But since they affect also the sun, moon, and planets, which, having motions inde- pendent of the general body of four stars, cannot without ex- traordinary coincidence be supposed to follow their laws, this idea falls to the ground; and there only remains, then, a real motion in the earth by which they can be accounted for. It is evident that this motion must be such that it are necessary consequences of the rotation of the earth, combined with its elliptical figure, and lie un- equal amounts of precession and nutation on its polar and equatorial regions. (271.) These are chiefly interesting because, in the approach places of the stars, they are of the utmost im- portance in practical astronomy. When we seek the right ascension and declination of a celestial object, it becomes necessary to know how far it has been moved since the moment when we first observed it. This argument, urged on it is, requires additional and definite force from the law of nutation; for if we suppose that it is caused by the action of the lunar orbit, we attribute it to a real motion of the celestial sphere; we must then suppose that place to be kept in a constant state of freedom by the motion of the moon.






































































































































Ellipse 18°50" Diameter Precession Over so much of its circle round the pole of ecliptic as corre- sponds to difference between mean motions of nineteen times 50° round the centre (which in a small circle of 23° 25' in diameter, corresponds to 3° 59') at each revolution of the earth About the sun, which it will pursue in virtue of the two motions, subsisting jointly, will be neither in eclipse nor an exact circle, but a greatly elongated ellipse. The eccentricity of this ellipse, however, the undulations are much exaggerated). (See fig. to art. 272).
Nutation
Precisio nance
ellipse Diameter 18°50" precession over so much of its circle round the pole of ecliptic as corresponds to the difference between the mean motions of nineteen times 50° round the centre (which in a small circle of 23° 25' in diameter, corresponds to 3° 59') at each revolution of the earth about the sun. nutation such that it are necessary consequences of the rotation of the earth, combined with its elliptical figure, and lie unequal amounts of precession and nutation on its polar and equatorial regions. moon's effect on precession and nutation on its polar and equatorial regions. This argument, urged on it is, requires additional and definite force from the law of nutation; for if we suppose that it is caused by the action of the lunar orbit. moon's effect on precession and nutation on its polar and equatorial regions. we attribute it to a real motion of the celestial sphere; we must then suppose that place to be kept in a constant state of freedom by the motion of the moon.
Description Data Type Data Value(s)