| The time that elapses between the returns to the various points of the ecliptic is nearly equal; for the sun's path is always about 5° 26' 56" in solar time, or 360° 5° 26' 56" in sidereal time, there being one more sidereal day from the beginning of each year than there is in solar time. This is due outward in the direction in which the earth spins, and therefore the sun appears to rise and set with a certain setting. In order that the seasons may always fall at the same times of the year, it is necessary that the fraction of a day (nearly a quarter) over the 365 in the Gregorian calendar, which is that of our present system of computing years, be added to every fourth year (leap year) consist of 366 days, the extra day being inserted on February 29th. If this rule were not applied, it would be evident rather than 365 days, the extra day is not added to any year. A year having only three days out of these three days are got rid of in every four years, making less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leap years is less than one day in every four years. The number of leapyears
RIGHT ASCENSION AND DECLINATION.
On the earth we say that its latitude, or the angle
between the plane of the equator and the plane of the
ecliptic, is 23° 27' 26". This is the angle which the
plane of the ecliptic makes with the plane of the
equator. Latitude is measured by this angle, and is
called the declination of a place. The declination of
the equator is zero. The declination of any other
place is equal to the difference between its latitude
and the latitude of the equator. Thus, if a place has
latitude 40° N., its declination will be 40° N.
Latitude is measured by this angle, and is called the
right ascension of a place. The right ascension of
the equator is zero. The right ascension of any other
place is equal to the difference between its right
ascension and the right ascension of the equator.
Thus, if a place has right ascension 40° E., its right
ascension will be 40° E.
The time required for the earth's rotation to bring
a given point on its surface into a new position,
which position is determined by its right ascension
and declination, is called sidereal time. Sidereal
time is measured by this period, and is called the
right ascension of a place. The right ascension of
the equator is zero. The right ascension of any other
place is equal to the difference between its right
ascension and the right ascension of the equator.
Thus, if a place has right ascension 40° E., its right
ascension will be 40° E.
The time required for the earth's rotation to bring
a given point on its surface into a new position,
which position is determined by its right ascension
and declination, is called sidereal time. Sidereal time
is measured by this period, and is called the right
ascension of a place. The right ascension of the equa-
tor is zero. The right ascension of any other place is
equal to the difference between its right ascen-
sion and the right ascension of the equator. Thus,
if a place has right ascension 40° E., its right as-
cension will be 40° E.
The time required for the earth's rotation to bring
a given point on its surface into a new position,
which position is determined by its right ascen-
sion and declination, is called sidereal time. Sidereal
25
The circle on the Key Map (Frontispiece) represents the meridian passing through Greenwich, England, at 18° 0' W. longitude, and at 0° latitude. It also represents one hour of time, or one degree of arc on a circle of 360 degrees.
The lines from the center represent the Hour Circles for every two hours.
between the successive passages of the same star across the meridian, and between the successive passages of two stars at different altitudes, we must use a solar or sidereal clock, which is so regulated that exactly one hour passes between the passage of each star across the meridian. Such a clock is set so as to indicate 0° exactly when the vernal equinox is on the meridian, and therefore takes 24 sidereal hours to return to the same point. The time required by this clock to reach the right ascension, which measures the distance from the meridian to the horizon, is called the mean solar time.
We must take a solar or sidereal clock, according as we take transits of the sun or of a star across the meridian. We must also take into account the proportion that the interval of time between the successive passages of two stars at different altitudes is to the interval of time between their transits across the meridian. In this way we can determine whether both intervals are expressed in solar or in sidereal hours, but it is convenient to take the mean solar time for all purposes. We must also consider whether both intervals are expressed in solar or in sidereal hours, and this determines whether we must use a solar or a sidereal clock. This consideration applies to all cases where it is used in practice.
The following illustration may put this in a clear light. In some parts of England a pound of butter is made into a roll of bread weighing about three-quarters of a pound. In France a pound of butter is made into a roll of meat worth about three-quarters of a pound. In England we buy a quarter of a yard in England for about three-quarters of a yard in France; and in France we buy a quarter of a yard in England for about three-quarters of a yard in France. This is usually troublesome to beginners, from the want of a proper standard.
To return to the sun. We have shown how to measure its altitude with respect to any given place, and we must find the right ascensions of one or more stars
ECLIPTIC.
by noting the difference of the times of transit (in
either half-year) of the sun's rays across the equinoxes,
at the several stations, and comparing these with the
times of transit at the same station when observed at
the transit of one (or more) of the known stars and of
the sun. The sun's right ascension will be found by
this method to be nearly correct, but the declination
several stars be observed, the mean (average) of the
results being taken, this will be found to be still more
accurate. This is a principle which can be applied to
all observations, and which may be used by any
observational science to reduce the inevitable errors
arising from the imperfections of our senses and of
the instruments employed in making them.
But very nearly balance one another when we take the
observations at different stations, and consider the
quantity: the errors which make it seem too big, being
counteracted by those which make it appear too small.
The principle that if a coin be tossed a large number
of times, it will turn up heads about as many times as
tails, is applicable to astronomical observations. For
every day of the year, we can plot down his course on
a diagram, and find out how often he passes through
(assuming that his apparent path is a great circle) "inclined"
to the plane of the equinoxes. The place of this circle is called the ecliptic.
The sun's motion along this path is quite uniform;
but the variation in longitude is not uniform either,
but the variation is only about 1° of the whole, the
sun's motion being always in one direction. This is
combined with the tilt of the sun's path, which makes
the sun's motion in longitude oblique to its apparent
motion in latitude. This causes an inequality in the time
Key hold where in a plane passing through the apogee,
nor matter what the plane in that plane, will appear to
be moving in a circle round a point in space, and that
point in which the sphere is cut by a plane through the center
of gravity of all bodies situated within it. This is called a focus of
the heavens, by looking along the planes in which it lies.
29
30
EQUATION OF TIME.
as shown by the sun, and if a clock be regulated to pro-
duce the same effect on the hands, the error of such a sun will be at certain times of the year fast or slow by the clock to the extent of one minute per hour, this being called the equation of time.
Further, the change in the sun's rate of movement
is not uniform throughout the year, but varies with its ap-
parent diameter, which is largest when the motion is
slowest, and smallest when it is fastest, so that we have
part of the whole. When an object increases in
apparent size, either by being nearer or by being more
distant from us. In the case of the sun, in the ease of the
sun, we have no reason to conclude that there is any
change in its actual diameter, but we may suppose it to be
being highly improbable, and we are therefore led to
conclude that it is due to some cause other than distance,
by about one-eighth part.
If we wish to represent the colatitude,
we lay down on it the position of the sun on every
fifth day of the year, the lines drawn from the centre
to those points will represent the differences in what.
THE sun's eccentricity is represented by a circle inscribed in a square.
The sun's eccentricity is represented by a circle inscribed in a square. The lines drawn from the centre to those points will represent the differences in what.
There is a curious optical illusion which makes one
think that he sees two suns at once. This is only the result of having lived under circumstances where there was
only one sun visible at any time, and it is easy to see how luminous bodies appear to be nearer or further away than they really are. It has been observed that when clouds are moving over a region where observations are being made, and when these observations are continued for several days without interruption, there is always a difference between them and their results agree exactly with the results of observations near the earth.
![]() A diagram showing the sun's eccentricity represented by a circle inscribed in a square.
THE sun's eccentricity is represented by a circle inscribed in a square.
ORBIT OF THE EARTH.
the sun is seen by us at the corresponding times
but as his apparent diameter is very small to represent his
apparent motion fully, set off on these radii lengths
representing the sun's diameter, and draw lines parallel
to them through the points where they intersect the
circle. We thus conclude that the sun appears to move round
us once a year in a slightly oval and eccentric path.
But this is not all. For we have observed that when
the sun is moving round the earth, than that the earth
is also moving round the sun. This fact will explain
the sun's apparent motion, just as we saw that the
moon's apparent motion was explained by a rotation of
a rotation of the earth in the opposite direction.
Now there are several circumstances which show that
the earth does not carry the sun, which goes round the sun,
and not the sun round the earth. In the first place,
when we look at the stars at night, we see them appear
to fall slowly towards the horizon, but when we come to discuss the means of find-
ing out whether they really do so, we shall find that this
question is answered in another way. Then, again, we shall find that there are
other heavenly bodies of which the apparent move-
ment is exactly similar to that of the sun, and which,
moving them to recede from the Sun, at distances which
are nearly equal to those of the sun from us, and from
the earth from the sun, and as these bodies themselves
move in orbits which are nearly circular, it follows that
the sun is carrying such masses along with him,
which are so small compared with himself that their
highest degree improbable. But it is when we come
to discuss the physical causes of these motions that the
true explanation of them is found.
In anticipation, then, of the conclusions of sub-
sequent chapters, I may say that our planet revolves round the sun once in a year in a slightly
elliptical orbit, having its perihelion at about 93000 miles,
at a distance about 83.500 of the earth's mean diam-
eter, and with an average velocity of 18 miles a second.
The moon moves over eight times her own diameter every hour.
The planets move over their own diameters more than half a degree at their mean distance; it follows that
22 RELATIVE MOTION--THE SEASONS.
he be at a distance from us of 513 times his own semi-
axis, he would appear to move with the earth.** Now although we may at first feel some difficulty in
conceiving that the earth could move with such a great speed without our being conscious of it, yet if we con-
sider that the earth bears the same proportion to the sun as the moon does to the earth, we shall find it far more difficult to conceive that such an in-
stance can occur than that of the moon's motion.
But whatever the earth be moving with respect to us, it will always appear to us as if it were moving about some other point in the line joining them, their apparent motion will be the same ; and as far as these two points are concerned, they will appear to move in
motion in that way which confuses most to elementary of
the sciences. The sun rises and sets every day, and stars rising and setting, though these are more
commonly observed, are but the same thing. The annual motion round the earth ; but when we have to
consider the motion of another heavenly body relatively to the earth, we must consider that we have a very
peculiar position. We cannot see this body directly,
but we must depend on its reflection from the sun. In
this way we ourselves seem to be standing still, and by
any way of speaking, provided we remember that we
are not looking at the sun itself, but at its reflection.
Standing we will proceed to show how the apparent
for relative motion of the sun gives rise to the sea-
ons.
At the verbal equinox the days and nights, as be-
longing to opposite hemispheres, are equal. But in
world, the equinox being everywhere divided into two
equal parts, one part being in daylight and the other in
moving along his oblique path, passes north of the
equator, and two results follow from this, both of which are observable in nature.
* This is equivalent to $2\pi$ at the centre of a circle being $\frac{1}{2}$ of the whole circumference, which is 81 time the dis-
tance between A and B, and half the length of arc $A$ is $\frac{1}{4}$ of the radius nearly.
THE SEASONS.
33
more heat from the sun. In the first place the day is longer than night, and this circumstance, to say nothing of the fact that the time during which heat is received from the sun is increas- ed by the inclination of the earth's axis, so that the heat re- ceived in every hour is greater on account of the greater elevation of the sun, for his rays have a less oblique direction to the earth's surface. Secondly, because of their way, and further, a larger proportion of them reach the earth's surface, and are reflected back into space, when obliquely, just as in a driving shower a larger quantity of water is thrown out than when it falls perpendicu- larly. Thirdly, the earth is heated more uniformly than any other body, and this circumstance is very important. It is worth remarking the enormous decrease in brightness of the sun at its greatest distance from us, and at its greatest height, which reduces the sun's brightness to 47 eleva- tion. Now we must remember that the temperature of any body results from a series of exchanges with surround- ing bodies. The sun has no such exchange with anything else but sends out hot bodies send out more heat than they re- ceive from cold bodies. This is true also of all other bodies. Now the earth receives a balance of heat from the sun, and sends out a balance of heat to space, and it will remain in the same state as before, but if it re- ceives more than it can send away it will get hotter, and if it receives less than it can send away it will get colder. Sphere at the time we are considering; for, as we have seen before, the sun is always in the same place in the sky at the day, and have less time in the night to send it off again. But what happens? The earth gets hotter than the sun at the equinox. But the quantity of heat received by the whole earth and sent out into space is equal to that which comes from the sun. For if we go below the equator (the north pole being below), and above it (the south pole being above), we find that countries get cooler than they were at the normal latitude. These observations show that our atmosphere gains on increasing as the sun gets further
II
34
THE SEASONS.
any further north, till June 31st; the northern hemi-
sphere has by that time reached such an accumula-
tion of heat in the soil itself, that it does not begin to generate any more heat than it can absorb. The heat off the fire will continue to boil on another part of the stove, though the heat there is not sufficient to set it in motion. This heat will be dissipated as the sun moves southwards in the autumn, and then again northwards in the spring. At these latitudes, the reverse taking place in the southern hemisphere, will be formed in the northern hemisphere, in conse-
quence of the absorption of heat which then takes place at the surface of the earth. This is what we call the winter solstice, before the northern motion of the sun.
Thus we may consider winter in the northern hemi-
sphere as beginning about December 22nd (in the
months of December, January, and February); spring
(or autumn) from March, April, and May; summer (or
autumn) from June, July, and August; and autumn
from September, October, and November. But there
is no reason why this should be so. The sun does not hold, viz., the regions near the equator. As
the seasons change, they do not move through
such places twice in the year, and the same will be true for any place which is less than 23° 27' north or south of the equator. The sun's rays fall perpendicularly upon
the equator is less than 23° 27' from the zenith. The ball
of fire is then at its highest point in the heavens.
This is called the tropic of cancer, and it is at this time that
it is called the tropics, and since the heat at any place
is greatest when the sun is at its highest point in two summers; but rarely the change is very slight,
and the year is usually divided into wet and dry seasons,
according to latitude, being scarcely applicable. We may here
insinuate that we have been too much concerned with
the amount of light as well as heat. The sun at midwinter being
![]() A diagram showing different seasons and their corresponding dates.
THE SEASONS.
35
below the equator, will not rise above the hori-
zon at any time during the year. The equator-axe does
not reach a elevation of 23°8', which will be the case
when the sun is at its highest point in the sky.
It has a latitude (north or south) greater than 66°47'.
The circles of latitude 60°1 north and south are called
the Arctic and Antarctic circles. The belts included between these and the tropics are called
the Temperate zones. It is evident that the tempera-
tures in the Arctic and Antarctic regions is clear that the sun will in
no part of the year be below the horizon. At this
time, that he is further below the equator than
the distance of the place (in degrees) from the pole of the
earth to the place. This is true of all places on the
horizon for a similar period, so that the alternation of
day and night is due to the rotation of the earth. The
sun will remain visible for several weeks or even months at a
time, depending upon the latitude of the place. At the poles themselves these periods last for
six months each, so that there is only one day and one
night every month. In other words, we can circle round the pole once in twenty-four hours without seeing any change in the position of
the Great Bear with us, he never dips below the horizon.
In short, some causes of confusion arise when we
term day causes some confusion.
We have already spoken of the effect of twilight in
the morning and evening. It is due to the fact that a cer-
tain degree in polar regions, some light being receiv-
ed by reflection from clouds and snow, while others are re-
flected to a certain extent from ice and snow.
As has been already stated, it is perfectly legitimate to explain the alternation of seasons, as
has just been done, from the standpoint of the earth,
but it is also possible to explain it from another stand-
point. It is possible to explain it from another stand-
point. It is possible to explain it from another stand-
point. It is possible to explain it from another stand-
point. It is possible to explain it from another stand-
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35
36
THE SEASONS.
of relative motion, a point of cumulative importance for the study of astronomy, is that of the conclusion that the earth moves round the sun in a plane oblique to the plane of the ecliptic, and that the axis of the earth's orbit is also inclined. Now this axis always points to the same place among the stars, very near the pole star, and therefore we may say that it remains during the year. Let us picture to ourselves then, the earth revolving round its own axis, and moving in its course around the sun, and imagine that at each moment of nightlight a little out of the centre (in the direction of the longer axis of the oval) to represent the sun's light, and that at each moment of daylight a little inwards, core of an orange, which will represent the earth and its atmosphere, and that between these two figures as the earth moves in the ecliptic, keeping the wire straight, so that it does not change its position at all; at the same time we keep the orange spinning pretty rapidly, the circumstances of the earth's motion will be represented by a figure like this. The sun will not be far from the proportionate size of the sun, but it will be much nearer than any other object which ought to be represented by the minutest grain of sand on a table top.
But our object being to explain the appearances pre-
sented to an observer on the earth, we must suppose
that he is looking through a telescope at a scene about
seen from one side, the view being omitted.
Now let us suppose that we have a line (at the
top of the picture), when the sun appears to go on
the equator, an observer on the sun will look at the
earth as seen from above, and another observer on
both poles. As the earth moves on in her orbit, the
sun will appear to move round in a circle below him,
and will show his north side more and more to the sur-
rounding objects. The line passing through him (for-
wards) is in the direction passing through the sun,
![]() A diagram showing Earth's orbit around Sun with Earth's axis tilted at an angle. The Sun is shown as a small dot at one end of an ellipse representing Earth's orbit. The Earth is shown as an orange with a wire through it representing its axis. The wire is shown rotating around a central point. The Sun is shown as a small dot at one end of an ellipse representing Earth's orbit. The Earth is shown as an orange with a wire through it representing its axis. The wire is shown rotating around a central point.
THE SEASONS
which corresponds to the seasons (the left of the figure), after which less and less of the life is in the sun's di-
rection, till at length, at the autumnal equinox, the equinoxes, the two poles are in opposite directions (the
son of our figure). During this period the north pole will receive more than its fair share of light and heat, as will be seen by noticing where the boundary of darkness is situated on the right-hand side of the light-
lights. From the autumnal to the vernal equinox the
light will be more and more directed towards the
northwards, and therefore the north pole will be turned away so as receive less light and heat than
its south pole, which is presented to the sun. It is
therefore winter for the northern hemisphere and summer for the southern. We see at once from this fact that it is only the distribution of light and heat which varies with the seasons. At times during some
times the northern hemisphere receives more than
the southern, but this does not affect the common fund,
but this does not affect the common fund.
As a matter of fact, we have more light and heat in January than in July, but this is because
PHYSICAL CONSTITUTION OF THE SUN.
she is nearer the sun at the former epoch; the effect of this circumstance being that the rays which reach her are more concentrated, and marked by the very great much greater changes of the seasons. The constitution of that wonderful body which produces effects of such importance to our well-being. When we consider how much the atmosphere diminishes the intensity of its light and heat by means of reflection and absorption, we may easily see why the most distant planets, with their mottled surfaces, shilling off slightly towards the edge, are not so hot as the earth. This is accompanied by streaks brighter than the ordinary surface, and hence called faculae (urches). If one of these bright spots be placed on a plane surface, it will appear to move across the sun's disc, from east to west, during about 30 minutes. It then remains stationary for some time, and after an interval of nearly 14 days at the eastern limb, it appears again in the same place, but moving in the opposite direction. On extending our observations, it is found that all spots move across the sun's disc in about the same time, and in exactly the same manner. We have therefore led to conclude that their motion is due to a rotation of the sun upon its axis, from east to west, or in the same direction as the earth in her revolution round the sun. This rotation must therefore take place once again after an interval of some 27 days. But this is not the true time of rotation of the sun, for the earth does not complete a whole revolution in 27 days. For instance, when the sun has to turn through a corresponding angle in order to bring his face towards us from his present position on the earth's disk, just as we saw the earth had to do to bring his face towards us from his present position on the earth's disk when he goes round the sun in 365 days. We have since, therefore times are proportional to the angles turned through, and consequently, is rather more than 25 days. As the result of these observations, when we follow their passage across the disc, it is found that they do not always pass from east to west in exactly 27 days. Thus on December 11, showing that the circles which they de-
BOTATION OF THE SUN.
scites, and therefore also the sun's equator, are tilted with respect to the plane of the ecliptic, which is the plane of the apsestris, so that we see these circles edgewise (from opposite sides) on the two days given above, just as we see the poles of the earth edgewise (which are the diametral paths of spots on the earth) when they are seen at their greatest distances from us. The tilt of the sun's equator to the ecliptic is therefore equal to the inclination of the earth's axis to its orbit. We have something very similar to what we were led to conclude in the case of the earth, and thus the great difficulty which has been experienced in explaining this phenomenon is completely removed, for though the sun's rotation about its own axis is slow compared with that of the earth, yet it is difficult, indeed, to realize the size of this enormous difference. It is true that a spot on the sun's surface will make one revolution in 25 days, but according to the statement that a spot on the sun's equator moves four times as fast as a point on the earth's equator—i.e., at 60 degrees per hour—the time required by a spot on the sun's equator to complete one circuit would be only 3 days. But though this may seem to be a very small difference round with our sun, the changes that take place in them show that they are by no means features on his surface which can be neglected. They move towards and away from him in all directions, forwards relatively to another, so that they do not all move in one direction. In fact, they move in all directions, and even backwards. The individual movements, however, are small as compared with those of the general motion. These changes in their form are most remarkable. Cases have been observed of the formation of a large spot, which then disappears after a few hours; then again it appears after a few hours; then again it disappears after a few hours; and so on. This process continues for several months, and in this period it will often break up into a group of smaller spots, or such a group may coalesce into one large spot. As a general rule, spots are com-
SOLAR PROMINENCES.
posed of a central black portion, which is called the umbra, and two lateral portions, one on each side of this part called the penumbra (halfshade), and these two portions are separated by a line of light, which is called the limb, and is at the same distance from the umbra as the umbra is from the centre of the sun, and both of them below the bright surface which we see ordinarily. That a spot may be seen in the atmosphere of the sun, is shown by the appearance of a star-like object when looking at the spot obliquely, and it is found that more light is reflected from the spot than from any other part of the sun's surface. The spot itself is very much foreshortened, as we should expect on the supposition that the spot is in reality a small body, and that its light is reflected from a very narrow space with a little icy water at the bottom will produce a star-like appearance to us, just as a star does at a spot. Of the causes which give rise to sun spots are many different opinions; but it is generally agreed amongst every seventh year, and there is a suspicion that this is due to the influence of the planet Venus. In some cases, however, it has been observed that the sun appears to have no spots whatever, and then it is supposed that they have been obscured by the interposition of an opaque body like the moon, in order to prevent their being seen. This is a beautiful application of the spectroscope, an instru-
ment designed to determine the nature of the light emitted by bodies. The following passage briefly explain the principle on which this is founded. A piece of glass is placed between two prisms, one of them having a large aperture, and the other a narrow one, and between these two prisms there is placed a thin plate of glass with a hole in it through which light can pass. When light passes through this hole it is refracted by the prism on one side, and by another prism on the other side, so that it becomes parallel to itself again. Now suppose that there be a body in front of this hole which emits light; this light will be refracted by both prisms in exactly the same way as if it had come from behind them; but since it comes from behind them it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be coming from behind them; therefore it must be
40
SPECTROSCOPE.
of the glass is termed reflection (breaking), and is common in all transparent substances; it is best seen when the glass is in the shape of a sphere, e. g., a triangular bar, or prism, as in the figure. In this case, the light which enters the prism is found to be divided into three rays, one proceeding from red to yellow, green, blue, and finally violet, while the other two proceed from yellow to violet. The first ray is called the flame first begins to be seen in the prism. Thus it appears that the light of all the colors of the spectrum is really reflected by the glass, but that the light of each color has a phenomenon caused by a somewhat similar action in passing through the prism. This is shown in fig. 3, where it may be separated into three colours by a prism of glass. The rays of light which enter the prism are refracted towards its base, and the red heat, the other rays lying between red and yellow, are refracted towards its top. They spread out into their component colors, i. e., so far as they can be separated, and it is to be remarked that though for convenience we have separated them into three distinct colors, yet in nature there is no sharp boundary between two contiguous colors. The same thing happens with respect to yellow and blue, and it corresponds to every degree of bending or deviation there is a certain hue. Now it will be observed that if we take a piece of glass and place it on a table, some of the light which passes through it may then be spread out into a continuous spectrum, and we shall see that the different colors are produced by hydrogen giving out these definite kinds of rays only, cor- poral bodies being unable to give out any other kind of light than those already mentioned. The prominence of the sun arises from its giving out light of these three hues abundantly; indicating that they are most abundant in nature. It is evident that in the intensity of the light must be very much enlivened by the presence of these three colors; and this is what we call it as it is called, an effect which may be deduced by put- ting a prism before a source of light such as a candle burning through the glass, so that by making the rays go through a number of prisms one after another, we can thus direct all the light of the sun may be made quite fine, while the
2 MODE OF VIKING PROMINENCES.
light of the prominences is scarcely affected, since it consists only of the red rays of light, which are the least of being spread out. The light which falls on the prisms is therefore all of the same color, and the prism will show the length of the spectrum, and lenses are placed just in front of the first prism, and just after the last, so that they may intercept the rays which have passed through the prism. This arrangement shows us a line of light, which appears to be a reflection of the sun's surface, but this appearance thus appears like a ribbon of shaded colors on an otherwise clear blue sky. Such an instrument is called a spectroscope.
If now an image of the sun be formed on the slit of a projection apparatus, and if we look at this image through a slit which is directly between it and the first prism, a line image of the sun will appear on the screen. If we then move part of the spectrum, when the slit is so placed that it is exactly over one of its lines, we shall see that these lines correspond with those parts of the spectrum which are reflected by the sun. In this way we may see these prominences by means of the ground glass screen. If we wish to see them more distinctly, if we look at those parts of the spectrum, respec-
tively corresponding with those parts of the sun's surface which are visible to us, and known as the "photosphere" (or sphere of light), a layer of glowing body is seen to extend from the sun's surface up to about 30 miles, or two times the diameter of the earth. This layer is very thin, but the thickness varies very much, as its surface is almost always in a state of great agitation, which, although it may be caused by solar winds or by hydrogen, there are no. In its lower strata, the vapors of matter are condensed into drops of water or drops of hydrogen. The position of these drops can be determined by means of hydrogen, the line being determined accurately by the position
COBONIA—ZODIACAL LIGHT. 43
the spectrum of the corresponding image of the slit, and the appearance of the sun's corona when viewed across the spectrum. There is another appendage of the sun which has been observed by several observers, but which has only been seen in total eclipses, and which appears on the evidence of the spectroscopist to consist chiefly of a very thin layer of gas, which is situated at an enormous distance from the sun's surface, perpendicularly below it, and which is composed of two portions, the upper corona being applied to the sun's disc, and the lower corona being a sort of halo or corona of glory which is frequently seen round the moon in a hazy sky. The lower portion forms an atmosphere of a very faint blue color, and appears to contain hydrogen as well as the unknown rays and interplanetary matter, which can be traced to a certain extent to the earth. This portion of the corona gaps reaching nearly down to its limb. This portion appears to shine partly by its own light, and partly by reflection.
From this account it will be seen that the sun is made up of three distinct parts, viz., (1) The photosphere, or luminous surface, two or possibly three layers of gas, which are visible through the solar corona; (2) The chromosphere, or gaseous envelope of a spotted above it the chromosphere, the atmosphere or inner corona, and the outer corona; (3) The corona, or outermost envelope of gases. The periphery of the sun, which is seen under favorable circumstances, is a source of light in the plane of the ecliptic, and is supposed to be composed of rays from the solar disk; but these rays are not visible in the radial light, and is now supposed to be composed of myriad of small particles which reflect the sun's light, and are supposed to be distributed over all parts of the earth's orbit.
The spectrum of the sun's light and heat, both of which appear to come almost entirely from the photosphere, shows a strong absorption band near 5800 A. green, and this remains one of the most important subjects of
44
AFFEART MOTION OF THE MOON.
inquiry, the sun's rays being the immediate source of almost all the phenomena which take place on the surface of the earth or in its atmosphere.
CHAPTER III.
"The moon, as will be soon shortly, pays a very insigni-
ficient part in the solar system, but next to the sun,
it, from its comparative proximity, the heavenly body
which is nearest to us, is somewhat like that of the sun, but far more rapid
and more easily visible. The moon returns to the same posi-
tions with respect to the stars and the sun respectively, the latter period
being called a synodic month (or the real moon's motion), and
(our earth's real motion) in the interval, since the
earth revolves around the sun much more slowly in the same direction. The former is called a
lunar month (or our earth's lunar motion).
The determination of the moon's motion is a far more
complicated question than that of the sun's, but by
watching carefully we can see that they move much more readily than in the case of the sun, as moon-
sight shows that the moon moves in an orbit about 15° to 17°
per year, while the sun's orbit changes only about 30" per year.
I found that the moon moves in an orbit tilted about 5° to 6°
to our ecliptic plane, and this inclination remains constant.
It is described in a day varying from about 14° to 17°,
while the diameter changes from 292 to 282", showing that
the moon's orbit is inclined at an angle of about 5° to 6°.
In this way it appears that the moon seems to describe
a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does it? Its ellipse is much more oval, it will be seen
that it describes a circle round the earth, and yet it does not really do so,
does它
IRREGULARITIES IN THE MOON'S MOTION. 45
factors of the case, and is a fair approximation to the truth.
In the first place, it will be seen that while the moon comes back to the ecliptic after having made the tour of the zodiac, she does not return to the same point on that great circles, but that the point where it crosses the ecliptic is not exactly the same as before. This is not really in a plane. It will, however, give us a clearer notion of the path of the moon, and of supposing this plane to be continually shifted, man would follow, as he does now, a different course than he actually takes. This plan is what we call shifting planes, and it may thus in some cases be very important to take into account this thing at all, or any extent, in realizing what the motion actually is. Looking upon this fact, surely one cannot help being struck by the fact that one may say that the moon moves in a plane, inclined about 3° 20' with respect to the ecliptic. But this inclination is still at the rate of 14° westward every lunation, so that it is only a very slight inclination.
Again, when the moon is observed through several observations, at points where she is at maximum or minimum of her greatest or least crescent, it is found to shift eastward by about 3° in every lunation, so that this inclination is not constant. The moon may be in a circle or ellipse, though for the reason given above it is not possible to suppose that she is always in a circle (or ellipse), which is continually turning round eastward at the rate of 3° every lunation, completing a circuit in about 27 days. In order to make this proposition plausible, it must be necessary to suppose the size and shape of this ellipse to change more than once in each lunation by changes of more than one-ninth when different
The plane of the moon's path may at any instant be deter-
mined by supposing it tilted 3° 20' clockwise along a plane,
which passes through its center and intersects the ecliptic
(note fig. 8). The lines marked A B C D show the points where
the moon was at maximum and minimum of her greatest crescent
at different times during one lunation. The moon's path
during this time may be drawn along line ZDZ', passing through
the center of the earth and intersecting the ecliptic at point Z.
This line ZDZ' represents the plane of the moon's orbit. The
angle between this plane and the ecliptic is represented by angle
A B C D. This angle varies from 3° 20' to 3° 20'.
longitude found by moon's motion.
functions are compared, the apparent diameters of the moon will be nearly equal to each other, but the actual diameters will be very different, according to their positions and dimensions! But, in answer to this, it must be remarked that these alterations are small, and that they do not affect the accuracy of the observations. It is by this mode of considering the question that the determination of longitude by the moon's motions aims at presenting her place at any future time, has been brought to a high state of perfection, and has been applied with great success to navigation, as the moon's somewhat rapid motion enables us to determine her position at Greenwich or Washington within a few seconds of an hour. The navigator selects a number of selected stars, and in this way to determine the longitude (which, as already explained, is simply the difference between the meridian on which he is situated and the meridian of Greenwich), thus fixing a ship's position at sea. This method is applicable only when the purpose of the hand is a clock which always shows Greenwich time. When we wish to find out what the minutes are not at equal distances; and the great object of the lunar theory is to tell us where those stations are situated, we cannot apply it without error. For instance, if we wished to find out what movements we were unable to alter the hands, and had no means of determining accurately what was the correct time. This question was considered one of such great national importance that the Royal Society of London appointed a committee in 1761, for the express purpose of watching the motions of the moon. They have made these observations for more than 100 years, and at every quarter of a century they send their results to the practical places of the moon, though these are of much
![]() A diagram showing the positions of stars and their relative distances from Greenwich.
PHASES OF THE MOON.
smaller amount than the uncertainty of measures of the moon's diameter, which is about 3000 miles.
It is now time to give an explanation of the most striking phenomenon connected with the moon. The sun always appears as a round orb, but not so the moon. This is called "the conjunction" with the sun, the first appearance presented by the young moon, a day or two afterwards, is that of a crescent, which is formed by the thinness of this crescent gradually increasing until it becomes full. The moon is at its greatest distance from the sun when the moon is 0° from the sun: from this point it moves towards the sun, and as it does so it becomes more and more convex, till when the moon is almost exactly opposite the sun at full moon, we see a nearly circular object. When the moon is between the sun and our eyes, or bottom only being wanting, according as she is near or far from us, we say she is in conjunction with the sun; and exactly opposite the sun. After this the west side of the moon begins to appear, and then we have a half-circle, but with the round side towards the east, the sun being now on that side; the crescent form continues to increase until it reaches its maximum at new moon approaches. Thus from last quarter to new moon, we have seen a crescent, and from new moon to first quarter to last quarter she is said to be gibbous. From last quarter to new moon we see a crescent, and from new moon to first quarter she is said to be gibbous. From first quarter to last quarter she is said to be gibbous. From last quarter to new moon we see a crescent, and from new moon to first quarter she is said to be gibbous. From first quarter to last quarter she is said to be gibbous. From last quarter to new moon we see a crescent, and from new moon to first quarter she is said to be gibbous. From first quarter to last quarter she is said to be gibbous.
One heavenly body is said to be in conjunction with another when they are in one line with each other, or when they are in other lines in direct line with each other, or due north or south of each other.
41
48
THEIR CAUSE.
verified by holding a white ball at man's length between the eye and the moon, the light falls on the ball turning round with its front right to left. Care being taken that the ball does not touch the moon, it will be found that the ball is always divided into two halves, a height end turned to the light and a dark
![]() A diagram showing the phases of the moon.
PHASES OF THE MOON.
In the upper figure a bird's view of the earth and moon is shown, with arrows indicating the direction in which the sun's light falls on the side of the earth opposite to that of the moon. The corresponding phases of the moon--the lower part, from new to full, is to be looked at upside down.
EARTH LIGHT—OCULTATIONS.
side turned away, and as the ball goes round us, more light will fall upon the moon, and therefore at least the whole of it is seen; but after this the bright side turns away, and we lose it altogether when the ball has gone round once. This is very evident to the eye. It will be noticed that the edge of the ball turned to the moon's back is always dark, and therefore not well seen, and this is just the case with the moon. The moon is always seen in one way, the circle being always away from the sun; but since it really shines, though on account of the overpowering darkness of the night, it does not appear to shine so much as it ought to do. This is shown by the fact that near new moon, when the moon is almost in line with the sun, faint, we can readily trace the outline of the whole moon, which is not visible at other times. This too contributes to the visibility of the dark portion at such times, viz., that this part of the moon is always turned towards us, and therefore we see it just as the part of the earth turned away from the sun is seen. But at full moon, when all parts of us to its is full earth to the moon, its ricey, and, consequently, we cannot see any part of it. At new moon, earthlight to the moon will be something like sixteen times as bright as at midnight is to us, that is, about six times as bright as at noon. This is about the same, as is probably the case. But besides this there are other causes which contribute to its being seen at night. For instance, we cannot see it in eclipses of the sun, and in occultations of stars. To take the latter first. It is clear that no star can be hidden behind another star (which are at an enormous distance from us) unless it be behind a body which is between them. Now in the moon's course will be hidden or occluded by a body which is between them. In this case we shall have to take place as soon as the cause of such part of the moon's circle comes up to our star showing that an opaque body having
50 ECLIPSES OF THE SUN.
this circular outline is interrupted between the star and its reflection on the water surface. The eye can easily peruse till it reaches the western edge of the same circle, where it will find that the moon has already passed this point. It is remarkable here that these oscillations of stars afford the most accurate means of determining longitudes where they are situated at night. The moon's appearance takes place quite instantaneously, so that it is impossible to see her before she appears, and only a second of time. As the plane of the moon's orbit is inclined to that of the earth's, it follows that during that period the moon will have occurred at some time or other every star which lies within 3° on either side of the meridian will have been eclipsed by the sun. This fact is very important, because it enables us to determine the exact position of the sun's centre in respect to our own station, since we know that all stars which lie within 3° of the meridian must be eclipsed by the sun. We can thus ascertain the points where the moon's path cuts the ecliptic, and also those places where it does not cut it. If we look above or below the sun, being tilted out of the ecliptic. If the new moon takes place exactly at the node she will be seen at its greatest elongation, and if she takes place at any other point, then one of the two nodes belongs on the average about equidistant from us and from the sun. The distance between us and the sun is known with great accuracy, but we do not know how far away from us the node is. In order to find this distance from us, especially in the case of the new moon, we must observe when it passes through the line of sight of our telescope (the line of sight of our telescope is called a transit). When the moon's light cuts off for a few minutes (a total eclipse), and at other eclipses (known as annular) there is no interruption in her light, we can observe her light from the sun round a black circular disc (the umbra) which surrounds her. If this umbra touches any star, none or less of the star's disc will be cut off, and we say that this star is in transit. Now it happens when the moon's centre appears to pass within the distance of her radius from the sun's edge, which will be equal to 17°. If this condition does not occur it is greater than 17°, or when the passage occurs outside this limit, we call it a new moon. But though an eclipse will occur under these circumstances, sometimes places on land will not see eclipses at any particular moment because of season.
ECLIPSES OF THE MOON.
and total or annular eclipses are exceedingly rare, for a change of 30° in the longitude of the earth will throw the moon out of the direct line between him and the sun, so that he cannot see it at all, or at one place when it is at so another a little north or south of it. There will be no total eclipse visible in this country until the year 1857, and then only in being a d. n. 1867. As the moon sometimes cuts off the light of the sun from the earth, and sometimes allows it to pass through her, she may be said to cast a shadow on the earth, and the moon passing into the earth's shadow, and so disapparing, more or less completely, through the sun's rays, is called an eclipse of the sun. The same thing happens by eclipses in our atmosphere, owing to which effect the moon is often called a "darkness" or "shadow." The moon's shadow barely reaches to the earth from its diameter, but owing to certain circumstances, throws a black spot on the earth not more than 120 miles in diameter; but the earth being very large compared with this spot, it is seen far beyond the moon's orbit, and is at the distance of about 100 million miles from it. This is nearly half a million times its diameter. If this moon when full be near enough to take place, and this will happen whenever the dis- tance from either moon at opposition is less than 100', the moon will appear to pass through her own shadow. This passage seems an eclipse. Unlike an eclipse of the sun there is no such thing as an eclipse of the moon; for when the moon is above the horizon, l. c., on the hemisphere where we are situated, she does not cast any shadow upon us; and therefore no matter what position of the spectator not affecting the entry of the moon into the earth's shadow. From the earliest times men have been observing eclipses of both suns and moons, having in one notable instance (the eclipse predicted by Hipparchus) a difference of 12 minutes between his time and that of Julius Caesar, as related by Herodotus, so that a method of measuring time was found by means of these eclip- ses of years could be found, such eclipses would
![]()
![]() Diagram showing the positions of the Sun, Earth, and Moon during a solar eclipse. |
![]() Diagram showing the positions of the Sun, Earth, and Moon during a lunar eclipse. |
![]() Diagram showing the positions of the Sun, Earth, and Moon during a solar eclipse. |
![]() Diagram showing the positions of the Sun, Earth, and Moon during a lunar eclipse. |
ECLIPSES OF SUN AND MOON.
The sun ought to be removed to nearly 400 times the distance at 6, and to be 25 times as large. The earth and moon are very much less proper sizes.
II
CYCLE OF ECLIPSES-GOLDEN NUMBER.
In the same order in each successive cycle, the questions of the moon's motion and its eclipses become necessary for an eclipse - (1) The moon's node moves through 360 degrees in 18 years, and therefore, at any given time, the moon is new for a solar, or full for a lunar eclipse. If, then, after one such period has elapsed a complete exact revolution with the sun, the moon will return to the same place again, whilst in the same time the earth will have moved on through 18 degrees. The moon is again new or full, as the case may be, under similar circumstances. The Chaldeans discovered such a period, which they called a cycle of 18 years and 11 days, in which the nodes move through 360 degrees with respect to the sun, which differ from 223.5 degrees that happen at any particular date, it will recur after 18 years and 11 days. This is called the "Golden Number," thrown beyond the limit for an eclipse by the accumula- tion of the lagging in 11 hours for each cycle; an average of 18 years and 11 days being required for a cycle of 18 years and 11 days for some 1000 years, and one of these cycles being completed every 223.5 degrees. The lagging of the node interferes with its regularity.
A consequence of this is that when the moon is new or full, it gives the days on which the new moon occurs is called the Metonic ecycle, from which it derives its name. It was discovered by Ptolemy in 140 A.D., corresponding almost exactly to 255 lunations, or about 27.2 years. In this cycle, however, eclipses fall regularly after this interval; the number of eclipses per year in this cycle is called the Golden Number.
A consequence of the moon's moving in a path in- clined to that of the earth is that it causes seasons of some importance to the farmer. From the tilt of the earth's axis towards the sun during summer, we get the equator, and is partly easternly and partly north of it. When the sun is at its highest point in the sky, the sun is at the vertical equinox, her northern moth- nents are most rapid, and in high northern latitude it
HARVEST MOON—PARALLAX.
nearly parallel to the horizon, so that her motion east and west is very slow, but her motion north and south is rapid, being indicated by the northern part of her motion, and con-
sequently she appears to move more slowly than she does actually, nearly the same time on two or three successive nights, and this will happen once in every lunation. There is another cause which may account for this effect, viz., when the full moon falls at this part of the orbit, for instance, at the beginning of September, the sun is then in Sagittarius, and thus gives light enough to get in the harvest,
and consequently the moon will appear to move more slowly than in other cases; in this case, the moon is fall in the vernal equinox, the sun,
which is exactly opposite, must be at the autumnal equinox, which is nearest to September 23. In England and France, this effect has been observed for several weeks before this, but in many countries this length-
ening of the day by the harvest moon is of great
value.
The moon's distance from the earth has been very
greatly exaggerated by astronomers, owing to the fact that as an observer moves forwards, objects on
his right hand appear to move with greater rapidity proportional to their distances from him, an-
d those on his left hand appear to move with less
rapidity. Thus, when he moves towards his mo-
tion, the trees and houses in the landscape appear-
ing to wheel about a point in the extreme distance on
his right hand. This is called parallax. As we advance everything will appear to move a yard back-
wards for every mile we go forward. The angle subtended by a yard at the distance of the
moon is one second of arc; therefore, if we measure
the more distant objects by measuring them,
the angular shift of any object, we determine the angle subtended by it at our distance. By measuring
object and house until they reach distance. For an
example, let us suppose that the circumference of
360° being 31 times the diameter (distance),
whereof we have only 30 days; that is we measure
about 27°50' to find how many times the radius contains
DISTANCE OF THE MOON.
the arc, which, in the case we are considering, is one yard; the number of times so found will, of course, give the distance in yards. It is not necessary that the object shall be placed at any particular distance from the observer's eye; but it is convenient to place it at a point where the angle subtended by it is large enough to make the calculation easy. The method is easily applied for whose accurate calculations are required.
Now let us apply this principle to the case of the moon, remembering that the distances we are here concerned with are very great compared with those of the earth. We have only to deal with thousands of miles in the plane of yards, and to find how many yards correspond to a given fraction of the hemisphere visible to the moon, which is, therefore, equal to 360 degrees. In order to do this, we must first determine the north horizon in the orbit of the moon. The southern observer will see the moon shifted north among the stars (which he would call south) when he looks towards the zenith; and as the angular diameter of the earth seen from the moon is about 1°, it follows that the fraction that the earth's diameter is of the distance of the moon's orbit is equal to 1° divided by 360°, or 1/360. This fraction being known, it is easy to find what part of the circumference of the moon's distance is easily found in miles. But in practice it would not be very easy to make observations at such a distance as that of the moon; and it would be better to be satisfied with a rather less shift in order to get rid of the uncertainties of refraction near the boundary of our atmosphere. For this purpose are those of Greenwich and Cape of Good Hope, at both of which the moon is observed with sufficient accuracy for determining its distance; and as a large number of observations are available, the accuracy may be expected to be high.
The mode of determining the moon's distance by observation at these stations has been described in my "Astronomical Almanac," and I need not repeat it here. As far as I am aware, no other method has been suggested for determining its distance except by means of a telescope; but this is not so desirable as the ideal case given above, because the matter may be made clear by the following consideration. From every position on earth, say A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z (fig. 1), we can observe a certain part of the moon's disc; and if we plot down all these points corresponding to different positions on earth (fig. 2), we shall obtain a curve representing a portion of a sphere. Now if we draw lines through each point parallel to a line drawn from some fixed point on earth (say A), we shall obtain a series of circles concentric with that line; and if we join together all these circles we shall obtain a series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say A and B), and draw a line between them parallel to another line drawn from some fixed point on earth (say C), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say C and D), and draw a line between them parallel to another line drawn from some fixed point on earth (say E), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say E and F), and draw a line between them parallel to another line drawn from some fixed point on earth (say G), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say G and H), and draw a line between them parallel to another line drawn from some fixed point on earth (say I), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say I and J), and draw a line between them parallel to another line drawn from some fixed point on earth (say K), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say K and L), and draw a line between them parallel to another line drawn from some fixed point on earth (say M), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say M and N), and draw a line between them parallel to another line drawn from some fixed point on earth (say O), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say O and P), and draw a line between them parallel to another line drawn from some fixed point on earth (say Q), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say Q and R), and draw a line between them parallel to another line drawn from some fixed point on earth (say S), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say S and T), and draw a line between them parallel to another line drawn from some fixed point on earth (say U), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say U and V), and draw a line between them parallel to another line drawn from some fixed point on earth (say W), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say W and X), and draw a line between them parallel to another line drawn from some fixed point on earth (say Y), we shall obtain another series of circles concentric with that line; and if we join together all these circles we shall obtain another series of arcs which represent portions of a sphere. If now we take any two points on these arcs (say Y and Z), and draw a line between them parallel to another line drawn from some fixed point on earth (say Z'),
EQUATORIAL HORIZONTAL PARALLAX.
The left hand figure represents the disc of the moon as seen from five stations on the earth; the lower figures represent the same disc as seen from six different stations, marked out by the moon as seen from different places of the earth's surface. The light for so, as looked at from out- side a celestial globe.
moon is at the given instant on the horizon, and the line joining its centre to the observer is parallel to the horizon. The earth's disc as seen from the moon, not being a plane, but a sphere, has a parallax equal to half the angular diameter of the equator, the horizontal parallax being measured at the equator, since the two points where the equator intersects the horizon are equally distant from the moon, and therefore have equal parallaxes; this value is called the Equatorial Parallax. It is also observed that on account of the earth's rotation the disc visible
![]() A diagram showing a celestial globe with a line drawn from a point on the horizon to another point on the horizon, representing the apparent shift of position of an object due to Earth's rotation. The diagram includes labels for "Equatorial Parallax" and "Horizon Parallax".
PARALLAX OF THE MOON.
The left hand figure represents the disc of the moon as seen from five stations on the earth; the lower figures represent the same disc as seen from six different stations, marked out by the moon as seen from different places of the earth's surface. The light for so, as looked at from out- side a celestial globe.
moon is at the given instant on the horizon, and the line joining its centre to the observer is parallel to the horizon. The earth's disc as seen from the moon, not being a plane, but a sphere, has a parallax equal to half the angular diameter of the equator, the horizontal parallax being measured at the equator, since the two points where the equator intersects the horizon are equally distant from the moon, and therefore have equal parallaxes; this value is called the Equatorial Parallax. It is also observed that on account of the earth's rotation the disc visible
METHOD OF FINDING MOON'S P.P.B.L.A.X. 57
to the moon is continually changing, and that, consequently, the parallax at any place changes as the moon rises or sets. The moon being in the zenith of the observer's meridian, the parallax is zero; but for that position of the moon, and increases as she moves away from the zenith. As the moon is on the meridian of Greenwich, it is easy, from her position, to find the apparent distance of Greenwich from the middle of the earth's dih., as soon as the moon, is off of the dih. by one degree. For this purpose, let us take two fractions together, the proportion of the apparent distance of Greenwich from the meridian of the Cape Observatory, the corresponding fraction of the diameter of the earth, and their sum will give the shift far the two extremities of a diameter.
The shift corresponding to Greenwich and the Cape is shown in Table I. It will be seen that these shifts are very nearly equal to those obtained by comparing with those of selected stars at both observatories, and that they agree well with respect to stars near; allowance being made for the difference between Greenwich and Cape Observatory in their meridians of Greenwich to that of the Cape. In this way it is found that the shift for two extremities of an arc is about 0.0036 degrees per second. This gives a diameter of the earth's disc at the moon's average dis- tance from 388 times its distance (33,400 miles) at 1° latitude. The moon's distance is therefore (since $d^2 = r^2 - l^2$) $\sqrt{r^2 - 33400^2}$ where $r$ is the earth's radius at the equator, or 399 times its diameter, which is about 230,000 miles. Since the moon's apparent di- stance from the earth is about 1°, it follows that the real diameter of the earth is about 1° × 399 = 399 miles. The moon's distance from the earth being very nearly 3150 miles. We may now proceed to calculate how much we know about the sun, for we see that while she is moving round the earth at a distance of 88 times its diameter (33,400 miles), he sun at 88 times this distance (31,500 miles)
In MOTION OF MOON ROUND THE SUN.
earth's radius) once a year, and carrying the moon round the earth once a month. The path of the moon is drawn of four inches radius to represent the path of the earth round the sun, and that of the moon round the earth into 13 parts about; and supposing the moon at these points to be represented by a point, we shall see that the moon is always within the middle of the line representing the circumference of the earth, and that she is always on one side of the line representing the circumference of the earth, so that her motion will be altogether in one direction. But this is only true when the moon is in the middle of her course, and therefore it is evident that her motion must be in two directions, viz., towards and away from the earth. This is easily seen by considering what happens when the moon is in opposition to the sun. In this case she is on one side of the line representing the circumference of the earth, and therefore she must be moving towards it; but when she is in quadrature with the sun, she is on the other side of the line representing the circumference of the earth, and therefore she must be moving away from it. This is easily seen by considering what happens when the moon is in opposition to the sun. In this case she is on one side of the line representing the circumference of the earth, and therefore she must be moving towards it; but when she is in quadrature with the sun, she is on the other side of the line representing the circumference of the earth, and therefore she must be moving away from it.
The revolution of the moon round the earth marks its circumference and also its deviation of her path from a true circle (or nearly a true circle), which deviation may be perceived by the eye on each scale. It may seem strange that such a small body as a moon can make an ellipse round the earth when she really moves very nearly in a circle about it; but this is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while it appears as though she was moving in a circle, yet it is sufficient to remark that while它
ELEOTRIES OF THE MOON.
move round the sun in nearly circular paths, so long as we confine ourselves to the relative motions of these two bodies, without reference to any real (as dis- cussed in the preceding chapter) motion of the earth among the stars.
The peculiar facility of the moon which striketh every one who watches her disc through a tele- scope, by its rapid rotation on her own axis, is owing to the earth as she circulates round it. Now this can only arise from her turning round on her own axis in such a manner that she always presents the same face towards us, though at first sight it may seem a little difficult to understand how this can be done, but it will be seen if we allow any sign of it to us. A little consideration of the motions of the two bodies will show that their mutual motion of two bodies will remove this difficulty. It was there pointed out that, as far as the two bodies are concerned, they move in circles about each other, and that the same is true of a spectator on either the earth or the sun, and that they both move in circles about the earth, and that so long as we were dealing with perfect bodies, all would have been well; but in fact there is a force which expression we used. Now the same prin- ciple applies to the earth and moon ; so that so long as we consider them as perfect bodies, all will be well; but not her motion among the stars, we shall have the same difficulty as before. For instance, if we suppose the moon, as in the actual case. But if the earth be supposed to be stationary, then, according to our former suppositions, the moon must turn on her own axis exactly at the same rate as she revolves round the earth. To represent the moon's motion round the earth, we must suppose her to turn on her own axis more than once in a certain time faster and sometimes slower; so that she is alter- nately presenting one side to us and then another. In her proper place, just as in the case of the sun ; the moon, on the other hand, turns quite uniformly on her own axis. This difference between their motions is very great; for while the moon makes one revolution round the earth in about seven days, and thus moves over a much greater distance than does the sun in a similar time, yet she makes only one revolution on her own axis during that period. The reason why this difference is not observed is because we see only one side of her at any one time; for when she is turned away from us by half a revolution, she is turned towards us again by half a revolution; and thus we see her always from one side. Now let us suppose that we could see her from all sides at once; then we should see her always from one side. We should see her always from one side at once; then we should see her always from one side. We should see her always from one side at once; then we should see her always from one side. We should see her always from one side at once; then we should see her always from one side. 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6) HEE ASPECT—ABSENCE OF ATMOSPHERE.
round the other side at another, through her out-
sized aperture, and thus obtain a view of the sun's
disc. The moon being such a very near neighbor of ours,
astronomers have been enabled to observe her disc, which
has been studied with great success by means of powerful
telescopes, and careful charts have been made in which
the different parts of the disc have been accurately de-
scribed. The disc of the moon has been laid down with an accuracy suggesting that of the sun's disc. The moon is about 380,000 miles distant from us.
The moon is about 380,000 miles distant from us. At this distance, therefore, the moon appears to us as a point of light. But when we approach within about 500 miles, a distance at which the principal features of a country would readily be visible, the moon appears to be quite distinct of any appreciable amount of atmosphere between herself and us. When we look at the moon rays from a star grazes her surface just before an occultation takes place, and then disappears behind her disc. The absence of atmosphere exposes the moon to most violent changes of temperature, the surface
being heated during the day and cooled during the night. This is shown by the fact that when we look below the freezing point during the heating period of a day, and above it during the cooling period, we find that the surface is always covered with ice. In consequence it is fatal to any form of life with which we are acquainted.
The moon's surface almost everywhere shows signs of violent volcanic action far exceeding anything found on our own earth. There are many craters on its sur-
face, which are found all over, from eighty miles across to less than one mile in diameter. These craters are
gathered closely in many regions that they overlap each other. The great peculiarities of these lunar craters is that they are filled with water. This water is found on the outside surface, as may be shown by measuring the length of a line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from the center of a lunar crater to the floor and on the surface of the moon next to it. A line drawn from
LARGE SIZE OF CRATERS.
of the crater from the illuminated edge to determine the height of the rim of a crater or of a mountain, and in this way to ascertain how high the moon has been obtained. Although the moon is only a quarter the diameter of the earth, there are both mountains and craters on its surface which are elevated peaks on the earth; nor is this to be wondered at, since the heat of the sun falling upon a body of volcanic energy is less for a small planet; whilst gravitiy, and therefore weight, being less, would cause a smaller body to be raised into a higher position than one of greater weight. The elevation of mountains is not so great as that of craters on the moon. Though such craters and mountains are not visible from the earth, yet they are more frequent, there being only three principal ranges of mountains, called respectively the Alps, the Pyrenees, and the Himalayas, presenting a marked contrast to the earth. The craters on the moon are much larger than those on the earth; whilst the southern portion of the moon is remarkable for its craters. The craters on the earth are of various kinds, of which Tycho, seems to form a centre of eruption, from which proceed in all directions bright rays, ex- cepting those which fall upon the sea. This crater is over fifty furlongs in breadth and some hundred in depth; it is situated at a considerable height, and with its system of radiating streaks is dis- tinctly visible from the earth. Similar systems of bright rays proceed from several other craters, among which may be mentioned Copernicus and Tycho. These rays appear to be at the boundary of the bright part of the moon a day or two after their origin; but they soon become invisible and come into view as an exceedingly bright spot in the sky. It is probable that these rays are due to eruptions; and I have before stated that they suggest itself with reference to these rays, that they are streams of lava flowing from the
62
BRIGHT EATS—PLAINs ON MOON
craters, but a fatal objection to this explanation is that the moon has no atmosphere, and therefore cannot retain any regurgitation of the dust of its surface, and can actually be seen at night. The craters have been formed before this eruption, the way in which one crater overthrows another affording an indication of the manner in which they were formed. It is evident that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption, as yet seems to be that the rays are cracks, like stars, and that the rays are not the result of a recent eruption.
It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It is evident from this description how much more plausible it is than any other theory for explaining these phenomena. It
CHAPTER IV.
Hayton discussed some theories on what he thought was happening with respect to studying our moon's movements around us.
The planet Venus appears in our sky about 30 degrees below our horizon at sunset or sunrise; when she rises in her morning aspect she appears about 50 degrees above our horizon at sunrise; when she sets in her evening aspect she appears about 50 degrees below our horizon at sunset; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian she appears about 180 degrees above our horizon at noon; when she passes through her meridian
![]() A diagram showing Venus' apparent motion across Earth's sky.
MOTION AND PHASES OF VENUS. 61
evening star, setting soon after the sun; it can be found that her angular distance from the sun increases day after day, till after seven months she arrives at a point where her diameter is equal to that of the sun. At this time she begins to approach him again, and after another two months she has reached the same position as at her original time, whilst she goes through phases like the moon, from nearly full when first seen, to a crescent, and then back to full again. After a short interval she may begin piqued up, but, as the sun's light is too weak for observation, continued watching will show that her distance west of the sun remains constant until she reaches the distance east of the sun, and then that after reaching it $x$ it diminishes for the next two months, till she is again at the same point as before. The variations in size and changes of diameter corresponding to those seen by the naked eye are very small indeed, and may be watched more closely with a telescope, which will show that they are not uniform throughout the planet, the corresponding quantities being also different for different parts of the planet. The longitudes and declinations of both bodies are found, and therefore their motions are known. From these observations the motions above described, it appears that Venus moves in some way about the sun, never getting very far from him; and that when she changes from a morning to an evening star, her motion is towards him. Her phase shows that when nearest, or in inferior conjunction, she is beyond the sun; so that we see this side of her face when near new, whilst when furthest out, or in superior conjunction, she is behind the sun; so that we see this side of her face when near full. Hence we may conclude that Venus shines by light reflected
64
ORBIT OF VENUS
from the sun, though she is never seen in the quarter of the heavens which is opposite to that of the earth at the full moon. It follows from all this that Venus de-
scends into the earth's sphere every 30 days, and that consequently she is always inside the earth's path; the time she takes to complete a revolution with respect to the earth being about 224 days. During this period she must have made 32 revolutions round the sun, and therefore, since her revolution is one year, and that period must have been 7 years and 8 months, or about 84 days (more exactly 842 days), which is somewhat over 7 years. This is a very remarkable fact, as it shows that Venus described by Venus is a more complicated matter, than what we might suppose from the simple appearance of the earth's positions as seen from the sun; but when we consider that Venus describes an ellipse round the sun, and that this ellipse is inclined to the plane of the ecliptic, so that the earth's position is not always in the same place with respect to the earth's path. Since Venus describes an ellipse round the sun, and comes from us in superior conjunction, we may conclude that the diameter of her per-
hit,bit, which is the difference of her two great axes, must be five times greater than her distance from the sun; so that her distance from the sun is about 24 times and the earth's distance from the sun about 150 times. But this does not include only her distance from the sun; it is divided by 32, or about 4 of the earth's distance from the sun. Hence we see that Venus describes an ellipse whose greatest angular distance from the sun (or elongation) is about 1 degree and 3 minutes. A similar angle of sound bower may be found by observing the angle between two lines drawn through two points on the centre. We shall see presently how the relative dis-
ORBIT OF SECRECY, 65
tances of the planets may be determined more ac-
curately indirectly by means of their times of involution,
or years as they may be called.
In the case of Venus, Mercury, whose motions
are similar to those of Venus, though he is much closer
to the sun than she, his period of revolution is shorter;
circumstances, when his angular distance is greatest,
and therefore his apparent motion most rapid, will
pass through all its phases in four months (nearly 11 days)
whereas it follows, by the same reasoning as in
the case of Venus, that Mercury's orbit is much smaller
(more exactly 88 days); the distance from the sun
being less than that of Venus. In the case of Mars,
Mercury's orbit being much more oval. His distance
from the sun varies considerably during his revolution,
an increase or decrease of one-fifth of its mean value,
which causes a change in the maximum elongation from
that which would have been produced by a circular orbit.
In this planet's motion there is the case of Venus,
whose orbit is also very elliptical. In both these cases,
as their orbits are within that of the earth; the other
planets being outside it, they cannot be seen at any time
being limited to a certain distance from the sun, but,
moving westward from him continually, they arrive at
the point where they are seen at their greatest elongation
when moving westward respect to the sun, they begin to
appear in the morning sky. The same thing happens with
regard to the sun itself; for when he is seen at his greatest
elongation towards the east, he is seen in the evening sky.
A complete circuit of the sun in an eastern direction
with reference to the sun, the result of the sun's appar-
ent motion being observed by us, is a complete circuit
of the planets, in consequence of which they lag behind him;
but when he is seen at his greatest elongation towards
westward like the sun, but slower, and with periods of
about 30 days. To fix our ideas let us take the case of the planet Mars.
Starting from conjunction with the sun, Mars will
(by solar time) every day till he comes to opposition,
6
68
MOTION AND PHASES OF MARS.
at which time he passes the meridian at midnight.
Exactly one year later, on the same day at the same hour,
continuing the same course he now rises before sunset
and sets after sunrise, and so continues until he reaches
the star, which he continues to be until his westward
course with respect to the sun is completed. He then
returns to the same star again at the same time,
and is thus lost in his rays. The period of these
changes is two years and two months exactly, during
which time the earth has gone one revolution on Mars,
as he has been continually lagging behind her.
Since 1570, therefore, it appears that Mars must have made 24 revolutions in 22 years, whereas his year
is 684 days long. This is a very remarkable fact;
for at this time no man has presented to us a fair, or nearly fair, disc,
a star, or any other body in the heavens, whose
size does, such as he can never be between us and
the sun, as is the case with Mars. It is evident that
he must therefore be an orb about the sun
(which extended observations show to be somewhat
smaller than our own), and that his orbit round
being in the proportion of 9 to 113, and that this orbit
is always in opposition to ours. Now Mars is five times at great in opposition as in con-
junction, while the earth's position is much more im-
portant from us than in the former by the breadth of
![]() A diagram showing a circle divided into four quadrants labeled "EAST," "WEST," "NORTH," and "SOUTH." The center of the circle contains a smaller circle with a line drawn through its center, dividing it into two equal parts. The larger circle is divided into four equal parts by lines radiating from the center. The smaller circle is also divided into four equal parts by lines radiating from its center.
which time the earth has gone one revolution on Mars,
as he has been continually lagging behind her.
Since 1570, therefore, it appears that Mars must have made 24 revolutions in 22 years, whereas his year
is 684 days long. This is a very remarkable fact;
for at this time no man has presented to us a fair, or nearly fair, disc,
a star, or any other body in the heavens, whose
size does, such as he can never be between us and
the sun, as is the case with Mars. It is evident that
he must therefore be an orb about the sun
(which extended observations show to be somewhat
smaller than our own), and that his orbit round
being in the proportion of 9 to 113, and that this orbit
is always in opposition to ours. Now Mars is five times at great in opposition as in con-
junction, while the earth's position is much more im-
portant from us than in the former by the breadth of
MOTIONS OF THE OTHER SUPERIOR PLANETS. 6.
the earth's orbit, which is therefore, four times his distance.
The earth's year is nearly one-eighth of Jupiter's. From this we may
see that the earth's distance from the sun is twice her own diameter,
between him and the sun, whereas the distance of Mars from the sun is three times his least distance
![]() A diagram showing the relative distances of the planets from the sun.
UNIVERSAL KEY
from us, or 14 times our distance from the sun. The earth's year is therefore similar. Jupiter's year is nearly twelve of ours, the intervals between successive oppositions being about two years and six months; his distance from the sun is rather over ten times our diameter, and his least distance from us only varies from four to six times the earth's diameter. Saturn's year is nearly twenty-four of ours, and his succes-
sive oppositions for Saturn are only a fortnight over a
year, in which time he must have described one-third
of his circuit round the sun. Uranus has been seen by
ours, and his path round the sun is described at a disti-
ance of more than five times our diameter. Of all the planets known to the ancients, but two more
![]() A diagram showing the relative distances of the planets from the sun.
UNIVERSAL KEY
THE ASTEROIDS.
have been added since—one of which, Uranus, dis-
covered by Sir William Herschel in 1781—has a mean
distance from the sun, and has a year about 84 days in
length. The period of revolution of the earth through its attraction on Uranus is 30 times as fast from the sun as we are, and its period is 164 of our years.
Besides these, there is a class of bodies called Aster-
oids, which have been discovered since the year 1850,
on the first day of this century; about 220 of them being
known at present. Each of these bodies adds one to
every year adds some to the list. These bodies are
as minute as they are numerous; probably none of them
are more than 10 miles in diameter, and many are not
much more than 10 miles. Their orbits all lie be-
tween the orbits of Mars and Jupiter, and their periods
from 2 to 32 times that of the earth, with periods of
from 3 to 6 years. The orbits of these very oval and
marked contrast to the orbits of the large planets.
These asteroids form a connecting link in the gradation from the large planets to the small ones, and those which perhaps constitute the asteroidal light and form the boundary between the planets and comets.
It is probable that these small bodies, so different from the primi-
tal planets, may perhaps be the result of an explosion, when the sun was formed. It is possible that this ex-
plosion in an orbit intermean between those of Mars and Ju-
piter might have produced these asteroids.
Though this theory would account for certain peculiarities
in their motions, yet it does not explain why any such supposition is a great catastrophe removed by the
discovery of systems of much smaller bodies, the mate-
rial of which must have been derived from the sun. But
great difficulty in accepting it, that the asteroids hav-
ing no other source but the sun, cannot be explained. They
cannot come round the sun, all return to it, so that all their orbits ought to have some common point of intersection.
Which is not only not the case now, but he as
MOTION OF PLANETS AMONG THE STARS. 65
we can judge from theory, never could have been true unless the present orbits have been disturbed by some unknown cause.
We have confined our attention to the apparent motions of the planets with respect to the sun, and we shall now consider their motions with respect to each other, by allowing for the motion of the sun among the stars as a whole. This will enable us to see how far the motions of the planets differ from those of the sun.
The first point of which we must take account is that, since they move nearly uniformly in circles about the sun, they cannot all be at the same distance from him at any one time. The nearer ones are always near the sun when they are near us. It is further necessary to allow for the fact that they do not all move in the same direction, but that they oscillate about the sun, moving sometimes towards him and sometimes away from him. The latter move round and round always eastward, as explained above. Taking any inferior planet at such a moment as that when its motion is westward, it will be found that it is moving away from the sun, and the sun is moving eastward among the stars. If this planet continues to move westward, it will continue to move away from the sun until it has gone so far eastward, or direct, as it is called; this will continue until it has moved so far westward that it has come out on the opposite side of the sun. At this point it will have come quite out to the sun's motion among the stars, when for a moment it will be stationary among them. Then it will begin to move towards the sun again, and will continue to do so until it has reached a point where its motion among the stars is exactly equal to that of the sun. When this happens, it will be in retrograde motion, and will continue so until it has passed through a circle of 360 degrees around the sun. After this it will again begin to move towards the sun and will continue so until it has reached a point where its motion among the stars is again equal to that of the sun. This process will go on indefinitely, and will be repeated every time that the sun does pass among the stars, its motion being reversed each time.
This will always be the case as inferior conjunctions occur for several planets more frequently than they occur for others. The reason for this is that those planets whose orbits are nearest to those of the sun change their distances from him more rapidly than those whose orbits are farther away. Venus takes less than half a day to cross by the earth, but her distance from us changes less than $\frac{1}{2}$ of a second; Mercury takes less than $\frac{1}{2}$ of an hour; Mars takes less than $\frac{1}{2}$ of a day; Jupiter takes less than $\frac{1}{2}$ of an hour; Saturn takes less than $\frac{1}{2}$ of a day; Uranus takes less than $\frac{1}{2}$ of an hour; Neptune takes less than $\frac{1}{2}$ of an hour. The velocities of the different planets are given in the table at page 78.
Let us now take the case of a superior planet. In
50 CAUSE OF APPARENT RETROGRADE MOTION.
conjunction its motion westward with respect to the sun's center, and when the conjunction is at opposition, resulting motion among the stars is eastward or direct, according as the conjunction is before or after the sun is approached, the motion westward with respect to the sun's center being equal to the sun's motion eastward or stationary among the stars, after which, the westward motion among the stars ceases, and the earth moves among the stars in a westward or retrograde direction.
It is evident that this explanation is correct, but it is desirable to explain how they follow from the motions of the planets in their orbits with the consideration of their positions.
At conjunction, the earth is between the sun and an inferior or superior planet, the earth and the planet being on opposite sides of the sun. When moving in opposite directions, so that the earth's motion appears westward, the effect of a motion of the spectator being, as explained before, to make objects move in the same direction as themselves. At conjunction, therefore, an inferior planet, or at opposition for a superior, the earth appears to move westward, while a superior planet appears to move in the same direction; in the case of an inferior planet at conjunction, or a superior at opposition, the earth is westward, as seen from the earth, which is outside the orbit, in the same way as sun appears to move westward from a point outside his orbit. Although such a rotation is like the motions of the earth and moon around each other. But at conjunction the planet appears to move westward, as though it were moving in a circle round the earth. The actual velocity and that of the earth; this would be for Mercury about 11 miles, and for Venus about 3 miles per second. At opposition, however, because of its greater distance from the earth, the earth's motion makes the planet appear to move eastward in its orbit, so that the apparent motion of a superior planet at conjunction is eastward with a velocity of $\frac{3}{2}$ miles in a second. Jupiter with
ITS AMOUNT
A velocity of 10 miles, Sause of 12 miles, Uranus of 14, and Neptune of 11, showing the difference between the earth's velocity and that of these several planets in their orbits. Of course in conjunction and opposition.
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The apparent motion of the several planes in cyclic order.
CONJUNCTION AND OPPOSITION OF VENUS, MERCURY, THE EARTH, AND MARS.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
The apparent motion of the several planes in cyclic order.
Since Mercury and Venus pass between the earth and its sun at conjunction, they will sometimes appear to us with less light than when they do not size the quantity of light they cut off, when directly
TRANSITS OF MERCURY.
between us and the sun, is scarcely appreciable, these transits being usually accompanied by a few small round black spots, on account of which these phenomena are sometimes mistaken for eclipses. As in the case of eclipses caused by the moon, such transits will only occur when the planet is near one of the nodes of its orbit, and at this time, owing to its inferior conjunction, when it next comes to inferior con-
junction with the sun, it will appear to pass between the earth and the sun, and then between the earth and the sun. Next time the earth will have moved about 30° in its orbit since the last conjunction, and at the third conjunction will have returned nearly to its place of first conjunction, so that we shall have very nearly one revolution; if it had come so exactly to the same place as before, we should have had two conjunctions the earth has still about 4° of a revolution (77 days) to go, and therefore too far from the sun to be seen. The earth will now be at a second revolution, short, and so on, until after 24 conjunc-
tions it will again be at a first conjunction. At this starting place, so that the next conjunction brings it back to its place of first conjunction, Mercury having completed 29 revolutions in 7 years, very nearly, and another transit may now take place. The earth will then move about 30° in its orbit in seven years, so that after thirteen years there is a third conjunction. After another thirteen years there is a fourth conjunction; during this interval, though the eccentricity of Mercury's orbit is much greater than that of any other planet, all this refers to one node only; at the other three will be another series of transits.
The period of one year is 8½ of our own; the return to the node will take place very nearly after 8½ years; but as Mercury moves more slowly than our moon does, only 1 day in 15 months may again transit the sun, but after twelve years may be left there again; and this is the truth which takes place; no transit will occur; nor
will one take place again till after ten years, when the error of 14 minutes of arc in Venus in every eight years has amounted to one-fifth of 223 days, so that the transit will occur at the same time of the year in eight years at different parts of the orbit of Venus. The transit of Venus on June 6th, 1769, was observed by Halley, and the transit of Venus in 1874 will be observed by the same observer. The transit of Venus is in a line with the earth at the beginning of December, and transits have taken place in that month since the year 1639. The transit of Venus in 1874 will be seen at the descending node the transits, which occur always at the ascending node. Transit of Venus is also the greatest value to the astrono-
mer, because he can determine the distance between the earth and the sun by observing the sines of distances, and thus fixing the scale of the whole solar system. This distance of the sun is so great that it cannot be determined by any means on the earth, that his parallax can not be determined with any degree of accuracy. But this is not true of Venus, but as the planet Venus, when nearest, is only 4th of the distance of the sun from us, we can determine its distance by means of its parallax, which is greater than that of the sun. Even this quantity is very small, and instead of attempting to determine it directly it is better to observe its motion relative to other stars. This is a slightly different problem from the other, for in this case we must consider that all stars are moving on the same straight line, the nearer appears to be shifted relatively to the other by a shift in the space occupied by them. In this case, however, all bodies may be removed to twice their distance from the spec-
tator, the amount of this shift will be halved, whilst if they are removed to three times their distance it will be doubled. If then the proportions of these dis-
tances be known, the shift of parallactic displacement may be calculated. In this way we can determine in the case of Venus and Mars, the proportion of their distances from us by means of the periods of revolutions of Venus and
Transits of Venus
70
DETERMINATION OF SUN'S PARALLAX
The sun's equinoxes will be in the same place on Venus being 1. The shift of Venus being 3. times that of the sun, and 6. times the sun's parallax. The most accurate way of measuring this parallax would be to refer it to the very slow motion of Venus in her passage across the sun's disc, by noting at two stations where the sun is seen to enter wholly on the sun's disc, or to begin to leave it, and then to measure the time between these two observations, which will be the greatest effect on the time of ingress, the shift must therefore be measured with great accuracy, and therefore the two stations should be separated from each other in the direction of a line joining this point with the centre of the earth.
In the transit of 1874 Venus crossed the northern hemisphere, and in 1875 she passed through Australia, and in 1876 she passed through the southern hemisphere. In 1874 and 1875, when Venus was in the northern hemisphere, and in 1876 when she was in the southern hemisphere, we have a good opportunity of observing her transit, and we can observe her transit from different parts of the world. In 1874 she passed over the North America and in the Southern Ocean, about 10° south of the Cape of Good Hope. In 1875 she passed over Australia, and in 1876 she passed over New Zealand.
Antarctic continent. **The greatest shift would be produced by a transit near the South Pole, because it would be horizon for the two stations; but as in that case we cannot see any part of the phenomenon until on account of the low altitude of the sun, it would be difficult to see whether the sun was sufficiently high, and yet that the phenomenon could not be observed.
In the transit of 1884 Venus passed still in a northward direction, over the south part of the earth's face.
The explanation given in one of the most popular books on astronomy is that Venus passes through a ring of dust which is revolving round our planet. This diagram will represent Venus on each of the days during which she passes through this ring. On Monday morning we look out, if it were transparent and we looked through it.
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Watermark: "DETERMINATION OF SUN'S PARALLAX" (repeated)
DEBSL'S METHOD.
the transit occurring before she arrives at the ascending
node. At ingress the east of Brazil, and at ingress
the West Pacific Ocean, are respectively in the middle
of the transit. The transit will therefore be longest at
ingress most extended on the west coast of North
America, and shortest on the east coast of Australia,
while for corresponding effects at ingress Australia
will be longest and America shortest. So far we have considered the effect of parallax on
the ingress at two places, as distinct from the ef-
fect of parallax on the transit itself. This is to be
treated the question; and this implies that we can
not consider the difference between the two times
as due to the difference of the two observed times. Now
the difference of time is caused by the difference of
longitude, and this difference is known by tele-
graph, so is set the clock to local time, and then
to determine the difference between local and Wash-
ington time. But this difference is not known until
it has been made, the value of the longitude so found will
be subject to error. In order to avoid this erro-
rity we have to measure it, under the most favorable
circumstances, only 50 seconds of arc, a magnitude
which cannot be determined with accuracy within
30 minutes of time to move over this part on the sun's
disk. It is therefore necessary to employ a moving
clock to Washington in time at the different stations Another method has, however, been proposed for tak-
ing advantage of this slow motion of the planet without
any change in longitude. This consists in observing at
Suppose we can find a station at which ingress will be
meridional and agree retardated, and therefore the dis-
*The American astronomers have pointed out these base
stations as being suitable for observing transits. They are
the best positions for observing the transit. The other ex-
cellent stations are: 1st Cape Horn (Chile), 2nd Cape Horn,
from New Zealand to Australia.
73
HALLEY'S METHOD—PHOTOGRAPHY. tion of the whole transit lengthened, and another station at which exactly opposite effects will be pro-
duced and the duration shortened, then it is evident that the method is not applicable to the transit of Venus without comparing the clocks, and this is the method adopted by Halley. The difference between the times of transit is the result of two causes: In the first place, an ob-
server at the centre of the earth's rotation would see the transit of Venus at its greatest duration, and therefore nearer the sun's centre, in the track of 1761, which lengthened the path across the sun ; and, secondly, the observer at the equator would be further from the sun than an observer at the poles, and this hastened the egress. But this latter cause affected both stations equally, and we have only to consider the transit of 1761, so that we have only to consider the difference of paths, which was greatest for stations in
the south parts of the hemisphere turned to the sun. In
the north parts of the hemisphere turned away from
the southern stations; and further, as the south pole is
farther from the sun than the north pole, and as
the south part of the earth's disc as seen from the sun,
the earth's rotation would carry the place westward
and eastward respectively, and thus would further lengthen the duration of transit as compared with that observed at a place on the meridian where the earth's rotation combines with the paral-
lelism of latitude. It is evident that in some places some of these places which give the greatest parallactic shift are practically inaccessible, and astronomers have been obliged to make observations in other southern areas, the great Antarctic continent being one. Before dismissing this subject we must allude to
another point connected with this transit of Venus,
with Venus as a black spot on his face, taken during transit, at northern and southern stations, having
case the distances of the planet from the sun's centre, ![]() A diagram showing a transit of Venus.
as measured afterwards on the photographs. The way in which these measures may be made available will be explained later on. It is evident that the results obtained at the times when Venus is at the same distance from the sun's centre for both transit and eclipse are exactly equivalent, since they depend only upon the distance of the sun's semi-diameter, i. e., on the sun's distance. This result has already been considered. The same result may be obtained by means of the photograph, but though such measure may be made with great accuracy, the photograph has the advantage that it can be examined with the greatest care afterwards.
As to the second point, concerning the favourable opportunity of determining the sun's distance, there are two reasons why this cannot be done in the contest with treating them alone, but have obtained very accurate results from another planet, Mercury, which is much nearer to us than Venus, and which passes through our solar system more closely as Venus herself; this is especially the case when we consider that Mercury is situated in a part of its oval where he is nearest to the sun, which will make it possible to determine his distance with great accuracy. On the other hand, the distance in opposition, while, if this take place in summer, when the earth is farthest from the sun, will still be smaller, being less than 0.8 of the sun's distance. The mode of measuring this distance by means of photographs of the moon, though the quantity to be measured is a very small one, would involve considerable uncertainty; it appears, however, from the comparison of many observations made in different years that it was possible to obtain good agreeable opposites of 1862 and 1873; that Riccio's value for 1854 was too large by about 10 millionths of a millimetre, and that his value for 1862 was in consequence over-estimated, making it about 90 millionths of a millimetre instead of 90 millionths, ![]() A diagram showing a celestial body (likely a planet) orbiting around a central body (likely the Sun). The diagram includes labels for various points on the orbit.
ECLIPSES OF JUPITER'S MOONS.
an error which has been referred to a misunderstanding
about the place of the transit seen by some of the
observers, and which was probably occasioned by the
determination of the sun's distances, from the velocity of
the moon's motion, and from the time of its transit.
In consequence of which eclipses of Jupiter's moons,
of which there have been several, we find that they
occur on the average, 81 minutes earlier than the predicted
times when we are nearest to him in opposition, and
so much later when he is at his greatest distance.
Jupiter near conjunction, flying high, having thus to traverse
the earth's orbit in a short time, and with the length of his journey in the former case, from which we may infer that he traverses the earth's orbit, which, with a velocity of about 160,000 miles a second, makes the distance of one revolution nearly 300 million miles.
It follows from the relation between the velocity of the earth's motion and that of Jupiter, that when the earth were at rest we should see all the heavenly bodies appear to move in a circle round us, but moving
with about a ten-thousandth part of the velocity of light, the light of a star will seem to come from a slight inclination towards our direction, and not from a direct
motion. This effect was first observed by Beulley and
by Halley. The inclination of the plane in which the position of a star (which he called aberration) was supposed to be situated to that of our own
hearing against a head-wind, the wave pointed in slightly different directions according as the boat was
going straight ahead or round a bend. A head-
wind to the boat's motion would make the wind seem
to blow against it; but if it were blowing from behind
the boat would make a slight head-wind, which, combining
with that from behind, would give rise to a slight
lifth from the bow of the boat, whichever way that might be.
Thus, suppose the wind blowing from the stern,
it would make a slight head-wind; but if it blew from
the wind will, according to the same, seem to come a little from the contrary way. The value so well approxi-
73
DIRECT PROOF OF EARTH'S MOTION.
shift to N.W. when the boat sails in a westerly direction. The same effect may be noticed from the motion of the stars, which appear to move with the wind, the result being that the wind seems to come from the opposite quarter.
Just the same happens with the light of a star, which, though it appears to move in one direction, moves in another direction in which the earth is moving. It is accordingly found that the apparent position of a star shifts in such a manner as to indicate that the earth is moving in a certain direction.
The effect is most remarkable when the stars are very near to the horizon, and becomes greater when the earth is moving sideways with respect to the observer, so that he sees the star directly or from its opposite side. The faster the earth moves the more remarkable this effect becomes.
It is evident that the amount of shift depends on the velocity of the earth's velocity at which of light will be given by the amount of shift. It may be remarked that the observed shift is always less than half of the actual motion of the earth round the sun, as such a shift can only occur when both sides of the earth are involved. In the case of the planets there will be a double shift, corresponding to each side of the planet being involved, and instead of allowing for both of these separately, it is more convenient to find, from the known distance between sun and planet, what would have been required to reach us from $R_0$, and to consider whether this would anticipate or retard our observation by this interval. A little consideration will show that we shall find that no thing as correcting for the shift; for as the earth's motion will shift the planet apparently forward (i.e., in the direction of its motion), while at any time during which it was moving while it was coming, and then again while it was going back, but if it remained where it was when it was on the ray left it and right hand side of it respectively. This is true at all times, since as we have already explained, each shift of the earth backward will apparently shift the planet forward.
Tables being formed which gives the place of the planet at any given time during its period of
KEPLER'S THIRD LAW
compare the observations made at any particular time with the places from the tables for an instant preced-
ing that time, and then compare the distances between the
cover the distance between the planet and us, and thus
tions to them made when necessary. On comparing the velocities of different planets at various times, we find that Mercury has the greatest
the former decrease as the distances increase, but not
Mercury, but his distance is four times great; the ve-
Mercury, but his distance is four times great; the ve-
distance is about nine times as great; the velocity of
Ceres is about one-fifth that of Venus, while his dis-
numbers (which are only approximately) suggest a con-
distance increases as the square of the velocity de-
distance increases as the cube of the distance in-
crease; thus the square of the velocity of Mars is one-
fourth that of Mercury, while his distance is four times,
and so on. The law which governs this relation is found to hold in all cases. This great law was dis-
different form, viz. that the squares of the periodic
cubus of their distances from the sun. This follows
from what has just been stated, since the period in-
velocity decreases so; thus the square of the periodic
time increases as the cube of the distance from
sun increases, and as the square of the velocity de-
increases as the cube of the distance in-
creases, whereas firstly the square of the
periodic time increases as the cube of the distance.
This law was first discovered by Kepler, who
which were derived from heronical calculations found
by him to agree with observation. He applied it to
Mars in the first instance, and afterwards extended it
to other planets, are first, The planes describe or
THE KEPLER'S FIRST AND SECOND LAWS. 1st law (or oval), of which the sun occupies one focus; second, the motion in these curves is more rapid in the inner than in the outer parts of the elliptical sector which the line drawn from the sun to the planet sweeps out in one day (or in one month) than in the same time in all parts of the orbit, the angle being larger when the planet is nearer the sun than when it is at any other point on its path. To form wedges with their points at the place of the sun, all these wedges will be of exactly the same weight. ![]() A diagram showing an ellipse with a wedge cut out of it, representing Kepler's first law.
NOTION IN AN ELLIPSE. The star marked A represents the sun, and B, C, D, E, F, G, H, I, J, K, L represent the moon at different times during a month or twelfth part of the planet's year. The lines from the centre to the moon represent the distance between them at different times during a month and in half a month respectively. The ellipse is therefore an oval curve, and is called an ellipse because it is like a flattened sphere. It is also called an oval because it is like an egg. An ellipse is an oval curve, which may be formed by tying together two pieces of string so that they are always equal in length, and so that they are joined by a pin or a nail; then if one end of this string be fixed at one point, and the other end be moved about freely, a circle will be described; but if both ends be fixed at two points, and moving about freely, an ellipse will be described. An ellipse will be less or more oval. 6
82 LAW OF GRAVITATION These three laws were established by Kepler as a result of observation; I remained for Newton to dis-
cover the principle from which these motions follow.
The first law is that all bodies move in a circle, or in virtue of
which every particle in the universe pulls every other particle with a force proportional to the square of the distance between the particles increases.
Secondly, this force is inversely proportional to the cube of the
square of the distance between the particles increases.
Thirdly, this force is directed towards the center of gravity of
the sun in accordance with Kepler's laws, i.e., according to the inverse square law (correspondence with his vast size) which explains why the moon moves much more slowly than the earth,
much less moving each effect in moving his large mass.
Similarly, the moon does not fall towards the earth but rather
is capable of making the moon move in such an orbit as she actually describes. The next step was to show that
if we consider the moon's motion as falling, it is really the force that keeps the moon in her ac-
tual orbit. This is because when we consider the moon's
force falls sixteen feet in the first second through the arc of one degree, and then twenty-eight feet in the second second through the arc of another degree, which is sixty times as far from the earth's centre, it would fall half a foot, or about an inch at any instant. It is clear that this force must increase
as the distance increases. Now the moon really falls towards
the earth, but not directly downwards, but rather in a direct line, for if left to herself at any instant she
would fall straight down. But since she is attracted by her a pull which brings her into a curve, and the dis-
tance between her position in this curve and the straight line
to her true position is constantly increasing. There- fore,
represents her fall towards the earth he first sec-
ond is 16 feet, and then 28 feet, and so on. It ap-
pears difficult to understand how the moon can be de-
scending towards the earth while at the same time rising away from it. But it must be remembered that her motion,
if left free at any instant, continues to rise away from
the earth to keep her in her course, this fall being, of
ILLUSTRATIONS.
81 course, in different directions at different parts of her
orbit, since its always directed towards the earth.
This continual pull towards the centre of motion is
the cause of the earth's being carried round in a nearly
circular; the passengers seem to be thrown outwards, be-
cause they are continually drawn inwards by the pull of
the earth to keep them to the rails, and being continually pull-
ed inwards, they are forced to move in a circular way.
If a stone tied to a string be whirled rapidly round, a
strong pull on the hand holding it will be felt, and as
soon as this is removed, it will continue to move in that
direction in which it was going at that instant. Al-
though the moon does not have any direct action upon
the moon, or the sun on the planets, yet really every
body attracts every other body. The earth attracts
pulls the earth, the law of gravitation being merely
that there is a pull between them which tends to bring
them together. This pull is so great that it overcomes
the force of gravity between the earth and the moon,
so that the moon is never moved from its orbit. A
string and flying into the air will illustrate thus: thin;
the moon is attracted towards the earth with a force equal
to that which would hold it in its orbit. But this is not
the case, but the small stone will circle round the large
one, which pursues nearly the same course as if alone.
The moon is attracted towards the earth with a force equal
to that which would hold it in its orbit. The earth and moon
the real state of the case is
that there is no such thing as a fixed point in space,
and every particle of the earth pulls every par-
ticle of the moon with a force equal to that which would
hold these particles in their orbits. But since all these
particles are moving with respect to each other, and since
every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these
particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of the earth pulls every part of the moon with a force equal to that which would hold these particles in their orbits. But since all these particles are moving with respect to each other, and since every particle of
CENTER OF GRAVITY—TIDES once will approach about a point in the line joining them, which is much nearer the earth than the moon. This is because the two bodies are so near together that they may be considered as one body, and is such that if I imagined them connected by an enormous rod, they would balance about the centre of gravity of the whole. Now, if we imagine the two ends of such a stick to balance about a point of the earth's surface, then the centre of gravity of the earth and moon will then be exactly the same as if they were joined by a rod. But this is not so, because the centre of gravity of the two bodies is made to revolve round the sun once a year, which both earth and moon do. The earth revolves in about 365 days, but the moon, in her month, the string stretching more or less, so that the distance between them varies. When the moon is seen from the earth she will then be exactly due north or south, according to whether she is on the side of the earth at rest; but the earth's motion about the sun will not be an exact ellipse, but an oblate, something like an egg. Hence, when she is on the side of the earth at rest from the true ellipse (namely by the pull of the moon) she will be nearer. One consequence of this pull on the earth remains to be noticed. It is that it attracts the moon and sea pulling the waters of the ocean, which are turned toward them (see therefor- ward). This attraction causes a bulge in the water around the earth (which is pulled just as if it were all surrounded by one body), and this bulge is called high water. The water toward the moon is heaped up; and similarly for the water toward the opposite side of the earth. There is more than the water on the other side, and therefore draws down the earth away, causing high water also on this side. Thus there are two tides every day, one high water on each side with high water when the moon is on the mer- cular track with high water at noon and midnight. And when she is on her track with low water at noon and to the south or nadir of the place, whence it follows that in summer the higher of the two solar tracks is at 84
SPRING AND NEAR YEARS. 85 now, when the sun is nearer to the zenith than it is to the nadir at midnight, whilst in winter the opposite takes place; and this difference is greater in the equinoxes than as she is north or south of the equator. In all this the earth's rotation has been neglected, the effect of this being that the sun appears to rise and set at different times according as he is nearer or farther from the zenith; but the reasoning only applies to the open ocean, there being no such thing as a closed sea, and therefore no great mass of water is acted upon; even in the Medi-
terranean, the rise of the tide is hardly perceptible. The same may be said of lakes, rivers, and canals, the ocean, and often takes many hours to traverse them; but in these bodies of water there is a difference to what is known as the establishment of the port, and the time of high and low water, which is called the passage of the moon and sun, when they transit together at new and full moon. Some both sun and moon pro-
duce tides; others produce none whatever. The oppo-
sition dates, cause a much higher tide than when
the sun is in conjunction with the moon; and this in
the latter case partly filling up the low water
which occurs at new moon. The height of high water from both sources are the same, and they
conspire to produce high tides, known as spring tides;
but when the moon is in quadrature with the sun,
there is little or no tide at either place if found to be about 2½ times that of map at the same place; and
as the solar tide is added to lunar in the former
case, and subtracted from it in the latter, it follows
that the effects of the moon and sun are as 5 to 3.
This difference between their effects on water (being
the difference of her pull on the water)
is nearly equal to that between two squares of
the moon multiplied by the difference between $A$ squared and $A$ squared, which is very nearly twice the mass of
RELATIVE MASS AND DENSITY OF the moon divided by the cube of 60°. Similarly the effect of the sun will be twice his mass divided by the cube of 30°, and that of the earth, which is 33,400, and this latter effect is such that it is nearly equal to that of the moon, which is 24,000, and this latter effect is nearly equal to that of the earth, whilst the earth's is not quite four times that of the moon. The sun's effect is nearly equal to that of the moon, and its bulk 400 times that of the moon, and its bulk 400 cubed (or 64 million times) is nearly equal to that of the earth, and its bulk 64 million times that of the earth. In this it follows that, as the sun's mass is 8.1 times that of the earth, so the sun's attraction on the earth must be eight times greater than that of the earth upon itself; but since the attraction is proportional to the quantities of matter in equal bodies, it follows that the attraction of the sun upon the earth must be eight times greater than that of the earth upon itself; indeed this method is not susceptible of any great ac-
curacy, and is only given as a rough approximation; but it may be weighed, as it were, against another. In the case of the card and the string, we have seen that one-fifth part of the area was occupied by a fifth part of the mass; for it is easy to see that if we had a square card with a square hole in it, we would go round the sun at the same distance as the moon from the earth, although we should travel much nearer than that of the moon's orbit. The earth's distance from the sun is about 93 million miles; therefore its velocity is about 18 miles per second; whereas the square of the velocity of this imaginary body would be about 3276 miles per second squared; and this being three times the square of its velocity, or 364 miles a second; whilst the moon's velocity under its own attraction is about 18 miles a second; therefore its velocity under its own attraction is about 18 miles a second. Thus the sun's attraction can re-
\begin{align*}
& \text{The sun's attraction on} \
& \text{the earth is nearly equal to} \
& \text{that of the moon.}
\end{align*} \begin{align*}
& \text{The sun's mass divided by} \
& \text{the cube of 60°.}\
& \text{Similarly the effect of} \
& \text{the sun will be twice his} \
& \text{mass divided by} \
& \text{the cube of 30°.}\
& \text{And that of the earth, which} \
& \text{is 33,400, and this latter} \
& \text{effect is such that it is nearly} \
& \text{equal to that of the moon,} \
& \text{which is 24,000, and this} \
& \text{latter effect is nearly equal} \
& \text{to that of the earth, whilst} \
& \text{the earth's is not quite four} \
& \text{times that of the moon.}\
& \text{The sun's effect is nearly equal} \
& \text{to that of the moon, and its} \
& \text{bulk 400 times that of} \
& \text{the moon, and its bulk 400} \
& \text{cubed (or 64 million times)} \
& \text{is nearly equal to that of} \
& \text{the earth, and its bulk 64} \
& \text{million times that of} \
& \text{the earth.}\
& \text{In this it follows that, as} \
& \text{the sun's mass is 8.1 times} \
& \text{that of the earth, so the sun's} \
& \text{attraction on the earth must be} \
& \text{nearly equal to eight times} \
& \text{greater than that of the earth} \
& \text{upon itself; but since the} \
& \text{attraction is proportional to} \
& \text{the quantities of matter in} \
& \text{equal bodies, it follows that} \
& \text{the attraction of the sun upon} \
& \text{the earth must be eight times} \
& \text{greater than that of the earth} \
& \text{upon itself; indeed this method} \
& \text{is not susceptible of any great} \
& \text{accuracy, and is only given as a} \
& \text{rough approximation; but it may} \
& \text{be weighed, as it were, against} \
& \text{another. In the case of the card} \
& \text{and the string, we have seen} \
& \text{that one-fifth part of the area}\
& &\text{was occupied by a fifth part}\
& &\text{of the mass; for it is easy to}\
& &\text{see that if we had a square}\
& &\text{card with a square hole in}\
& &\text{it, we would go round}\
& &\text{the sun at}\
& &\text{the same distance as}\
& &\text{the moon from}\
& &\text{the earth, although we}\
& &\text{should travel much nearer}\
& &\text{than that of}\
& &\text{the moon's orbit.}\
& &\text{The earth's distance from}\
& &\text{the sun is about}\
& &\text{93 million miles; therefore}\
& &\text{its velocity is about}\
& &\text{(18) miles per second;}\
& &\text{whereas}\quad\
& &\quad\quad\quad\quad\
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SUN AND MOON. tain a body in an orbit of the same size as the moon's when moving with a velocity nearly 600 times as great as that of the earth, and therefore in about 300000 seconds would pass through it at a rate of one inch in one second; the sun would pull a body through it at a rate of one inch in two seconds. Now from the laws of falling bodies, a body pulled through A inch in the second would be pulled through B inches in the second and so on, and since A is 300000 seconds so that the sun's pull in one second would be 300000 times greater than its pull in three seconds, and so on, the same distance, and therefore he must have 300,000 times more mass than the moon has. His mass is really about 330,000 times that of the earth; but his bulk is 100 cubic feet, or about 1250,000 cubic yards; and this is only a quarter that of the earth, or about 1/6 that of water. The moon's density is therefore about 1/6 that of water, or about 1/6 that of the earth, and she uses about 54 times that of water. The moon's density is therefore about 54 times that of water, or about 54 times that of the earth, and she uses almost 1/4th of the earth's mass. The above method may be applied to find the masses of other planets. For instance, if we take the moon to be our unit of mass, then to the sun, all that is wanted is to find the dis- tance between them. This can be done by observing eclipses of the sun; but in the case of other planets the problem is more difficult. We cannot see their eclipses because they are too far away; but an approximation to the masses of such planets by the help of the attraction which they exert on their neigh- bours will give us a fair idea of their masses. For instance, if they would pursue us like the sun were the only attracting body in space, they would make elliptical orbits around us; but since they do not do so, they must be attracted by some other body in space which pulls them into elliptical orbits around it. These orbits are known as "mean" orbits; and from these mean orbits we can calculate their masses. The mean orbit is always an ellipse whose major axis is equal to twice the semi-major axis of an ellipse formed by drawing lines from any point on the orbit to two points on opposite sides of the sun. The semi-major axis is half the length of the major axis. The semi-minor axis is half the length of the minor axis. The eccentricity is equal to one minus the square root of one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). The semi-major axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The semi-minor axis is equal to (semi-major axis squared)/(semi-minor axis squared)^(1/2). The eccentricity is equal to one minus (semi-major axis squared)/(semi-minor axis squared). A heavy body on the earth falls through about 16 feet in first second of its fall, or -L.C. in feet in two seconds; and if we suppose that it fell through L.C. feet in four seconds, then it would fall through L.C./4 feet in first second; and if we suppose that it fell through L.C./8 feet in third second, then it would fall through L.C./8 feet in first second; and if we suppose that it fell through L.C./16 feet in fourth second, then it would fall through L.C./16 feet in first second; and if we suppose that it fell through L.C./32 feet in fifth second, then it would fall through L.C./32 feet in first second; and if we suppose that it fell through L.C./64 feet in sixth second, then it would fall through L.C./64 feet in first second; and if we suppose that it fell through L.C./128 feet in seventh second, then it would fall through L.C./128 feet in first second; and if we suppose that it fell through L.C./256 feet in eighth second, then it would fall through L.C./256 feet in first second; and if we suppose that it fell through L.C./512 feet in ninth second, then it would fall through L.C./512 feet in first second; and if we suppose that it fell through L.C./1024 feet in tenth second, then it would fall through L.C./1024 feet in first second; and if we suppose that it fell through L.C./2048 feet in eleventh second, then it would fall through L.C./2048 feet in first second; and if we suppose that it fell through L.C./4096 feet in twelfth second, then it would fall through L.C./4096 feet in first second; and if we suppose that it fell through L.C./8192 feet in thirteenth second, then it would fall through L.C./8192 feet in first second; and if we suppose that it fell through L.C./16384 feet in fourteenth second, then it would fall through L.C./16384 feet in first second; and if we suppose that it fell through L.C./32768 feet in fifteenth second, then it would fall through L.C./32768 feet in first second; and if we suppose that it fell through L.C./65536 feet in sixteenth second, then it would fall through L.C./65536 feet in first second; and if we suppose that it fell through L.C./131072 feet in seventeenth second, then it would fall through L.C./131072 feet in first second; and if we suppose that it fell through L.C./262144 feet in eighteenth second, then it would fall through L.C./262144 feet in first second; and if we suppose that it fell through L.C./524288 feet in nineteenth second, then it would fall through L.C./524288 feet in first second; and if we suppose that it fell through L.C./1048576 feet in twentieth second, then it would fall through L.C./1048576 feet in first second; and if we suppose that it fell through L.C./2097152 feet in twenty-first second, then it would fall through L.C./2097152 feet in first second; and if we suppose that it fell through L.C./4194304 feet in twenty-second second, then it would fall through L.C./4194304 feet in first second; and if we suppose that it fell through L.C./8388608 feet in twenty-third second, then it would fall through L.C./8388608 feet in first second; and if we suppose that it fell through L.C./16777216 feet in twenty-fourth second, then it would fall through L.C./16777216 feet in first second; and if we suppose that it fell through L.C./33554432 feet in twenty-fifth second, then it would fall through L.C./33554432 feet in first second; and if we suppose that it fell through L.C./67108864 feet in twenty-sixth second, then it would fall through L.C./67108864 feet in first second; and if we suppose that it fell through L.C./134217728 feet in twenty-seventh second, then it would fall through L.C./134217728 feet in first second; and if we suppose that it fell through L.C./268435456 feet in twenty-eighth second, then it would fall through L.C./268435456 feet in first second; and if we suppose that it fell through L.C./536870912 feet in twenty-ninth second, then it would fall through L.C./536870912 feet in first second; and if we suppose that it fell through L.C./1073741824 feet in thirtieth sec
MASS AND DENSITY OF THE EARTH so small that it is only where great accuracy is aimed at that the application of Kepler's Laws has to be digested with care. The earth is not a perfect sphere, which is greatly disturbed by the sun's attraction. It remains now to determine the mass of the earth, and this can be done either by measuring its weight or by measuring its volume. The first method is very difficult, but the second is much easier. It consists in measuring the angle between the sun's rays and the line joining the observer to the top of a mountain, the angle between the sun's rays and the line joining the observer to the bottom of a mountain, and then subtracting one from the other. This gives us the height of the mountain, and we know how far away it is from us. We can therefore calculate its volume, and knowing its density (which is nearly constant), we can calculate its mass. The difficulty lies in finding out what is the distance between us and the mountain. This can be done by observing the time taken for light to travel from the mountain to us. This time is called the "time of transit," and it depends on the distance between us and the mountain. The farther away we are from the mountain, the longer it takes for light to travel from it to us. This means that we can find out how far away we are from the mountain by observing how long it takes for light to travel from it to us. This method was used by Sir George Airy in his determination of the mass of the earth. He observed that when he was standing on a hilltop, he could see a distant mountain, but when he was standing on a lower hill, he could not see it. This meant that he was closer to the mountain than he had thought. By measuring how far away he was from the mountain, he could calculate its volume and therefore its mass. In this way Airy determined that the mass of the earth was about 5.97 times that of water. This means that if we were to fill up all of space with water, we would need about 5.97 times as much water as there is in our oceans. Airy's experiment was very important because it showed that we could use mathematics to determine things about the earth that we could not see directly. It also showed that we could use mathematics to determine things about other objects in space that we could not see directly. In conclusion, I want to say that I believe that mathematics will continue to be an important tool for determining things about the earth and other objects in space. I also believe that mathematics will continue to be an important tool for determining things about ourselves and our world. I hope that you have enjoyed this lecture and that you will continue to study mathematics in order to learn more about yourself and your world. Thank you.
8
BODEN'S LAW. In this case the attractions were measured by observ-
ing the number of vibrations made in equal times by
a pendulum at the surface and at the bottom of the
sea. The results obtained show that the attraction vary-
ing as the square of the number of vibrations in
one second, and that the attraction at the bottom of
the sea was found to gain 32 seconds a day more than at the
surface. This result is very nearly what was pre-
dicted to be about 60 minutes of time. The other
methods gave similar values, so that the average of
all these experiments gives us a value for the time
of one revolution of the earth, or about 24 hours,
and also for the time of one revolution of the moon,
or about 27 days. From its radius, there is no difficulty in calculating
the distance between the earth and the moon, but it conveys no idea to the mind, and is therefore not given here.
The progressive regression has been observed to hold approximately in the distances of the planets from the sun, and it is evident that this is due to their
own laws. In each case, it is useful aid to the memory, and de-
cides many questions which would otherwise remain in the gap between Mars and Jupiter, and thus led to the
discovery of the minor planets. According to this law, we find that Mercury is nearer to the sun than any other planet except Venus, and that Venus is nearer to the sun than any other planet except Mercury. The next nearest planet is Mars, which is farther from the sun than the several planets, Mercury, Venus, Earth, Jupiter, Saturn, Uranus, and Neptune. It is true that
18° 35' 44" 44' 31" 31' 54" 44' 22" 44' 10" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44' 00" 44'
90
ROTATION OF PLANETS which all, as far as is known, turn from west to east, like the sun and the earth, may be divided into two parts, one of which is called the diurnal rotation, and the other the sidereal rotation. The diurnal rotation of the earth, Mars, and Venus, rotating about the same time, whilst the diurnal rotation of Jupiter (and Saturn) is about ten hours. In the case of Mercury and Neptune (or Uranus), the diurnal rotation is nearly equal to the sidereal rotation. COMPARATIVE SIZES OF THE PLANETS. and Venus, evidence as to markings or spots is so con-
flicting that very little confidence can be placed in
calculations based on this subject. They are
generally seen as brilliant spidery lines, gil beams or
lines, but their reality is doubtful. The following
are the relative sizes of the planets: ![]() A diagram showing comparative sizes of planets. The largest circle represents Earth, followed by Venus, Mars, Jupiter, Saturn, Uranus, and Neptune. The smallest circle represents Mercury.
| 1 DETERMINATION OF SUN'S PARALLAX |
|
| Watermark: "DETERMINATION OF SUN'S PARALLAX" |
|
| The sun's equinoxes will be in the same place on Venus being 1. |
|
| The shift of Venus being 3. times that of the sun, and 6. times the sun's parallax. |
|
| The most accurate way of measuring this parallax would be to refer it to the very slow motion of Venus in her passage across the sun's disc, by noting at two stations where the sun is seen to enter wholly on the sun's disc, or to begin to leave it. |
|
| which will be the greatest effect on the time of ingress, the shift must therefore be measured with great accuracy, |
|
| and therefore the two stations should be separated from each other in the direction of a line joining this point with the centre of the earth. |
|
| In the transit of 1874 Venus crossed the northern hemisphere, |
|
| and in 1875 she passed through Australia, |
|
| and in 1876 she passed through the southern hemisphere. |
|
| In 1874 and 1875, when Venus was in the northern hemisphere, |
|
| and in 1876 when she was in the southern hemisphere, |
|
| We have a good opportunity of observing her transit, |
|
| and we can observe her transit from different parts of the world. |
|
| In 1874 she passed over North America and in 1875 she passed over Australia, |
|
| and in 1876 she passed over New Zealand. |
|
| Antarctic continent. **The greatest shift would be produced by a transit near the South Pole, |
|
| because it would be horizon for the two stations; |
|
| but as in that case we cannot see any part of the phenomenon until on account of |
|
| the low altitude of the sun, |
|
| it would be difficult to see whether the sun was sufficiently high, |
|
| and yet that the phenomenon could not be observed. |
|
| In the transit of 1884 Venus passed still in a northward direction, |
|
| over the south part of the earth's face. | |
| Mercury |
Venus |
Mars |
Jupiter |
Saturn |
Uranus |
Neptune |
| Smallest |
Second Smallest |
Third Smallest |
Largest |
Fourth Largest |
Fifth Largest |
Sixth Largest |
**ASPECT OF MERCURY—FEBRUARY—MARS.** 41
dazzlingly white in a powerful telescope as to require
the use of a colored glass to moderate her light.
The sun, therefore, is not the only body which
lights the earth, whilst Venus is nearly as large as the earth, and
yet she appears so much smaller than the sun, owing
to their physical nature, except that they show in their
respective orbits at different distances from us, and
therefore giving rise to a ring of light, which is seen
round the edge outside the sun's disc, and probably
accounts for the appearance of the moon when seen
seeming the real body of either planet. The moon,
however, has no atmosphere, and consequently no
white spots at the poles of rotation,—supposed to be
snow or ice. Those conditions can only be accepted
as true of the moon, because there is no explana-
tion for the terms in the case of the moon ; Mars
being nearer to us than the moon, and being also
rather more than half the size of the earth, and of
course less dense than our own globe.
Of such minute bodies as the asteroids nothing is to
be made out ; but the next planet Jupiter, is a magni-
ficent object in a telescope, being about three times
the size of the earth, though only 1/7th of its density, and attended by a host of satellites. In one of his most
times cross his disc, the shadow being also seen to tra-
verse the face of the earth. This is called "the transit"
of Jupiter's satellite ; whilst at other times they are
themselves eclipsed in the planet's shadow, or occulted
by it. The first phenomenon is observed when they are
distinct, the former taking place when the satellite is
in front of Jupiter's disc, and passing behind him at some distance from the planet's disc, the latter when
the satellite is hidden from view by Jupiter's disc. The
shadow of any body will be different unless the earth and sun happen to be in a line with the planet, which will be rare in opposition. Before
This work is used in referring to manors, not bulk.
| Aspect of Mercury - February - Mars. |
**JUPITER**
opposition, Jupiter being eastward of the prolongation of the line joining the earth and sun, the eclipses will take place when Jupiter is at its greatest distance from the earth looking round that side as it were, whilst the eclipses of the moon will occur when the motions of the satellites are eastward, and, like our moon, they have been supposed to turn on their axes in opposite directions to those of the earth. The stations of brightness having been observed to recur at similar times in different years, it is evident that they proceed towards us in succession. Their orbits are very elongated, and their periods are 11.85 and 13.06 years respectively; but the three inner moons occur every twenty-one days, and the fourth has frequently Jupiter's shadow being large as compared with the diameter of the earth. The distances of these four bodies from Jupiter are 7.4, 7.6, and 10.5 days, respectively, and their distances from each other are 10.5, 10.8, and 12.5 days.
The disc of Jupiter is usually distinguished by several spots which appear to be connected with one ano-
tor. These have been supposed to be clouds formed by the trade winds, which, from his rapid rotation, assume a form resembling a belt around the body. The torn of the belts confirm this idea. Some of the belts are white, some grey, and this variety of hue seems more marked in comparison with Saturn than with Jupiter.
Sometimes similar belts are seen on Saturn, but the striking feature of that planet is a wonderful ring, or system of rings, consisting of many concentric rings (diameter or one-third the size of the moon's orbit), which revolve round him in opposite directions and clined some 28° to Saturn's path. When we arc
looking at Jupiter through a telescope we see these rings with our eyes; they are seen as a bright line crossing the planet parallel to the belts; this fine structure is visible only when Jupiter is near opposition; otherwise, so that the thickness must be very small.
The disappearance will occur at intervals of nearly
thirteen years; half the Saturnian year; there being
92
SATEURN.
two parts of this orbit corresponding to our spring and autumn, for which the ring is placed edgeways with respect to the plane of the ecliptic, and so with the earth, which to an inhabitant of Saturn never crosses the equator, but always remains in one hemisphere.
When the earth and Sun look at opposite sides of the ring (which is sometimes the case about the time of
83
1869 1872
![]() A diagram showing two views of Saturn's rings, one from the side and one from above. The rings appear as a series of concentric circles around the planet.
S81 S81
1873 1877
PHASES OF SATURN'S RING FROM 1869 TO 1877, AND FROM 1878 TO 1885. (For the latter turn the figures upside down.)
The following table gives the times of the eclipses, which can be inferred from the figure of the Seasons, p. 30.
| Year |
Eclipse Time |
| 1869 |
Not applicable |
| 1870 |
Not applicable |
| 1871 |
Not applicable |
| 1872 |
Not applicable |
| 1873 |
Not applicable |
| 1874 |
Not applicable |
| 1875 |
Not applicable |
| 1876 |
Not applicable |
| 1877 |
Not applicable |
| 1878 |
Not applicable |
| 1879 |
Not applicable |
| 1880 |
Not applicable |
| 1881 |
Not applicable |
| 1882 |
Not applicable |
| 1883 |
Not applicable |
| 1884 |
Not applicable |
| 1885 |
Not applicable |
![]() A diagram showing two views of Saturn's rings, one from the side and one from above. The rings appear as a series of concentric circles around the planet.
S82 S82
PHASES OF SATURN'S RINGS.
disappearance) it will only be seen as a black belt crossing the planet, and invisible outside the disc. The ring will then appear to be composed of two belts, one together, the first when the earth crosses from the bright side to the dark side, and the second when it crosses from the dark to the bright side of the ring. The phases presented by Saturn's equator to an observer on the Earth's equator to an observer on the Sun, which we have already described, are those which occur during the year for Saturn is nearly thirty of our years, and that we do not always see the same phases.
Thus, starting from what would be visible for Saturn's northern summer, we find that when the ring is seen edgeways, the northern side will be presented more and more towards us until it is seen directly opposite us in Saturn's northern summer; the rings will after this appear to close up again, and will remain so for about ten years, from which point the Southern side is seen for fifteen years, going through the same phase as before.
The system of rings consists of three bright and at intervals dark belts. The outermost belt is very faint, but its parent, allowing the body of the planet to be seen through it, shows that it is not a solid disk. The innermost belt is very thin and has been observed to be a mere line. It is therefore evident that these belts are not solid disks, but are composed of particles of matter which are held together by their mutual attraction. This conclusion is supported by the fact that when a particle of matter falls into one of these belts, it does not fall straight down into the planet, but is deflected sideways by the particles of matter in front of it. This deflection is due to the fact that each particle of matter in front of it exerts a force on it which tends to keep it in a circular path around the planet. This force is called centrifugal force, and it is equal to the weight of the particle divided by its distance from the center of rotation. When this force is greater than the weight of the particle, it will tend to keep it in a circular path around the planet. When this force is less than the weight of the particle, it will tend to make it fall towards the center of rotation. When this force is equal to the weight of the particle, it will be in equilibrium and neither fall nor rise.
The rings are composed of particles of matter which are held together by their mutual attraction. These particles are called "rings" because they appear as a series of concentric circles around the planet. The rings are not solid disks, but are composed of particles of matter which are held together by their mutual attraction. This conclusion is supported by the fact that when a particle of matter falls into one of these rings, it does not fall straight down into the planet, but is deflected sideways by the particles of matter in front of it. This deflection is due to the fact that each particle of matter in front of it exerts a force on it which tends to keep it in a circular path around the planet. This force is called centrifugal force, and it is equal to the weight of the particle divided by its distance from the center of rotation. When this force is greater than the weight of the particle, it will tend to keep it in a circular path around the planet. When this force is less than the weight of the particle, it will tend to make it fall towards the center of rotation. When this force is equal to the weight of the particle, it will be in equilibrium and neither fall nor rise.
The rings are composed of particles of matter which are held together by their mutual attraction. These particles are called "rings" because they appear as a series of concentric circles around the planet. The rings are not solid disks, but are composed of particles of matter which are held together by their mutual attraction. This conclusion is supported by the fact that when a particle of matter falls into one of these rings, it does not fall straight down into the planet, but is deflected sideways by the particles of matter in front of it. This deflection is due to the fact that each particle of matter in front of it exerts a force on it which tends to keep it in a circular path around the planet. This force is called centrifugal force, and it is equal to the weight of the particle divided by its distance from the center of rotation. When this force is greater than the weight of the particle, it will tend to keep it in a circular path around the planet. When this force is less than the weight of the particle, it will tend to make it fall towards the center of rotation. When this force is equal to the weight of
CRATES AND NEPTUNE.
of judging, and can therefore say nothing of the density of the true body of the planet (if he have any) but that its diameter is about 30 times that of the earth's, his bulk, including its atmos-
phere, being equal to that of the earth's. This remark applies to Jupiter, which has also in all prob-
ability, a very extensive atmosphere. Saturn is at-
tained by the same proportion, and extends from 1 to 80 days, and at distances of from 30 to 60
degrees from the sun, or from a half to ten
times the distance of our moon.
The motions of these planets are so different,
can be made out about them, except that they have nearly circular discs of 4° and 2° apparent diameter respectively, and are at least 50 times the distance of the earth's orbit, nor far from the density of water. Four
of them have been discovered up to the present time, but there are only a very few telescopes in the world capable of showing their motions with any degree of accuracy. The moons move in paths very much inclined to that of the sun, and in a retrograde or westward direction.
It is evident that these bodies are ex-
posed so rare as that it is difficult for any one
conception of their state; to Mercury the sun appears
to be at a distance of 1° or 2° from its center; to
Neptune it appears of only 6th the area, and the
sun is seen to be at a distance of 10° or 12°.
This will be proportional to the apparent area of the sun's disc when viewed from Neptune. What pro-
portion of this heat is reflected away into space,
and what portion is transmitted through the atmospheres of the several planets is not exactly known; but it seems probable that some re-
venting the radiation of heat which takes place
in the interior of these bodies. It is not known
causes of this kind could operate to such an
extent as to raise the surface of the outer planets,
PHYSICAL CONDITIONS FOR THE PLANETS.
Uranus and Neptune, much above the temperature of space, which is known to be much farther below the temperature of the sun than that of the earth. The water, though internal heat may be those bodies be far greater than that of the earth, has comparatively high temperature without much being from the sun.
The force which makes bodies fall must be very different for the several planets. On the sun it is about 300 times as great as on the earth. Jupiter two-and-a-half times, on Saturn and Venus four times, and on Mars six times as great as on the earth. The force of gravity varies every one-half, and on the moon only one-eighth, whilst on the asteroids it would perhaps range from 2 to 5 times as great as on the earth. The surface of different planets, volcanic and other forms of surface, vary greatly in their resistance, and the same remark applies to successive forces. A mass of matter will fall with a velocity sufficient to jump off the moon, and some 5,000 feet on the smallest asteroid, whilst on Jupiter he could leap over a mountain 100 miles high. The muscular effort required to raise a mass of 100 pounds to a height of 100 feet is equal to that of a man who weighs 150 pounds; but only 4 pounds on the sun. Further, the expenditure of muscular energy is inversely proportional to the square of the distance from the center; at the quarter, varies greatly for the different planets, being very large in the case of Jupiter and Saturn, where it is nearly double that of the earth. The extent of $A$ and $d$ of their diameters respectively, that of the earth being only $\frac{1}{4}$th and of Mars $\frac{1}{6}$th.
CHAPTER V.
The bodies which we have next to consider, though belonging, at least temporarily, to the solar system, present conditions which separate them completely
COMETS—THEIR MOTIONS.
from all the planets, whether large or small. Whilst the planets are massive globes with definite boundaries, comets are diffuse bodies with no distinct outline, and their motions are irregular and erratic. The small mass that no appreciable disturbance is caused by them, and they are consequently incapable of causing any effect on the orbits of these strange bodies. But it is not only in their motions that comets are remarkable, but also in their equal rarity, which is equally remarkable for the irregularity of their motions. Thus in a single year the comet of 1873 (which was a very large comet) passed through the solar system once only, and that of 1851 through 24 times; the appar- ent motion of the former being nearly parallel to the ecliptic, and the other comets have moved nearly as rap- idly as the sun itself. It is evident that this apparent motion arises from our own motion in the opposite direction to that of the comet, which in this case is nearly parallel to the ecliptic. This fact shows that the parallactic effect must, as in the case of the moon's motion, be due to the earth's motion in its orbit, and not to any peculiar path of the earth about the sun.
The comets, therefore, move in one direction towards or away from us in accordance with their nearly circular orbits, very slightly inclined to the earth's axis (except in the case of some of the more massive planets), and so that they appear to move in all directions. The ellipses which they describe are not perfect ellipses, but are somewhat elongated so that in most cases they cannot be dis- tinguished from parabolas. In some cases they may be only parabolas when we follow them from another curve called a parabola, which is something like the earth's orbit. In such cases the comet describes a parabola till two branches separate further and fur- ther apart until at last it becomes a parabola again. The motions in these parabolas is, however, different from those described by comets moving in sectors (or wedges) formed by lines drawn from the sun to the comet every day are equal in area, so that they move with uniform velocity. This is not quite true, for to make up for the shortness in the radii of the
9
98
PARABOLA AND ELLIPSE
sector. Thus, Newton's comet of 1680, which passed within a third of the sun's radius from his surface, had a velocity of 30 miles per second; that of 1843, which passed even closer, almost touching the surface, had the still greater velocity of 320 miles a second, taking only two hours to go half.
ORBIT OF COMETS.
Bisai's and Tuttle's comets are taken as types of the Jupiter and Saturn classes of comets respectively. The former is shown in the upper part of the figure to show how an ellipse may be drawn round the sun on the inside, and Jupiter's path on the inside.
round the sun. On the other hand, the comet of Eyre, which revolves round the sun in 7 years and 5 months, resembles a parabola (see lower part of figure). It has no orbit, though its least distance from the sun is only 1.5 million miles. This is one of the small planets, Polybiusian. It is this being, perhaps, the most oval orbit among the planets.
GEBITS OF COMETS.
With regard to the indications of their orbits, comets seem rather to avoid the ecliptic, only 1/4 of the whole number having inclinations lying between 0° and 30°, while the rest lie between 30° and 90°, in proportions between 69° and 93°; and further, this inclination is not uniform throughout the orbit, but direct, through the great majority of the pericentric comets being inclined at about 50°, while those which have one of those which move in parabolas (or exceedingly long ellipse), two-thirds have a retrograde or westward inclination. The inclination of the perihelion is generally not much inclined into the paths of the earth.
Comets are as various in their aspects as in their movements, but there is a family resemblance among them all, so that they are all similar just to somewhat similar conditions. A large proportion of the comets are seen at small apsides, and in large telescopes at small spots of light very few can be distinguished from stars. The average number of new comets on the average picked up every year, is about three hundred, but vary considerably on the view, but this is hardly ever true of them. Astronomers are continually on the watch to detect any new comet, and when they find one, they mark it down, so that by the time it has become at all conspicuous its place is known. This is a very important thing, as it attains in daily better assimilation. Since the invention of the telescope, astronomers have been able to watch many more comets than before; and since they are seen as spots of nebulous light, and have thus formed some idea of their nature, they have been able to say what a comet consists with, viz., the nucleus, the coma or head, and the tail. The nucleus is supposed to be a body approaching its approach to the sun, nothing will probably be seen until it reaches the point where it becomes visible in the centre called the nucleus. It is supposed to be a body moving in the sun's coma. As the comet comes nearer under observation, it becomes more and more distinct, and commonly throws out jets of light towards the sun, which
NO GROTHUS OF COMETS—THEIR TAILS.
curve back and apparently give rise to the tail—a band of light sometimes extending many degrees from the plane of the ecliptic. The comet of 1867 (for which see the article on comets) was seen to have a tail of this kind, and having a real length in some cases exceeding 30°. Ordinarily the tail does not attain its full development till after the appearance of the head has been observed. Light is emitted from the nucleus; but the apparent length of tail is greater than that of the head.
This resemblance may be considered as a paradoxa, with the nucleus as focus, and having a dark division between the nucleus and the tail. The nucleus is usually very small, being only a few miles in diameter, and is usually covered by a layer of dust or gas, which is frequently observed to be thrown out in great masses at intervals of time. The tails are usually long, and are often very narrow, like a plume, and they are frequently curved backwards towards a plane, and there are frequently secondary tails issuing from them. Sometimes there is no visible tail, but a faint haze is observable in the direction of the tail. It is known that comets are not always visible, and that their tails are not always visible; but it is not known whether these tails are always visible when the comet is visible, or whether they are visible when the comet is invisible. It is also not known whether these tails are always visible when the comet is invisible, or whether they are visible when the comet is invisible.
The following table gives the number of comets whose tails have been observed:
| Comet |
Number of Tails |
| 1858 |
1 |
| 1867 |
1 |
| 1872 |
1 |
| 1874 |
1 |
| 1876 |
1 |
| 1879 |
1 |
| 1882 |
1 |
| 1884 |
1 |
| 1885 |
1 |
| 1886 |
1 |
| 1887 |
1 |
| 1890 |
1 |
| 1892 |
1 |
| 1893 |
1 |
| 1894 |
1 |
| 1895 |
1 |
| 1896 |
1 |
| 1897 |
1 |
| 1899 |
1 |
| 1900 |
1 |
It will be seen that there are several comets whose tails have been observed more than once. This fact suggests that there may be some connection between the visibility of comets and their tails. It is possible that the visibility of comets may be influenced by factors other than those which affect their tails. For example, it is possible that the visibility of comets may be influenced by factors such as the distance between the comet and the observer, or by factors such as the angle between the line of sight and the plane of the comet's orbit.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day.
It is also possible that the visibility of comets may be influenced by factors such as the phase of the moon, or by factors such as the time of day. For example, it is possible that the visibility of comets may be influenced by factors such as the phase of
THEIR SPECTREUM-METEORS
which almost overpowered the bright bands. The light of the meteors alone also to be chiefly reflected sunlight, as in the case of the nodular light, and there was no visible reflection from the earth.
A connection has however in recent years been established between the meteoric group and a similar group of small particles called meteors, which in their journey round the sun sometimes pass through the earth's atmosphere at a height of 75 miles (a second on the average) that they are "ignited" by the heat of the air, and are seen as falling stars," at a height of about 73 miles on the average. These meteors are not only completely consumed in their passage through the air by the time they have got within about 85 miles of the earth, but they are so small that they consist of bodies, probably only a few grains in weight; but in some cases they may be larger than a grain of sand. The earth after the explosion of a large meteor, such as a meteorite, is left with a residue of dust which is said to be of different character from the ordinary falling stars, which generally appear moving in the same direction. This is shown by the fact that their paths all radiate from one point, which is known as the "point of origin." A system of parallel straight lines seen in photographs taken during the night when meteors are seen diverging from a point about mid-night, very frequently appears to be due to a stream, such as the Perseid, on account of their diverging from the constellation Perseus, is an example of this. Another well-marked shower, radiating from a Leoconic star, is that of the Leonids, which occurs every November 17th and again, on November 27th, another group di- verges from the same star. The Geminids are principally streams, a list of more than a hundred well ascertained groups being given by Mr. H. C. Rowan. In most cases these par- ticles are traveling nearly in the same direction.
![]() A diagram showing a series of parallel lines radiating from a central point.
PLATES OF METEOR STREAMS.
Now all this clearly points to an external origin for these haloes; and as the supposition that they are en-
dows thrown out from the lunar volatilizes seems
to be the only one which can account for such phenomena being
in itself improbable, we are thrown back on the theory
that they are meteoric haloes, and that the meteors circu-
lating round the sun in streams. This view is sup-
ported by the fact that Halley's Comet, which was
observed by the Lomelis, is that remarkable
displays of these meteors occur every 33 years,
and that the period of its revolution around the sun is 76 years.
That the time when we pass through the track of the shower
greatly influences the number of meteors seen.
The first circumstance might be explained by suppos-
ing this group of meteors to have been formed at a
little more than 35 years or a lit-
tle less, so that every 33 years the earth comes
into a position where it is at the point of the
path of the meteors and of the earth (which are
occasionally in opposition) and therefore does not come in the direction of a point in the ecliptic)
being at the same time approaching the meteoric stream to circulate
round the sun in a long ellipse in which it will be about 20° away from the plane of the earth and
meteors by 29° corresponding to half a year 35 years,
as it is found by elaborate calculations that the attrac-
tions of the planets do not affect appreciably the plane of a long ellipse. Now the
period during 33 years, the earth will pass through
the plane of this ellipse, as found by Kepler's Third
Law to be nearly that of Saturn, or about 10 times that
of Jupiter. But since no other planet has such an orbit,
they will, when farthest from the sun, be about
Half of this lagging is due to a shift of the equinoxial date along the ecliptic, so it will be explained by assuming that all these meteors with the earth's orbit, inferior to this star, being thus half a year off from
SIBILA'S COMET AND THE METEORS OF NOV. 168
as distant as Uranus. The direction in which they are moving is unknown, but their velocity can be calculated from Kepler's Second Law. The orbit of the comet was found very close to resemble that of the planet Mercury, and the case of the Perseids showed that they moved in the same path as the great comet of 1802, whilst the April meteor stream of 1873; but the connection between meteors and comets has not been established. On November 16th, 1680, a comet appeared in the east, and on the 25th it passed through the western part of the constellation of Sagittarius. It was visible until December 1st, when it had almost disappeared. This comet was probably Sibila's Comet, which appeared on November 16th, 1680, and was visible until January 2nd, 1681. It was a double comet, and its appearance was accompanied by a shower of meteors. The meteors were seen just about the time the comet was expected to be near us, but a comet was actually seen just before it appeared in the heavens. The meteors were seen in the heavens for several days after the comet had passed. A telegram predicting the probable appearance of a comet was sent only allowed the comet to be seen on two days, leaving it still an open question whether the meteors were caused by the comet or not. But however this may be, it is certain that the meteors were caused by a shower of falling stars. There is one noticeable feature about some of the meteor streams, especially that of the Perseids, which is that they are spread out. Thus the dense part of the stream passes through the earth's atmosphere at a point where it crosses the meeting place with the earth's orbit, the dense part being nearer to us than the rest. This is true of Sibila's Comet, as well as that of 1866; but though the foremost particles will have moved through a large area by the time the last particles reach us, they will still be moving towards us at a speed greater than that of light. They will therefore be able to reach us even if we are not looking directly at them. In other words, all that the particles will be tolerably near to...
104
BEER ACCOUNT OF
gether, and they may then form part of a moderately compact comet. This branch of astronomy is, however, every of such recent growth that much is still uncertain.
We will now give brief account of a few of the most remarkable comets which have appeared in our times, the records of the ancients being too vague to enable us to determine their orbits with any degree of certainty. The comet of 1861 has been already alluded to, as being remarkable for its near approach to the sun's surface, and also for the phenomenon of the tail being seen at the same time as the body was passing over fully 30° in the heavens. But this comet is almost unique in this respect, and we cannot conclude that these bodies move in parabolas, or in very long elliptical orbits, which would explain their sudden appearance and their attraction if the velocity were greater than that corresponding to the average distance from the sun. We can only conclude that they move in a way in which the velocity at the same distance from the sun is less than that corresponding to a circular orbit, and therefore must be moving with a greater velocity than that corresponding to a circular orbit. If the body have a greater velocity, and therefore move over a certain space in less time, than it would do if it moved with a uniform velocity, so that it will have run off the circle as it were, because it has passed through more space in the same time. If it be either a long parabola, or even a hyperbola, all of which lie outside the circle, just touching it at one point. If the velocity be about 1½ that in the circle, a parabola will be formed; but if it be greater than 1½ that in the circle, a hyperbola will be formed. On the other hand, if the body take a path between two circles, and have a velocity less than in the circle, the sun will have pulled it out of its orbit into one of these circles; but if it be greater than in the circle, it will escape from both circles, and go on to infinity. An ellipse, which fat's aperture inside the circle, reaches only at its point where it is furthest from the sun. The comet of 1758 was such an example; and so was that of 1861. The comets of 1862 and 1863 are also examples of this kind. The comet of 1866 has been described by Messrs. Lalande and Delisle as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1869 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1870 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1871 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1872 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1873 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1874 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1875 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1876 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1877 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1878 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1879 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity. The comet of 1880 has been described by Mr. Lalande as having approached within 2° of the sun's surface; but I am not aware that any observations have been made on its motion after leaving the sun's vicinity.
REMARKABLE COMETS.
a velocity greater than that of the earth, whose nearly circular path they just touch, and when, therefore, a velocity less than that of Uranus, whose orbit they describe, would cause them to fall into the sun. The comet of 1784 deserves mention from its having changed its place in the heavens during its passage, and respecting it resembled the great comet of 1811, on which account it was called the "Comet of 1811." This being as bright as Jupiter shortly before its perihelion passage. In 1760 appeared a bright comet, with a period of revolution of about 35 years, and a length of forty millions of miles (half the internal hori- zontal diameter of the earth's orbit), which was visible for seventeen months, and was accompa- nied by a tail of about 200 million miles long, though its apparent length never exceeded 23". From the length of time during which it was observed the distance between the comet and the sun must have been less than 1°. The period of revolution appears to be no less than three hundred years. It is probable that the greatest and least distances of the comet from the sun will be at those points where the plane of its orbit is perpendicular to that of the earth; so that the comet is carried to a distance fourteen times that of Neptune; but this, however, is only conjecture. The distance of the nearest fixed star. With regard to the comets which have passed through our solar system, it is sufficient to enable us to distinguish with certainty be- tween those which are periodic and those which are non-periodic. We may say that their eclipses must be exceedingly rare. In 1819 a fine comet appeared, which passed over the earth in 1825, and again in 1835. The comet of 1841 first showed itself in the northern hemisphere in 1843, and then returned in 1846.
In southern latitudes it was an most brilliant object, being seen for several days, with a tail several degrees long, and after- wards, when it got clear of its rays, in the evening until it had disappeared. Its greatest distance from the sun was about 200 million miles; its mean length being some 200 million of miles, or more
106
REMARKABLE COMETS
than the diameter of the earth's orbit. The orbit of this comet is the most remarkable known, passing within about 10,000 miles of the Sun's surface, but never coming nearer than 35 million miles. The period of its revolution cannot even of short period cannot be determined, as the path of the comet is so irregular that it could hardly be distinguished from a straight line. It has been observed to pass through the solar system at least twice, and that portion of the orbit which is about 300 times as distant from the sun as the perihelion (the point nearest the sun) was in 1858 (Lobatch), which was a most beautiful object in the autumn of 1857. The comet passed through the solar system on June 29th, corresponding to a real length of more than 50 millions of miles, and was then seen by observers in all parts of the world, nearly centrally over the bright star Arcturus, but nothing peculiar was noticed. The most remarkable feature of this comet was its great elongation, with two arcs or arches which formed the head and tail, arranged symmetrical to each other. The arc which formed the head appeared to be an ellipse of about 2,500 years' period, and that which formed the tail an ellipse of about 300 times that of the earth.
The comet of 1861 surprised astronomers in these latitudes by its sudden appearance above the horizon, and was visible for several days in all parts of the southern hemisphere. On June 30th, when it was first seen by observers in England, it was passing through the tail, which was then seen as a great fan, the only unusual appearance noticed being a phosphorescent light near its head.
At this time the head of the comet was some 14 million miles from the earth (about 12 million miles). On July 3rd the tail extended over 197°, reaching out to about 25 million miles, and as the comet receded from the earth the apparent length rapidly diminished. For a few days after this date it was still visible to those who had fans of light seen in the head were very fine. Its pe
GREAT COMET OF 1861.
103
[The above diagram shows the head of the great comet of 1861, as seen on the morning of June 31, through the Equatorial telescope at the Dominion Observatory, Ottawa.]
108
PEOEOIDAL COMETS.
rope appears to be about 400 years, the greatest and least distances being respectively 110 times and 3 times of the earth from the sun.
In 1769, when this comet appeared, the head when brightest being nearly equal to a star of the first magnitude, was seen to consist of two tails, one secondary tail. From one side of the nucleus very long rays extended, which curved round towards the tail, which appears to have been, contrary to the general rule, considerably in- creased by the action of the sun's rays on the comet.
It was a lap-sided character about this comet which pre- sented itself to the attention of astronomers. The orbit of this comet (which is similar to that of Halley's) was discovered in 1758. During the pe- riod of 180 years, the greatest distance from the sun be- ing about 50 times that of the earth (14 times that of Mars), it has been observed at intervals during each period of 400 years.
The comet of 1874 was similar to the late named comet in general appearance, and in position in the heavens. It was seen to emit a bright light, re- secting parabolic arcs of light, which gave it a very beautiful appearance in a large telescope.
The most remarkable of these flares suddenly into- ced in 1882, and continued for several days. This com- et. When first seen in the northern hemisphere it was estimated to be about 300,000,000 miles distant from the sun. When first seen in the southern hemisphere it was head around with two tails; but they were connected by a well defined bar, or bridge, of light between them. This comet was very famous, both for its size and for the regularity of its ap- pearance. It was seen at intervals during twenty-two years having been recorded between A. D. 121 and 143. In 1882 it returned again, and when it did so, the return was predicted. Halley having found the orbits of the comets of 1531, 1677, and 1831 to be very similar to each other, he concluded that we were really three apparitions of the same comet.
REMARKABLE COMETS.
109
which might be expected to return about the begin-
ning of 1750, the period from 1697 to 1683 being
the time of its last appearance, and that of
Jupiter. At its last appearance in 1835 the comet
was seen by many observers, but only under
conditions, when it filled Europe with alarm; though it
appears to have lost much of its glory, it will doubtless
reappear at some future period. It was discovered
in 1835, and has been observed since that date.
This comet approaches the sun within 1/8th of the
distance of the earth from the sun, and its motion
exceeding one-eighth of the planet Neptune.
CROOK'S COMET.
Another very regular periodic comet is that known
as Crook's, of which above twenty returns, correspond-
ing with periods varying between 12 and 17 years,
from 1786, the period being not quite 23 years. This is a
comet of great brilliancy, and is often seen under
favorable circumstances, and usually destitute of
a tail. It has been observed at intervals during its
periods, but has never been seen in any other state
than that of a bright star. Its first appearance was
about 1786, and it has been supposed to afford
![]() A small image of a comet.
10
PERIODEAL COMETS.
evidence of the existence of a very rare resisting me-
dium in space, which, by diminishing the comet's ve-
locity, would cause its orbit to become more elongated
and greater angular velocity. Its distance from the sun
is 385 million miles, and its period of revolution round
Jupiter, Iola's comet, with a period of 61 years, is remark-
able from the circumstance of its first inter-
ruption having occurred in 1872, November 27, as already mentioned.
The comet was discovered on January 14, 1872, when
it divided into two distinct comets, which separated
from each other at intervals of about three months,
from us; an interval which, at the next apparition in
1893, had increased to about six times the moon's
distance from the earth. The first of these comets
of two heads. Neither comet has been seen
since then, but the second one was observed again
and again in 1896, and if either of them caused the mate-
rial to be thrown off from Jupiter, it must have re-
tarded six months the interval since the last ap-
pearance in 1892. Iola's comet was first observed
in 1872, and has been seen ever since that time. Its greatest
and least distances from us vary respectively with those of Jupiter and Ve-
neus respectively. The perihelion comes at the end of this work, with a few particulars about their orbits. It will be noticed that the greater num-
ber of comets are found in the plane of the ecliptic;
further, the plane of the comet is so adjusted with ref-
erence to that of Jupiter that it passes near Jupiter,
which may therefore, by his
attraction, be made to pass through an ellipse of short peri-
od. This is what actually happened in the case of Lecchi's comet, which was
discovered in 1872. In this case it passed through a short
period, during its having passed very close to Jupiter
and Venus. The comet was afterwards again completely destroyed by another and still closer approach to the same planes, which appears to have
ORIGIN OF COMETS.
greatly increased the least distance from the sun, carri-
ying the comet altogether beyond the range of our
solar system, and even to the vicinity of the earth in 1780, within six times the distance of the moon. The comet was then in a retrograde course, though the comet's path was much disturbed.
[The remainder of this chapter is part of the Warner-
son article "On the Origin of Comets," published in
"Albany, N. Y."]
It is evident that testimony seems to favor the supposi-
tion that comets originate outside the solar system.
The failure of any one to discover a comet which has
no one as its origin, should move in elongated orbits,
and have no other origin than that of the sun, is very
striking. Let us suppose, however, that all comets must have
their origin in the sun, and that their orbit round the
sun's system has been evolved. It has been shown
that the viscosity of a comet is so great that it cannot
escape from the control of the sun, that it may escape from the control of the sun, and he projected into space with such velocity that it will not come
up on a given straight line forever; unless,
perhaps, by some means, it may return again to another sun, lying near its path, acquires its flight. The
possibility of such an occurrence is not excluded by
the fact that comets are found in every direction (Leavitt's 1779) is sup-
posed with good reason to have undergone that fate.
That they may have returned to the sun at some time
may have happened in other cases.
An examination of the laws of gravitation and reflection proves that the stars which surround us on all sides are remarkably like our own sun. Some of them are even brighter than our own sun. In order to understand this analogy, we must suppose that these suns are also at-
tached to a central body, and that they are kept in orien-
tation that encountered myriads of comets projected forth
from this central body. This hypothesis is supported by
now flying through space in every direction—reasons
thereof being from star to star. By mere chance some
112 NUCLEUS OF A COMET
of these bodies must come under the sun's far-reaching power and be drawn into our planetary system.
The nucleus of a comet is generally supposed to be very small in comparison with that of the comet itself, but this supposition has been found large enough to exert a sensible attraction upon any celestial body found in its vicinity. This attraction is so great that it can only be explained by the most extreme scepticism, that the real, solid nucleus, if it exists at all, is liquid.
It is certain that no body entirely gaseous could exist in the neighbourhood of the sun, because the heat of the sun would soon evaporate all such liquid bodies in their practical application to the explanation of elementary phenomena, are extremely conclusive against the existence of a solid nucleus. The unknown element—mass of the comet—radial radiation, which is supposed to be emitted from the nucleus, is extremely difficult to show how a swarm of such radials could possibly exist without being absorbed by the sun. It is impossible to resist the tremendous tidal action to which it would be subjected in the vicinity of the sun. In fact, we must suppose that the sun's action on a comet is more than usual catastrophe, into such a swarm, as the sun's pressure will cause them to disintegrate. It is probable that there is either a solid or partly liquid body within the comet, but it is impossible to say whether it consists of a mass of particles or of a solid body. The latter case seems more probable, since it is possible for a solid body to consist of an aggregation of loosely coalescing pieces or particles, than of a single firmly united mass.
If, now, we suppose the nucleus to be approaching some other body, and if we assume that the liquid or other volatile matter on the "sunary" side common to evaporate and be diffused about the atmosphere surrounding the comet, in order to explain why there are no comets in streaming jets, and of the necessity obscured by vapour, might be produced.
HOW THE TAIL IS FORMED.
To account for the backward curvature of the jets and the peculiar form and direction of the tail, we must look for some additional force. In all probably cases this force is to be sought in its effects on the power of gravitation. But since we have no means of measuring the effect of gravity with sufficient facility, we must find a relation which will enable us to calculate it from other data.
The only force suggested by experience as competent to these requirements is that of electrical repulsion. The electric charge of the particles of matter similarly electrified mutually repel each other. We know that when two bodies are charged by friction, their repulsion and attraction are equal, but that when one body is charged and another is neutral, the former attracts the latter, and the latter is electrified to a much higher degree than the former. This fact shows that the electric charge can be transferred from one body to another, and that it can be increased by contact with another body. It also shows that the electric charge can be removed from a body by contact with another body. It also shows that the electric charge can be removed from a body by contact with another body.
We may therefore suppose that the particles of matter in the jet are electrified positively, and that they are attracted towards the nucleus by the negative charge of the nucleus. When they reach a certain distance from the nucleus, they are repelled by the positive charge of the nucleus, and are driven back towards it. As they approach the nucleus, they are attracted again by the negative charge of the nucleus, and are driven forward again. This process continues until they reach a point where they are neither attracted nor repelled by the nucleus, and are therefore at rest.
It is evident that this explanation cannot account for the backward curvature of the jets. For if the particles of matter in the jet are attracted towards the nucleus by the negative charge of the nucleus, they should be driven forward towards it. But if they are repelled by the positive charge of the nucleus, they should be driven back towards it. And if they are attracted again by the negative charge of the nucleus, they should be driven forward again. But if they are repelled by the positive charge of the nucleus, they should be driven back towards it.
Since this explanation does not account for the backward curvature of the jets, we must seek for some other cause. One possible cause is that the particles of matter in the jet are electrified negatively, and that they are attracted towards the nucleus by the positive charge of the nucleus. When they reach a certain distance from the nucleus, they are repelled by the negative charge of the nucleus, and are driven back towards it. As they approach the nucleus, they are attracted again by the positive charge of the nucleus, and are driven forward again. This process continues until they reach a point where they are neither attracted nor repelled by the nucleus, and are therefore at rest.
It is evident that this explanation cannot account for the backward curvature of the jets. For if the particles of matter in the jet are attracted towards the nucleus by the positive charge of
114
MULTIPLE TAILS
ty. These would curve backward more than would the lightest molecules driven off at the same time, and so as to produce a tail of the opposite direction to that of their average observed direction and form suggest that the tail of the comet is not due to any peculiarity peculiar to itself. We may even venture to suppose that the tail of greatest velocity and least inclination is produced by the motion of the comet in its orbit, and that the other tails are due to some other cause, such as the action of the sun's rays on the tail carbon, with or without other elements; and assume one of these, therefore, would most likely be found.
It has been shown by Mr. Bessel that this hypothesis, as in the formation of the tail, is due to the force of imponderable power. The straightest tails which we have seen are those which are pro- posing a repulsive force not much greater than twelve times the force of attraction between two equal charges of electricity. It is probable that a quantity soon (sometime-like in form) may be produced by these above mentioned causes, and that they will be sufficient to overcome the attrac- tion of gravitation.
It is evident that it is equally erroneous to sup- pose any great amount of material wasted in the for- mation of the tails, or to suppose upon the trans- parent brightness of its structure. The comet is a body of considerable mass, and probably quite immense. They may, like the sun, affect the earth's magnetic condition, and thus to some extent influence our weather. This effect has never yet been perceived. In spite of some chance cor- relations between comets and remarkable public events, no well-informed person would venture to assert that comets cause them. By a literal and credulous interpretation of any frequently occurring celestial phenomenon, one might conclude that comets are always accompanied by earthquakes.
When a comet is converted into meteoric bodies, they are very small indeed, and may be supposed to fall upon us sometimes directly but usually through minute effect. Some have thought that a sensation portends of the like. When
COMETS AND METEORS. 110
the earth receives its generation in this way; but the weight of scientific opinion seems to be against that hypothesis. The impact of meteors upon our atmos-
phere has been observed by many observers, and is seen in the form of dust. This may be the origin of the comets, but it is not probable that they have been in recent times. The finer particles of it may have been produced by meteorological phenomena; but this is merely conjecture.
A more remote effect may be sought in the possible fall of comets into the sun's atmosphere, and into the sun.
Owing to his vast bulk, the sun would attract all bodies within his sphere of influence, and it is certain that his effect upon the sun's heat is insigni-
ficant. It is therefore necessary to look elsewhere for the origin of the sun's heat in a constant, though to us imperceptible, shrinkage of his vast bulk.
The sun's heat is constantly increasing, and comets and meteors have been rather vaguely suggested as the cause of it. But we cannot expect to find with equal persistence for a long period, we might expect to find them at any time.
Yet it would still be an open question whether comets cause the spots, or whether greater activity of the sun causes their appearance. We know that comets had more will be visible; with probability in favor of the latter supposition.
CHAPTER VI.
To the naked eye on a fine night, the stars bewildering us by their number, making it impossible to give each of them a name. The ancient astronomers were accustomed to adopt of grouping them into constellations,
named from some familiar resemblance to or con-
sideration of some object. These constellations were distinguished by their position in the constella-
111
116 THE STARS--THEIR NUMBER.
tion to which they belong, but afterwards, as the less conspicuous stars began to be observed, those in catalogue 300 were found to be brighter than the letters of the Greek alphabet in the order of their brightness, so that a Antigone would be the brightest star in the catalogue, and a Zephyrus the second brightest, and so on, numbers being used being when the alphabet was employed. The stars have been only once in modern times, it has, however, been necessary to make new catalogues in which the star's place is given, and the number corresponding to the star in that catalogue, and this has been done by means of a careful enumeration, for the smaller stars at any rate, and also for some of the larger ones. In 1850, 3,500 stars are to be seen in the United States, and of these only about 2,000 at any one time; the number thus visible varies with the season, for in the southern portion, always below our horizon, is only about 100; while in the northern part, a multitude of stars is enormously increased with every increase of latitude. This is very curious, and very agreeable to the eye. The gradation of brightness is found in the heavens (except in certain cases) by means of what are called "magnitudes," and these are numbers. For instance, the stars visible to the naked eyes are roughly classified into six classes. Those which are called very bright stars, ninetens or even tens of millions of times brighter than the sun; by no means exactly equal in brightness); after these come about 50 stars of the second magnitude; about 100 of the third magnitude; about 200 of the fourth magnitude; half magnitudes are introduced, a star of the 34 magnitude is said to be half a magnitude fainter than another of the same magnitude; and so on down to the third and fourth magnitudes. In delicate observations of changes in the brightness of certain stars,
| 116 THE STARS--THEIR NUMBER. |
| tion to which they belonged, but afterwards, as the less conspicuous stars began to be observed, those in catalogue 300 were found to be brighter than the letters of the Greek alphabet in the order of their brightness, so that a Antigone would be the brightest star in the catalogue, and a Zephyrus the second brightest, and so on, numbers being used being when the alphabet was employed. The stars have been only once in modern times, it has, however, |
| has been necessary to make new catalogues in which the star's place is given, and the number corresponding to the star in that catalogue, |
| and this has been done by means of a careful enumeration, for the smaller stars at any rate, |
| and also for some of the larger ones. In 1850, 3,500 stars are to be seen in the United States, |
| and of these only about 2,000 at any one time; the number thus visible varies with the season, |
| for in the southern portion, always below our horizon, |
| is only about 100; while in the northern part, |
| a multitude of stars is enormously increased with every increase of latitude. |
| This is very curious, |
| and very agreeable to the eye. The gradation of brightness is found in the heavens (except in certain cases) |
| by means of what are called "magnitudes," and these are numbers. |
| For instance, the stars visible to the naked eyes are roughly classified into six classes. |
| Those which are called very bright stars, |
| ninetens or even tens of millions of times brighter than the sun; |
| by no means exactly equal in brightness); after these come about 50 stars of the second magnitude; |
| about 100 of the third magnitude; |
| about 200 of the fourth magnitude; |
| half magnitudes are introduced, |
| a star of the 34 magnitude is said to be half a magnitude fainter than another of the same magnitude; |
| and so on down to the third and fourth magnitudes. |
| In delicate observations of changes in the brightness of certain stars, |
**Magnitudes—the constellations.** 117
tena, or even hundreds of a magnitude are used to express the difference between two stars, but we shall confine ourselves with those of the standard magnitudes, so that instead of saying that one star is 3.5 magnitudes brighter than another, we might call it 3.6, or perhaps more accurately, 3.62.
Below the sixth magnitude we have magnitudes only of very faint stars, which are not visible to the naked eye, being 21st times as bright as those of the magnitude 6.0. The stars of this class are called "nebulae," and their light together would not be quite so bright as a single star of the magnitude 6.0.
With the first six magnitudes this relation does not hold exactly, the classification being somewhat arbitrary, but it holds fairly well for the next three magnitudes, and considerably in their scales, though agreeing pretty nearly with the law stated above. For example, a fifth-magnitude star equals in brightness at an average first magnitude star, while a sixth-magnitude star is very nearly with the scale of 3 for each magnitude.
We shall now endeavor, with the help of the key Map (Plate II), to show how these relations apply to the most conspicuous stars, in which he will be much more likely to find himself than in any other way. We must be cautious and sceptical about our conclusions, and we did not point out how to find it out.
This map represents part of the imaginary sphere of the heavens so it would be seen on a moonlight night (when the moon is not too bright) by looking through a telescope at half the radius beyond the pole of each sphere, stars below the horizon being omitted. The principal stars are shown by dots, such as bengal lights; luminosity, etc., are necessarily much exaggerated in order to make them visible on a sheet of paper. The principal stars are distinguished by their position in the sky, and by their names; those which are not visible from this latitude are marked by a circle round them. Those which are visible at this latitude are shown in right ascension and declination; those which are visible at lower latitudes are shown in right ascension and declination; those which pass at a distance of 42° from the Pole for Chicago.
| Table |
Details |
| Magnitudes—The Constellations |
117 |
| Tenta, or even hundreds of a magnitude are used to express the difference between two stars, but we shall confine ourselves with those of the standard magnitudes, so that instead of saying that one star is 3.5 magnitudes brighter than another, we might call it 3.6, or perhaps more accurately, 3.62. |
Below the sixth magnitude we have magnitudes only of very faint stars, which are not visible to the naked eye, being 21st times as bright as those of the magnitude 6.0. The stars of this class are called "nebulae," and their light together would not be quite so bright as a single star of the magnitude 6.0. |
| With the first six magnitudes this relation does not hold exactly, the classification being somewhat arbitrary, but it holds fairly well for the next three magnitudes, and considerably in their scales, though agreeing pretty nearly with the law stated above. |
For example, a fifth-magnitude star equals in brightness at an average first magnitude star, while a sixth-magnitude star is very nearly with the scale of 3 for each magnitude. |
| We shall now endeavor, with the help of the key Map (Plate II), to show how these relations apply to the most conspicuous stars, in which he will be much more likely to find himself than in any other way. |
We must be cautious and sceptical about our conclusions, and we did not point out how to find it out. |
| This map represents part of the imaginary sphere of the heavens so it would be seen on a moonlight night (when the moon is not too bright) by looking through a telescope at half the radius beyond the pole of each sphere, stars below the horizon being omitted. |
The principal stars are shown by dots, such as bengal lights; luminosity, etc., are necessarily much exaggerated in order to make them visible on a sheet of paper. |
| The principal stars are distinguished by their position in the sky, and by their names; those which are not visible from this latitude are marked by a circle round them. |
Those which are visible at this latitude are shown in right ascension and declination; those which pass at a distance of 42° from the Pole for Chicago. |
115 GREAT AND LITTLE BEARS—CASSIOPEIA.
really. On any fine night, if we turn to the north (or south), we shall see two bright stars, which are called the Great Bear and the Little Bear. These are seven bright stars marking the constellation of Ursa Major, or the Great Bear, and Ursa Minor, or the Little Bear, at the centre of the map and a little to the left—the two lower stars of which point pretty nearly to the obelisk (the monument erected by the Romans to their gods). They are therefore called the pointers. In winter, when the sun is low in the south, these two stars will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round the pole, and thus the seven stars of each figure remain visible throughout the year. In the form of the constellation, however it be turned with respect to the observer's position on earth, it will be seen to form part of a somewhat similar though much smaller figure, that of Cassiopeia, or Cassiopea, who is supposed to be a queen of Ethiopia. The stars preserve the same positions among themselves, swinging as a whole round
NORTHERN CONSTELLATIONS.
consellation Persuas. A line through the two wander-
ing stars, Aldebaran and Regulus, forms the Andro-
mdea, and about as far beyond will pass a little west
of the same line a star which is not generally com-
monly visible to the naked eyes (though several
more may be seen on a very fine night), whilst nearly
opposite to this is another star, which is called
having a first magnitude star, Aldebaran, at one tip,
and having a second magnitude star, Regulus, at the
other. These two stars are in the Andromeda, and
including the path of all the principal planets,
which are never far from the ecliptic. The Zodiac is
divided into twelve constellations, each of which con-
tains about 30°-Aurora, Gemini, Cancer, Leo, Virgo,
Libra, Scorpio, Sagittarius, Capricornus, Aquarius,
Pisces—the other being given that in which it runs
through the zodiac. The two stars of the Andromeda
are two bright stars, $\alpha$ and $\beta$, apart, and nearly midway between the Perseus and Pegasus; in Gemini are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Aquarius are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus and Pegasus; in Pisces are two
bright stars, $\alpha$ and $\beta$, apart, and nearly midway
between the Perseus
NOTHERESI CONSTELLATIONS.
with the name of the constellation; thus Antares is also called a Scorpius; Acheronar, or Tauri, and so in other cases.
But the constellations most of the northern, Bootes is distinguished by the brightest star of the heavens, Vega, which is situated at the same distance as to be by the last two stars of the Great Bear's tail; 30° north of the pole-star, and 5° south of the Northern Crown (Vaurus), composed of a tolerably perfect wheel of stars. A line from the tip of the tail of the Great Bear to the pole-star will reach far beyond, will strike two stars 3° apart, α Hercules and β Hercules; and from this point, in the direction of the other stars of the constellation Hercules lying to the north of these two, and therefore east of Ceres, we shall find a second wheel of stars, which is further cast of the Crown in the very high first mag- nitude, Vega, and which is composed of four stars near forming a sector of a triangle to a hundred of four stars, and which is called by some the autumn evening. In the direction of the horizon (i. e., south-north) lie three bright stars, almost 3° apart, α and β Aquilae, and γ Aquilae; and from this point, in the direction of the square in Pegasus also points to them at a distance of about 3°. The third star is α Aquilae, or the bright star Pyxis on the west. The north-west diagonal of the same square will strike (at nearly 3°) β Aquilae; and then we have another constellation formed by a signing line of bright stars, which are situated at a distance of about 3° from each other. This is a sign of a saw flying, while the stretched head is shown by α Aquilae; and then we have another sign formed by α and β Aquilae. The S. W. continuing our course westward, we get to Pegasus and Andromeda, already noticed; then we have α Andromeda, or Alfa; and β Andromeda (α and β Persei), of which the tail is seen at a distance of about 3° from α Andromeda; and thus forms the tip of the tail to the square of Pegasus.
ORION AND THE DOG STAR.
Whilst a Perseus forms the apex of an obtuse angled triangle with the Dog Star, the other two angles are formed by a line from the square of Pegasus through $\gamma$ Andromedae, and from the square of Cassiopeia to $\beta$ Cassiopeiae (the Auriga), with $\beta$ Aurigae a little to the east, between the two lines. The line joining these two stars is the line of Orion.
Of the southern constellations visible in these lati-
tudes, by far the most striking is Orions, which is on
the meridian at about 3 o'clock. It is composed of
a line of three stars, $\alpha$, $\beta$, and $\gamma$ Orionis,
lying in the direction of a line from the south point
of the horizon to the north point. This line is very
difficult in identifying this magnificent assemblage
of stars, because it is so close to the horizon.
Four bright stars forming a quadrangle represent the shoulders and legs of Orions. Betelgeuse and Icarus are also represented by two stars, but they are not so prominent as those of Orions. These four stars form a quadrangle representing the body of Orions. The line joining them is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The line joining these four stars is called the line of Orions. The
line joining these four stars is called the
line of Orion.
The other two angles are formed by a
line from $\alpha$ Orionis through $\gamma$ Andromedae, and from $\beta$ Cassiopeiae to $\beta$ Aurigae, with $\beta$ Aurigae a little to
the east, between the two lines.
The
line
joining
these
two
stars
is
the
line
of
Orion.
Of
the
southern
constellations visible in these latitudes, by far
the most striking is Orion's, which lies on
the meridian at about 3 o'clock.
It consists
of a straight horizontal row consisting
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and $\gamma$
Orionis, lying in a direction from south to north.
This straight horizontal row consists
of three bright points, $\alpha$, $\beta$, and
10
127 MILKY WAY—CLUSTERS—NEBULAE.
Cylindrical constellations which will be on or near the meridian at the four seasons of the year about ten o'clock in the evening; if the appearance of the Milky Way is observed, it is only necessary to reckon every two hours later in the time we have just given, for ten o'clock a month later, and conversely for the earlier times of the evening. The appearance of the Milky Way in December will be the same as those at ten o'clock in January, whilst the appearances will be reversed in March and April.
Taking ten o'clock as the evening, then, we shall find that the Pleiades are on the meridian, Ursus Major usually overhead, the Pleiades being in the north-west, and Arcturus in the south-east; in midsummer they are in the east, and Arcturus with the Green in the south; at midnight they are in the north-west, and Arcturus setting, while Vaga, Aquila, and Cygnus are in the east, and Uranus rising. In winter, the Pleiades are on the meridian, Vaga and Aquila west of it, and Arcturus setting; at midnight they are in the south-west, and Persius and Capella with the Piscides and Hyades rising; at nine o'clock they are in the south-east, Pegasus in the west, Cygnus low down in the north-west, with Cassiopeia overhead; at ten o'clock they are in the north-west, Cassiopeia and Perseus setting; at eleven o'clock they are in the east; at Castor and Pollux, Iphigenia (rising), and Procyon (setting); at twelve o'clock they are in the south-east, Arcturus rising. At midnight they are in the north-west, Cassiopeia rising; at one o'clock they are in the east; but with what has been given before, they will be sufficient to enable us to understand how far it is possible for this purpose it will be enough to remember that about ten o'clock we have all of these constellations on or near our meridian; at sunrise, Arcturus and the Green; in summer, Ursus Major and Perseus; in autumn, Piscides and Hyades; all at about the position of the sun at noon in summer.
The Milky Way is a beautiful object, the milky way, which adds greatly to the beauty of the heavens as a
THEIR SPECTRA. 15
moonlight night, especially in summer. This belt of nebulae light is composed of countless zones with many patches and outbursts, but on the main coinciding with one another, and extending to the equator. With the telescope this bright band appears as a continuous spectrum, which can only be seen by the individually perceived by the naked eye, and in some cases to close together that a powerful telescope is required.
Sub divisions of stars are called clusters, and at times they appear as a group of stars, or even as a circle in form, if the more scattered ones be removed. The clusters are very numerous, and even in small telescopes, but powerful instruments are required to show the more compact clusters in all their splendour. The most beautiful cluster is in Cancer (nearst equi-distant from Castor, Procyon, and Pollux), and consists of about 300 stars. The distances from Cassiopeia to these are visible to the naked eyes, and the objects invisible, which have been observed by mistake as mistakings.
As we pass to clusters more and more numerous, we get to those which contain no stars at all. These are the most part nothing but clouds, that can only be resolved into a spectrum of lines when viewed through modern times. When first attention was directed to them, it was supposed that they were comets, but now kind between the clusters and the nebulae, but no more and more powerful instruments were made, until it was found that they were not separated into their component parts, stars this idea was given up. The clusters are composed of two kinds of clusters and most nebulae because only one of de- cidedly different kinds of stars is contained within them. They differ from the most powerful telescope, and the question of the constitution of these objects was left open till 1860, when Mr. Norman proved that the spectrum consisting of three bright lines. Now in addition to these three lines there is also a spectrum of that kind indicates glowing gas, whilst a
134
NEBULAE
Heated solid gives rise to a continuous spectrum, as in the case of the sun, of stars, and of the ordinary clusters. These nebulae, then, cannot be collections of gas, though what that gas remains an open question.
![]() A star cluster and nebula.
STAR CLUSTER AND NEBULA.
Two of the nebulae can be seen by the unassisted eye, one being in the middle of Orion's dagger, where it is visible at 10° north latitude, and at a third of the distance from $\beta$ Andromeda to $\beta$ Cassiopeia. The form of these, which from its spectrum appears to be gaseous, is an irregular shaped mass.
AND STEEL CLUSTERS.
without any decided boundary, in the midst of which is a pretty height multitude of stars, with others scattered about them, forming a sort of nebula. The most conspicuous spectrum, on the contrary of pretty definite shape, presenting the appearance of a long oval, in-
135
This nebula, however, has not yet been resolved into its component parts. It is composed of stars, not composed of gas, unless indeed it be in a very dense form. The light of these stars, when they shine the brightest lines, due to glowing gas, has been received into minute points of light, which, however, do not form a continuous surface, but a dis-
136
nary state. This nebula, midway between $\theta$ and $\gamma$ Lyrae, is one of the most remarkable objects in the heavens, even with a moderate telescope. The nebulae of this kind are much more common than those of the planetary
137
nebulae being far more common. The planetary nebulae form another remarkable class, presenting various degrees of complexity in their composition. They are all composed of gas, emitting the spectrum of glowing gas; allied to these are the nebulae of the "planetary" type.
There are also the strange spiral nebulae, or rather star-clouds. The most remarkable among these is the
138
Bear's tail is the finest example; but perhaps the most remarkable objects are the double nebulae, the double stars being often found within them. These
139
pecula, composed of two oral masses of inconspicuous gas, and containing many stars. Such double nebulae have been observed, though the vast majority have not been studied by modern instruments. The clusters are almost entirely confined to the Milky Way, whilst the nebulae appear to avoid that region. The most remarkable examples are
140
Cora Borealis and the adjacent parts of Virgo in the southern hemisphere. In some cases both clusters and ne-
141
bulae are found in every stage of condensa-
142
tion, passing from groups like the Pleiades through
134
NEBULAR THEORy.
The globular clusters and oval nebulae to masses of stars, like the spiral nebula and others of less regular shape; and the spiral nebula itself, which is a very large and conspicuous nebula, which is so much larger than any other known nebula that it must be regarded as a separate body. The spiral system was originally a gaseous nebula rotating about its centre, which in the course of time had broken up into several portions. Those ultimately coalescing together have formed the sun and planets, and formed a planet rotating about its axis in the same direction as that of the sun. The sun would have a greater velocity outward, and that from inside a less velocity than the outer parts. In consequence of this, the ring would be equivalent to a relative velocity westward. Now, if the outer particles were moving westward, and the inner westward, then in fact a rotation would take place at the centre, where a large central sun would be revolving with respect to the rest of the matter in its neighbourhood, so that only small planets would be able to revolve round it. But if the sun were a nebula, the attraction of the central sun would be lost, and the planets themselves would become independent bodies, and would continue to move in their orbits in the same way as the planets in the large nebula, circularly round their own axes. But if we consider the sphere of attraction of the larger planet being gradually increased by its increasing mass with increasing distance from the sun, and this would be exaggerated by its increasing velocity towards the outside,
though this is only an hypothesis, changes in the
DISTANCES OF THE STARS.
solar system of this nature requiring countless ages for their working out, and being therefore beyond the scope of our immediate observation. The sun is highly peculiar, from what is known of the molecular light that, on our sun is really a nebulous star, while the composition of its atmosphere is such that phosphorous gas may readily pass into the form of phosphorus, which is very rare in comparison with the minor planets than those are compared with each other. It is impossible to detect any change going on in the solar system, or up to the present time in any of the nebula which exist, but we find changes in going from one nebula to another whether they be gaseous or solid. We cannot take place taking in any particular nebula in the course of a few years, but we can see the various features of some of them to all appearance physically connected with stars; there are roundish bodies, which are probably clusters of large stars, in which the process of con- densation has been completed; and then there are others, whilst the spectroscopic reveals us stars which seem to be composed of a mixture of gases, and not from glowing gas, though in this case it is hydrogen, not the unknown substance of the true nebulae. But even when we have seen these stars, and know that the nebulae and clusters too far, for there are points of difference between them and the sun, yet it is evident that there is only a secondary system, forming part of some en- tity.
This much, however, is tolerably certain, that our sun is really one of the stars, and that the earth and other planets are revolving around it. In order to test nearest of them, careful observations showing that the earth revolves about the sun once every year, and not once second across. If, then, we view the star- from the earth's orbit, we shall find that we traverse this small shift of 3", and this is our only means of finding the star's distance, for clearly any parallax
138
DISTANCES OF THE STARS
from different stations on the earth will be quite insen-
sible. It is not necessary that the two observations at
different stations shall be made at the same time, but
at the same time, which would evidently be impracticable,
since the stars move with great velocity through space.
The star's position, and then to wait six months, when the
earth's motion will carry us to the other side of her
orbit, and thus obtain a second observation. The distance
of the earth in its orbit is called annual parallax, represent-
ing the angle subtended by the diameter of the earth's
orb seen from the sun and earth, and may be determined
by measuring this angle with a telescope. 1. By
per-
ception and declination. 2. By measures of angular
distance from neighboring stars. The first method is
the most accurate, but it has been applied with success to the
height of the sun above the horizon, and to the height of half a second—the largest yet found—the whole
of the heavens being divided into 60 seconds each, corre-
sponding to a distance 400,000 times that of the sun,
or some 13,000 times that of Neptune. The only
star which can be used for this purpose is Venus, which separates us from the nearest fixed star, is by a
little more than one degree, and therefore requires a
rate of 150,000 miles in a second, taking years to
reach it. This rate is very nearly that of light. Be-
fore. This in looking at this star we can see its dis-
tance in less than 6 years ago, and thus he it remembered, is one of the
most useful stars for this purpose. It was compared to the determination of the distance of Venus
from Earth by means of eclipses, but it was found that no such thing could be done until we knew the
true distance of Venus from Earth. We must therefore seek such stars for reference as we consider to be proba-
bly at a far greater distance than the star in question. For example, if we wish to find out how far away one of
them behind the other, they will be seen as two points in a line, and their apparent distance between them will alter after their apparent distance between them, bring-
ing them more nearly in a line or throwing their dis-
ABSOLUTE AND RELATIVE PARALLAX. 128
their out. In any case, if such a shift be found, we may expect to find that the stars which have the greatest parallax are those which are nearest to us, and that the number of stars with large parallaxes will be less than the number of stars with small ones. The number of stars with large parallaxes will be less than the number of stars with small ones. This is because the stars which have the largest parallaxes are those which are nearest to us, and that the number of stars with large parallaxes will be less than the number of stars with small ones.
The following list gives the parallaxes of the stars in which any shift has been observed. It will be seen that the stars with the smallest parallaxes are those which are nearest to us, and that the number of stars with large parallaxes will be less than the number of stars with small ones.
| First Method. |
Mag. |
Absolute Parallax |
Light in Years |
| $\alpha$ Contant |
1 |
0.57 |
36 (7) |
| $\beta$ Contant |
1 |
0.57 |
36 (7) |
| Arcturus |
1 |
0.57 |
36 (7) |
| Greenhouse 1850 |
1 |
0.57 |
36 (7) |
Second Method.
|
Mag. |
Parallax |
Light in Years |
| Cygni |
1 |
0.57 |
36 (7) |
| Lalande 1850 |
1 |
0.57 |
36 (7) |
| Vega |
1 |
0.57 |
36 (7) |
| Ophiuchus |
1 |
0.57 |
36 (7) |
| Greenhouse 1850 |
1 |
0.57 |
36 (7) |
In the case of the smaller parallaxes the results are very different from what was expected. For instance, in Greenhouse, 1850, for which a negative parallax relatively to one star in its neighbourhood has been found, indicating that this star is nearer to us than any other star in Greenhouse, 1850—but not much confidence is to be placed in these results.
It may seem strange that some of the small stars give such large parallaxes as they do, but attention was called to them by the discovery that 9
130
STARS IN MOTION
they were moving among the other stars at a rate which, though very small, was far greater than that of most other stars, from which it would seem that this star was moving with a velocity much greater than that of the earth. This statem
ment may strike a reader who is used to think these pha-
ses of motion are only those of the earth, and that we can
accurately observe motions, separated by a long interval, as
applied to the stars in contradistinction to such bodies as
the planets. The largest proper motion found among
the stars is 0°.0005 per year, but this is only 7° per cent,
which at rates of 0°.0005 per year would make a com-
plete revolution in about 68,000 years. In order to have
motion continued uniformly; the double star 61 Cygni
has been observed for nearly two centuries, and has
shown smaller, though still sensible motions, there-
fore being apparently every variety of motion, as there is
no reason why any one particular kind should predominate.
Cygni, the radius of the earth's orbit at the distance of
about 12 times the distance of the sun from us, when
observed from the earth's surface, shows no change in
earth's velocity, or at the rate of about 70 miles a sec-
ond. So many of the stars appear to move motions of
less than 0°.0005 per year that it is impossible to say
sun too may be in motion, carrying our earth and all its
bodies with it. It is therefore necessary to make out what is
to be made out of the stars appear to move in the opposite di-
rection to that supposed for the earth. This is not easy to de-
terminate, for it is only necessary to see whether there is any general drift of the stars which could be accounted for by any known cause. Of more than 10,000 stars,
5,000 stars have been examined, and in the midst of this large number I have never found any thing like a
found a general preponderance of motions away from the earth's direction. The earth itself appears to be moving,
therefore, appears to be moving. Although most of the
stars move, as nearly as we can tell, uniformly in one di-
rection, yet there are some exceptions, the most remarkable being Sirius, which is
to describe an ellipse about a point at its mean ap-
parent distance of $5^{\circ}$ in insomuching like 30 years, and
Pecorini, which recedes in 40 years nearly in a circle,
have been observed to move with such a rapidity as to
result from the attraction of another body, and in ac-
cordance with this supposition, the orbit of Pecorini
seems about 10$^{\circ}$ off, which revolves round Sirius some-
what more slowly than that of Orion, and much more
greater than that of Neptune from the same, whilst Siris-
nus describes in space an ellipse about the center of the
sun, whose eccentricity is greater than that of Neptune from the sun, whilst their ratio of velocity is nearly equal. The eccentricity of
must be much greater, and by removing so near to that
of the sun, it must be less than that of the sun and Ne-
ptune together. It is evident therefore that the center of
the gravity being twice as far from the com-
bined mass of the sun and Neptune as from either, the
angle between them must be very small. This can only be
accounted for by assuming that the apparent number
of bodies being extremely uncertain. In the case of
Pecorini, a similar companion star has been looked for,
but without success.
The two stars above mentioned are rather peculiar
cases, because they are both situated close together.
About each other. In a powerful telescope a large
number of stars which are apparently single to the naked eye appear to be double, and sometimes three or more stars very close together, a suffi-
ciently strong telescope will show that they are not.
In this manner it appears probable that many stars are scattered, and the interest-
ing question arises whether any one of these stars is revolving round the sun. To answer this question we have only to observe
the apparent direction of one star of such a system relatively to the other, combined with observations over a long period of time. By so doing,
tending over many years, the paths of a great many
SIRIUS—BINARY STARS. 181
132
BINARY STARS
have been determined; some of these are given in the following list, with the magnitudes of the two stars, their least and greatest distance apart, and the period in years:
| Star. |
Mag. |
Diameter. |
P.d. |
Orbital |
| C Hercules |
6.5 |
0.7 |
0.8 |
Yellowish and orange |
| C Hercules |
6.5 |
0.7 |
0.8 |
Yellowish and orange |
| Cassiopeia |
6.0 |
0.6 |
0.7 |
Triple; all white. |
| Cassiopeia |
6.0 |
0.6 |
0.7 |
Triple; all white. |
| Eros Majaus |
6.5 |
0.6 |
0.7 |
White. |
| Eros Majaus |
6.5 |
0.6 |
0.7 |
White. |
| Ophiuchus |
6.4 |
0.5 |
0.6 |
Violet and yellow. |
| Ophiuchus |
6.4 |
0.5 |
0.6 |
Violet and yellow. |
| Cassiopeia |
6.2 |
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
20
DOUBLE STARS--SPECTRA OF STARS. 105
Beautiful spectrum of colors in the two stars. The following may be selected as worth notice:
| Star. |
Color. |
Range. |
Class. |
| Cygni. |
Red. |
3 to 6 |
Doubly red and near blue. |
| Bacchus. |
Blue. |
7 to 8 |
Doubly blue and near green. |
| Polaris. |
Green. |
9 to 10 |
Doubly green and near yellow. |
| Orion. |
Yellow. |
11 to 12 |
Doubly yellow and near orange. |
From the evidence of the spectroscopic it appears probable that the temperature of the two stars corresponds in a general way to a difference of condition, the stars being divided broadly into three classes, those with high temperatures, those with low tempera-
ture, and exhibiting a continuous spectrum with very few lines, and those with intermediate temperatures, showing strong absorption lines in a continuous spectrum.
- Red stars, in which the temperature is so low that no molecular compounds can exist, but only free atoms take place, and compound molecules are formed, are called "red" stars.
In some of the stars of the first and second classes there are found lines of hydrogen, indicating a huge configuration of this gas, whilst with other stars, like our sun, the hydrogen is at a lower temperature than in the case of the red stars. In the sun's atmosphere than it emits, causing dark lines in the spectrum. In some cases these lines are due to temporary stars, such as were seen in 1873, 1884, and 1890. On other occasions bright stars burst suddenly on the view, and after a short time disappeared more or less com-
pletely. A star of this kind was observed by me sud-
denly appeared of the second magnitude, fading away
TEMPORARY AND FABULES STARS.
on 15 days to the 8th or 9th magnitude; and the star of 1370 was even more remarkable, at one time surpassing Jupiter in brilliancy.
In the following table, only extreme instances of a much wider class, the variable stars, in which are found all the stars of this kind, are given, their magnitudes ranging from nearly three days to an indefinite length. In some cases, the changes are very great, with the greatest regularity, whilst in others the changes seem to follow no definite law. Amongst the most remarkable of these stars is that of 1369, which at second magnitude, but at intervals of 2 hours, passes through a period of 12 hours, and again to the same, all within the space of 74 hours. The star of 1370 has a period of 24 days; a day, a Copernic from 3 to 5 magnitude in 24 days; and a Lyric fluctuating between 2 to 4 magnitude in 24 days (see Mira). This star goes through its change in about 11 months, and sometimes ranges from brighter than the second magnitude to fainter than the third. A second star of this kind is 2 Anglia is another remarkable variable, changing from first to sixth magnitude in an irregular period; a Oriens is also variable, but with a longer period; and a Cassiopeia, are also irregularly variable, sometimes to fourth magnitude. The periods of these stars are not conspicuous stars have been noted as variable. Nearly all the stars of this kind have been observed to have in several cases been suspected, which would seem to show a change of temperature as they passed through their periods. It is probable that many of them are thought to have changed colour, but accurate observations have not been made on such stars, owing alone being quite untrustworthy for absolute determination.
We saw that, when observations made at wide intervals came to be compared, many of the so-called variable stars were found to be constant. This is not the only startling result. The pole of the
heavens is also found to be moving among the stars, very slowly, but in such a manner that every year it will be remembered that at right ascensions and longitudes of 0°, the sun crosses the equator, so that if the point shifts, the right ascension and longitude of all objects will be altered by the same amount. The right ascensions and longitudes of all stars increase at the rate of about one degree per year. This is called precession of the equinoxes, which is known as the precession of the equinoxes.
The motion will be gained by considering the pole instead of the equinox, which of course always moves with it. It is evident that this pole must move in a circle around the earth's axis, and that in describing this circle (which is a circle about the pole itself) it describes a smaller circle than does the pole (at its rate that would carry it completely round in a few thousand years). But since the pole of the heavens is nothing but the direction of the earth's axis, which it appears has not really a fixed position, we cannot say that it describes a circle. In order to account for the motion of the seasons it was necessary to take account of our own motion on the earth's surface. As we know, our poles always remain in the same direction, it is clear that they must describe circles around their axes, and these circles must be in opposite directions. The sun and moon pull the near part of the earth's equator (which belongs out most) away from the other part (which belongs in most), and thus cause the earth to spin rapidly, the effect of this is not to bring the poles into line with each other, but to make them cross each other in two different ecliptics, so that to make the earth's axis circle round the sun once in twenty-two hundred years, it must turn through an angle equal to twice the angle between two successive ecliptics. Now suppose that during one revolution of the earth's axis round its own axis, its turning round horizontally so long as it is spinning round vertically, and then stops for a time while it is hanging straight down when at rest. This analogy will show how a similar result might follow. In the case of the moon, however, it would be impossible to make her horizontal axis at right angles to its own (as in a large)
136
PRECESSION—SITUATION
way would fall in falling, and the combination of this with its own rotation causes it to turn about an axis be-
tween the two, thus making the axis of the heavens to be inclined at an angle of 23° 27' 58" to the plane of the ecliptic; for there is at every instant a tendency (in consequence of the action of the earth) to make the axis of the heavens coincide with that of the actual axis. Similarly the sun and moon tend to turn the earth about their axes, so that the earth's axis turns round them, which combining with the actual rotation makes the earth spin on its axis at an inclination of 23° 27' 58" to the plane of the ecliptic. This inclination is such that the pole of the heavens (being the direction of the earth's axis) is always in a fixed position, and therefore a circle describing a very small arc of a circle about the pole of the ecliptic. Besides this regular motion, there is also a variation in the motion of the moon's orbit, causing the inclination of the axis of the heavens to vary between 22° 20' 00" and 24° 40' 00", varying over nineteen years (lunar nutation); and there are, besides these, irregularities in the motions of the equinoxes through which we have already spoken. The variations caused by Hipparchus in c. l. 125, increasing the inclinations of all stars by ten seconds, and diminishing those of all other stars by ten seconds, are sufficient to account for all changes in the constellations and the signs of the zodiac, as the twelfth century astronomers found.
Hipparchus observed that when he turned his sextant towards Cancer at its first point of conjunction with Aries, which was at that time near its first point of conjunction with Virgo, he saw that Cancer was then in Virgo. He therefore concluded that Cancer was moving backwards through Virgo, and that Virgo was moving forwards through Cancer. This was called retrograde motion. In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Aries at its first point of conjunction with Taurus, which was at that time near its first point of conjunction with Gemini, he saw that Aries was then in Gemini. He therefore concluded that Aries was moving backwards through Gemini, and that Gemini was moving forwards through Aries. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Taurus at its first point of conjunction with Gemini, which was at that time near its first point of conjunction with Cancer, he saw that Taurus was then in Cancer. He therefore concluded that Taurus was moving backwards through Cancer, and that Cancer was moving forwards through Taurus. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Gemini at its first point of conjunction with Cancer, which was at that time near its first point of conjunction with Leo, he saw that Gemini was then in Leo. He therefore concluded that Gemini was moving backwards through Leo, and that Leo was moving forwards through Gemini. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Cancer at its first point of conjunction with Leo, which was at that time near its first point of conjunction with Virgo, he saw that Cancer was then in Virgo. He therefore concluded that Cancer was moving backwards through Virgo, and that Virgo was moving forwards through Cancer. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Leo at its first point of conjunction with Virgo, which was at that time near its first point of conjunction with Libra, he saw that Leo was then in Libra. He therefore concluded that Leo was moving backwards through Libra, and that Libra was moving forwards through Leo. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Virgo at its first point of conjunction with Libra, which was at that time near its first point of conjunction with Scorpio, he saw that Virgo was then in Scorpio. He therefore concluded that Virgo was moving backwards through Scorpio, and that Scorpio was moving forwards through Virgo. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Libra at its first point of conjunction with Scorpio, which was at that time near its first point of conjunction with Sagittarius, he saw that Libra was then in Sagittarius. He therefore concluded that Libra was moving backwards through Sagittarius, and that Sagittarius was moving forwards through Libra. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Scorpio at its first point of conjunction with Sagittarius, which was at that time near its first point of conjunction with Capricornus, he saw that Scorpio was then in Capricornus. He therefore concluded that Scorpio was moving backwards through Capricornus, and that Capricornus was moving forwards through Scorpio. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Sagittarius at its first point of conjunction with Capricornus, which was at that time near its first point of conjunction with Aquarius, he saw that Sagittarius was then in Aquarius. He therefore concluded that Sagittarius was moving backwards through Aquarius, and that Aquarius was moving forwards through Sagittarius. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Capricornus at its first point of conjunction with Aquarius, which was at that time near its first point of conjunction with Pisces, he saw that Capricornus was then in Pisces. He therefore concluded that Capricornus was moving backwards through Pisces, and that Pisces was moving forwards through Capricornus. This was called retrograde motion.
In order to determine how much each star had moved backwards or forwards during one year, he observed that when he turned his sextant towards Aquarius at its first point of conjunction with Pisces, which was at that time near its first point of conjunction with Aries again (the same being now), he saw that Aquarius
| SIGNS OF THE ZODIAC |
537 |
| and so on. The practice, however, of referring the positions of the planets to the signs of the zodiac has died out with the increase in the accuracy of astronomical observations. The mean distance between the twelve signs and the twelve months of the year is no longer close enough even for the purposes of ordinary life. |
|
| SUN AND MOON. |
| This following table shows the principal periods of solar and lunar motion, with distances and diameters of the sun. |
|
Sun's mean distance, miles... 28,000,000
Sun's diameter, miles... 90,000
Mean period of revolution, days... 365.242 |
|
| Period of revolution, days... 365.242 |
|
Cycle of precession, years... 25,800
Mean period of revolution, days... 365.242 |
|
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.242
Mean period of revolution, days... 365.24 |
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Revolutions perigee years...
| Sun's (19) lunations, | days... | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) | (19) |
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| (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8) (8)... | (777777777777777777777777777777777777777777777777777777777777777777777777777777777 | (0000000000000000000000000000000000000000000000000000000000 | (111111111111111111111111111111111 | (IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIIIIIIII | (IIIIIIIIIIIIIIIIIIIIII | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (I | (IMasses earth times that offMasses earth times that off
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| Revolutions perigee years... | Revolutions perigee years...
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SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON. SUN AND MOON.
| ELEMENTS OF THE PHONICAL PLANETS. |
| No. |
Name. |
Long. of Asc. of |
Long. of Desc. of |
Long. of Asc. of |
Long. of Desc. of |
| Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
Equinox. |
| ① |
Venus- |
|
|
|
|
|
|
|
|
|
|
| 1.0° |
1.0° |
1.0° |
1.0° |
1.0° |
1.0° |
1.0° |
1.0° |
1.0° |
| ② |
Mercury- |
|
|
|
|
|
|
|
|
|
| 1.5° |
1.5° |
1.5° |
1.5° |
1.5° |
1.5° |
1.5° |
1.5° |
1.5° |
| Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic. | Ecliptic.
| ③
Mercury-
④
Mercury-⑤
Mercury-⑥
Mercury-⑦
Mercury-⑧
Mercury-⑨
Mercury-⑩
Mercury-⑪
Mercury-⑫
Mercury-⑬
Mercury-⑭
Mercury-⑮
Mercury-⑯
Mercury-⑰
Mercury-⑱
Mercury-⑲
Mercury-⑳
Mercury-㉑
Mercury-㉒
Mercury-㉓
Mercury-㉔
Mercury-㉕
Mercury-㉖
Mercury-㉗
Mercury-㉘
Mercury-㉙
Mercury-㉚
Mercury-㉛
Mercury-㉜
Mercury-㉝
Mercury-㉞
Mercury-㉟
Mercury-㊀Bisphorus-Cyanide-Sulfide-Pentoxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-Silicate-Magnesium Oxide-bBisphorus Bivalent Ion (B)iCyanide Ions (CN)iSulfide Ions (S)iPentoxide Ions (O_5)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)iSilicate Ions (SiO_4)iMagnesium Oxide Ions (MgO)i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i.i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-
| Governe |
| Period |
in Terms |
Duration |
Number of |
Time |
Approximate |
| Period |
Terms |
Total |
No. of |
Term |
Last |
| Basis |
|
|
|
|
|
| Taxation I |
06 |
04 |
01 |
01 |
01 |
| Taxation II |
08 |
05 |
01 |
01 |
01 |
| Taxation III |
07 |
04 |
01 |
01 |
01 |
| Taxation IV |
06 |
04 |
01 |
01 |
01 |
| Taxation V |
06 |
04 |
01 |
01 |
01 |
| The difference is expressed in terms of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from the Sum in the direction of the "half" difference from
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In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to the above, there is a separate volume containing a complete summary of the leading cases on all subjects which come within the province of the law of England and America. This volume is intended for those who have some knowledge of English law and wish to study the law of America.
In addition to
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