PART IV—THE FIXED STARS.

PAGES

Division of the Stars into Magnitudes—Division of 219-257

the Stars according to their Spectra—Stars

Larger and Smaller than the Sun—The Distances of

the Stars—Variable Stars—Double and Binary

Stars—Spectroscopic Binaries and how they are

Discovered—Proper Motions of the Stars—Number of

the Stars—New, or Temporary Stars—The Milky

Way—The Nebulæ—The Two Kinds of Nebulæ—Spiral

Nebulæ—The Nebular Hypothesis—Applications of

Photography to Stars and Nebulæ—The

Constellations—How to Learn the

Constellations—Their Antiquity—Description of

the Principal Constellations Visible from the

Northern Hemisphere at Various Times of the Year

INDEX 259

------------------------------------------------------------------------

ILLUSTRATIONS

PAGE

THE LUNAR “CRATER” COPERNICUS _Frontispiece_

PHOTOGRAPH OF SOUTH POLAR 8

REGION OF THE MOON

THE MOON NEAR THE “CRATER” 20

TYCHO

DRAWING OF JUPITER 28

DRAWING OF JUPITER 28

JUPITER 38

SATURN 46

SATURN 46

THE MILKY WAY ABOUT CHI CYGNI 58

THE GREAT SOUTHERN 64

STAR-CLUSTER IN CENTAURI

PHOTOGRAPH OF A GROUP OF 76

SUN-SPOTS

POLAR STREAMERS OF THE SUN, 89

ECLIPSE OF 1889

SOLAR CORONA AT THE ECLIPSE OF 89

1871

MOREHOUSE'S COMET, OCTOBER 15, 96

1908

MOREHOUSE'S COMET, NOVEMBER 96

15, 1908

HEAD OF THE GREAT COMET OF 105

1861

HALLEY'S COMET, MAY 5, 1910 105

THE SIX-TAILED COMET OF 1744 112

SPIRAL NEBULA IN URSA MAJOR (M 124

101)

THE WHIRLPOOL NEBULA IN CANES 124

VENATICI

TRESS NEBULA (N. G. C. 6992) 132

IN CYGNUS

THE GREAT ANDROMEDA NEBULA 140

SPIRAL NEBULA IN CEPHEUS (H. 154

IV. 76)

NEBULOUS GROUNDWORK IN TAURUS 154

NEBULA IN SAGITTARIUS (M. 8) 162

THE GREAT NEBULA IN ORION 180

PHOTOGRAPHS OF MARS 200

SCHIAPARRELLI’S CHART OF 220

MARTIAN “CANALS”

ILLUSTRATIONS IN THE TEXT

THE RATIONAL AND THE SENSIBLE 12

HORIZON

ALTITUDE AND AZIMUTH 14

RIGHT ASCENSION AND 35

DECLINATION

THE ECLIPTIC AND CELESTIAL 51

LATITUDE AND LONGITUDE

HOW THE EARTH CONTROLS THE 75

MOON

THE TIDAL FORCE OF THE MOON 79

REFRACTION 85

DIP OF THE HORIZON 87

SIDEREAL AND SOLAR TIME 93

THE CHANGE OF DAY 101

THE SEASONS 107

PARALLAX OF THE MOON 139

PARALLAX OF THE SUN FROM 141

TRANSIT OF VENUS

SPECTRUM ANALYSIS 147

THE PHASES OF THE MOON 160

ORBITS OF MARS AND THE EARTH 183

ELLIPSE, PARABOLA, AND 203

HYPERBOLA

THE NORTH CIRCUMPOLAR STARS 244

KEY TO NORTH CIRCUMPOLAR STARS 245

------------------------------------------------------------------------

PART I.

THE CELESTIAL SPHERE.

------------------------------------------------------------------------

PART I.

THE CELESTIAL SPHERE.

=1. Definition of Astronomy.= Astronomy has to do with the earth, sun,

moon, planets, comets, meteors, stars, and nebulæ; in other words, with

the universe, or “the aggregate of existing things.” It is the most

ancient of all sciences. The derivation of the name from two Greek

words, _aster_, “star,” and _nomos_, “law,” indicates its nature. It

deals with the _law of the stars_—the word “star” being understood, in

its widest signification, as including every heavenly body of whatever

kind. The earth itself is such a body. Since we happen to live on the

earth, it becomes our standpoint in space, from which we look out at the

others. But, if we lived on some other planet, we would see the earth as

a distant body in the sky, just as we now see Jupiter or Mars.

Astronomy teaches us that everything in the universe, from the sun and

the moon to the most remote star or the most extraordinary nebula, is

related to the earth. All are made of similar elementary substances and

all obey similar physical laws. The same substance which is a solid upon

the earth may be a gas or a vapour in the sun, but that does not alter

its essential nature. Iron appears in the sun in the form of a hot

vapour, but fundamentally it is the same substance which exists on the

earth as a hard, tough, and heavy metal. Its different states depend

upon the temperature to which it is subjected. The earth is a cool body,

while the sun is an intensely hot one; consequently iron is solid on the

earth and vaporous in the sun, just as in winter water is solid ice on

the surface of a pond and steamy vapour over the boiler in the kitchen.

Even on the earth we can make iron liquid in a blast furnace, and with

the still greater temperatures obtainable in a laboratory we can turn it

into vapour, thus reducing it to something like the state in which it

regularly exists in the sun.

This fact, that the entire universe is made up of similar substances,

differing only in state according to the local circumstances affecting

them, is the greatest thing that astronomy has to tell us. It may be

regarded as the fundamental law of the stars.

=2. The Situation of the Earth in the Heavens.= One of the greatest

triumphs of human intelligence is the discovery of the real place which

the earth occupies in the universe. This discovery has been made in

spite of the most deceptive appearances. If we accepted the sole

evidence of our eyes, as men once did, we could only conclude that the

earth was the centre of the universe. In the daytime we see the sun

apparently moving through the sky from east to west, as if it were

travelling in a circle round the earth, overhead by day and underfoot at

night. In the night-time, we see the stars apparently travelling round

the earth in the same way as the sun. The fact is, that all of them are

virtually motionless with regard to the earth, and their apparent

movements through the sky are produced by the earth's rotation on its

axis. The earth turns round on itself once every twenty-four hours, like

a spinning ball. Imagine a fly on a rotating school globe; the whole

room would appear to the fly to be revolving round it as the heavens

appear to revolve round the earth. It would have to be a very

intelligent insect to correct the deceptive evidence of its eyes.

The actual facts, revealed by many centuries of observation and

reasoning, are that the earth is a rotating globe, turning once on its

axis every twenty-four hours and revolving once round the sun every

three hundred and sixty-five days. The sun is also a globe, 1,300,000

times larger than the earth, but so hot that it glows with intense

brilliance, while the substances of which it consists are kept in a

gaseous or vaporous state. Besides the earth there are seven other

principal globes, or planets, which revolve round the sun, at various

distances and in various periods, and, in addition to these, there are

hundreds of smaller bodies, called asteroids or small planets. There are

also many singular bodies called comets, and swarms of still smaller

ones called meteors, which likewise revolve round the sun.

The earth and the other bodies of which we have just spoken are not only

cooler than the sun, but most of them are in a solid state and do not

shine with light of their own. The sun furnishes both heat and light to

the smaller and cooler bodies revolving round it. In fact, the sun is

simply a _star_, resembling the thousands of other stars which surround

us in the sky, and its apparent superiority to them is due only to the

fact that it is relatively near-by while they are far away. It is

probable that all, or most, of the stars also have planets, comets, and

meteors revolving round them, but invisible owing to their immense

distance.

The “paths” in which the earth and the other planets and bodies travel

in their revolutions round the sun are called their orbits. These orbits

are all elliptical in shape, but those of the earth and the other large

planets are not very different from circles. Some of the asteroids, and

all of the comets, however, travel in elliptical orbits of considerable

eccentricity, _i. e._, which differ markedly from circles. The orbit of

the earth differs so slightly from a circle that the eccentricity

amounts to only about one-sixtieth. The distance of the earth from the

sun being, on the average, 93,000,000 miles, the eccentricity of its

orbit causes it to approach to within about 91,500,000 miles in winter

(of the northern hemisphere) and to recede to about 94,500,000 miles in

summer. The point in its orbit where the earth is nearest the sun is

called perihelion, and the point where it is farthest from the sun,

aphelion. The earth is at perihelion about Jan. 1, and at aphelion about

July 4.

Now, in order to make a general picture in the mind of the earth's

situation, let the reader suppose himself to be placed out in space as

far from the sun as from the other stars. Then, if he could see it, he

would observe the earth as a little speck, shining like a mote in the

sunlight, and circling in its orbit close around the sun. The universe

would appear to him to be somewhat like an immense spherical room filled

with scattered electric-light bulbs, suspended above, below, and all

around him, each of these bulbs representing a sun, and if there were

minute insects flying around each light, these insects would represent

the planets belonging to the various suns. One of the glowing bulbs

among the multitude would stand for our sun, and one of the insects

circling round it would be the earth.

[Illustration:

=Photograph of the South Polar Region of the Moon=

Made by G. W. Ritchey with the forty-inch refractor of the Yerkes

Observatory.

]

We have already remarked that the rotation of the earth on its axis

causes all the other heavenly bodies to _appear_ to revolve round it

once every twenty-four hours, and we must now add that the earth's

revolution round the sun causes the same bodies to _appear_ to make

another, slower revolution round it once every year. This introduces a

complication of apparent motions which it is the business of astronomy

to deal with, and which we shall endeavour to explain.

=3. The Horizon, the Zenith, and the Meridian.= First, let us consider

what is the ordinary appearance of the sky. When we go out of doors on a

clear night we see the heavens in the shape of a great dome arched above

us and filled with stars. What we thus see is one half of the spherical

shell of the heavens which surrounds us on all sides, the earth being

apparently placed at its centre. The other half is concealed from our

sight behind, or below, the earth. This spherical shell, of which only

one half is visible to us at a time, is called the celestial sphere.

Now, the surface of the earth seems to us (for this is another of the

deceptive appearances which astronomy has to correct) to be a vast flat

expanse, whose level is broken by hills and mountains, and the visible

half of the celestial sphere seems to bend down on all sides and to rest

upon the earth in a circle which extends all around us. This circle,

where the heavens and the earth appear to meet, is called the horizon.

As we ordinarily see it, the horizon appears irregular and broken on

account of the unevenness of the earth's surface, but if we are at sea,

or in the midst of a great level prairie, the horizon appears as a

smooth circle, everywhere equally distant from the eye. This circle is

called the sensible horizon. But there is another, ideal, horizon, used

in astronomy, which is called the rational horizon. It is of the utmost

importance that we should clearly understand what is meant by the

rational horizon, and for this purpose we must consider another fact

concerning the dome of the sky.

We now turn our attention to the centre of that dome, which, of course,

is the point directly overhead. This point, which is of primary

importance, is called the zenith. The position of the zenith is

indicated by the direction of a plumb-line. If we imagine a plumb-line

to be suspended from the centre of the sky overhead, and to pass into

the earth at our feet, it would run through the centre of the earth,

and, if it were continued onward in the same direction, it would, after

emerging from the other side of the earth, reach the centre of the

invisible half of the sky-dome at a point diametrically opposite to the

zenith. This central point of the invisible half of the celestial

sphere, lying under our feet, is called the nadir.

Keeping in mind the definitions of zenith and nadir that have just been

given, we are in a position to understand what the rational horizon is.

It is a great circle whose plane cuts through the centre of the earth,

and which is situated exactly half-way between the zenith and the nadir.

This plane is necessarily perpendicular, or at right angles, to the

plumb-line joining the zenith and the nadir. In other words, the

rational horizon divides the celestial sphere into two precisely equal

halves, an upper and a lower half. In a hilly or mountainous country the

sensible or visible horizon differs widely from the rational, or true

horizon, but at sea the two are nearly identical. This arises from the

fact, that the earth is so excessively small in comparison with the

distances of most of the heavenly bodies that it may be regarded as a

mere point in the midst of the celestial sphere.

[Illustration:

_Fig. 1. The Rational and the Sensible Horizon._

Let C be the earth's centre, O the place of the observer, and H D the

rational horizon passing through the centre of the earth. For an

object situated near the earth, as at A, the sensible horizon makes

a large angle with the rational horizon. If the object is farther

away, as at B, the angle becomes less; and still less, again, if the

object is at D. It is evident that if the object be immensely

distant, like a star, the sensible horizon O S will be practically

parallel with the rational horizon, and will blend with it, because

the radius, or semi-diameter, of the earth, O C, is virtually

nothing in comparison with the distance of the star.

]

Besides the horizon and the zenith there is one other thing of

fundamental importance which we must learn about before proceeding

further,—the meridian. The meridian is an imaginary line, or semicircle,

beginning at the north point on the horizon, running up through the

zenith, and then curving down to the south point. It thus divides the

visible sky into two exactly equal halves, an eastern and a western

half. In the ordinary affairs of life we usually think only of that part

of the meridian which extends from the zenith to the south point on the

horizon (which is sometimes called the "noon-line” because the sun

crosses it at noon), but in astronomy the northern half of the meridian

is as important as the southern.

=4. Altitude and Azimuth.= Now, suppose that we wish to indicate the

location of a star, or other object, in the sky. To do so, we must have

some fixed basis of reference, and such a basis is furnished by the

horizon and the zenith. If we tried to describe the position of a star,

the most natural thing would be, first, to estimate, or measure, its

height above the horizon, and, second, to indicate the direction in

which it was situated with regard to the points of the compass. These

two measures, if they were accurately made, would enable another person

to find the star in the sky. And this is precisely what is done in

astronomy. The height above the horizon is called altitude, and the

bearing with reference to the points of the compass is called azimuth.

Together these are known as co-ordinates. In order to systematise this

method of measuring the location of a star, the astronomer uses

imaginary circles drawn on the celestial sphere. The horizon and the

meridian are two of these circles. In addition to these, other imaginary

circles are drawn parallel to the horizon and becoming smaller and

smaller until the uppermost one may run close round the zenith, which is

the common centre of the entire set. These are called altitude circles,

because each one throughout its whole extent is at an unvarying height,

or altitude, above the horizon. Such circles may be drawn anywhere we

please, so as to pass through any chosen star or stars. If two stars in

different quarters of the sky are found to lie on the same circle, then

we know that both have the same altitude.

[Illustration:

_Fig. 2. Altitude and Azimuth._

C is the place of the observer.

N C S, a north-and-south line drawn in the plane of the horizon.

E C W, an east-and-west line in the plane of the horizon.

N E S W, the circle of the horizon.

Z, the observer's zenith.

N Z S, vertically above N C S, the meridian.

E Z W, the prime vertical.

Z s s′, part of a vertical circle drawn through the star s.

The circle through s parallel to the horizon is an altitude circle.

The angle s C s′, or the arc s′ s, represents the star's altitude.

The angle s C Z, or the arc Z s, is the star's zenith distance.

To find the azimuth, the angular distance round the horizon from S

(0°), through W, N, E, to the point where the star's vertical circle

meets the horizon, is measured. In this case it is 315°. But if we

measured it eastward from the south point it would be—45°.

]

Then another set of circles is drawn perpendicular to the horizon, and

all intersecting at the zenith and the nadir. These are called vertical

circles, from the fact that they are upright to the horizon. That one of

the vertical circles which cuts the horizon at the north-and-south

points coincides with the meridian, which we have already described. The

vertical circle at right angles to the meridian is called the prime

vertical. It cuts the horizon at the east and west points, dividing the

visible sky into a northern and a southern half. Like the altitude

circles, vertical circles may be drawn anywhere we please so as to pass

through a star in any quarter of the sky—but the meridian and the prime

vertical are fixed.

With the two sets of circles that have just been described, it is

possible to indicate accurately the location of any heavenly body, at

any particular moment. Its altitude is ascertained by measuring, along

the vertical circle passing through it, its distance from the horizon.

(Sometimes it is convenient to measure, instead of the altitude of a

star, its zenith distance, which is also reckoned on the vertical

circle.)

To ascertain the azimuth, we must first choose a point of beginning on

the horizon. Any of the cardinal points, _i.e._, east, west, north, or

south, may be employed for this purpose, but in astronomy it is

customary to use only the south point, and to carry the measure westward

all round the circle of the horizon, and so back to the point of

beginning in the south. This involves circular, or degree, measure, to

which a few words must now be devoted.

Every circle, no matter how large or how small, is divided into 360

equal parts, called degrees, usually indicated by the sign (°); each

degree is subdivided into 60 equal parts called minutes, indicated by

the sign (′); and each minute is subdivided into 60 equal parts called

seconds, indicated by the sign (″). Thus there are 360°, or 21,600′, or

1,296,000″ in every complete circle. The actual length of a degree in

inches, yards, or miles, depends upon the size of the circle, but no

circle ever has more than 360°, and a degree of any particular circle is

precisely equal to any other degree of that same circle. Thus, if a

circle is 360 miles in circumference, every one of its degrees will be

one mile long. In mathematics, a degree usually means not a distance

measured along the circumference of a circle, but an angle formed at the

centre of the circle between two lines called radii (radius in the

singular), which lines, where they intersect the circumference, are

separated by a distance equal to one 360th of the entire circle. But,

for ordinary purposes, it is simpler to think of a degree as an arc

equal in length to one 360th of the circle. Now, since the horizon, and

the other imaginary lines drawn in the sky, are all circles, it is

evident that the principle of circular measure may be applied to them,

and indeed must be so applied in order that they shall be of use to us

in indicating the position of a star.

To return, then, to the measurement of the azimuth of a star. Since the

south point is the place of beginning, we mark it 0°, and we divide the

circle of the horizon into 360°, counting round westward. Suppose we see

a star somewhere in the south-western quarter of the sky; then the point

where the vertical circle passing through that star intersects the

horizon will indicate its azimuth. Suppose that this point is found to

be 25° west of south; then 25° will be the star's azimuth. Suppose it is

90°; then the azimuth is 90°, and the star must be on the prime vertical

in the west, because west, being one quarter of the way round the

horizon from south, is 90° in angular distance from the south point.

Suppose the azimuth is 180°; then the star must be on the meridian north

of the zenith, because north is exactly half-way, or 180° round the

horizon from the south point. Suppose the azimuth is 270°; then the star

must be on the prime vertical in the east, because east is 270°, or

three quarters of the way round from the south point. If the star is on

the meridian in the south its azimuth may be called either 0° or 360°,

because on any graduated circle the mark indicating 360° coincides in

position with 0°, that being at the same time the point of beginning and

the point of ending.

The same system of angular measure is applied in ascertaining a star's

altitude. Since the horizon is half-way between the zenith and the nadir

it must be just 90° from either. If a star is in the zenith, then its

altitude is 90°, and if it is below the zenith its altitude lies

somewhere between 0° and 90°. In any case it cannot be less than 0° nor

more than 90°. Having measured the altitude and the azimuth we have the

two co-ordinates which are needed to indicate accurately the place of a

star in the sky. But, as we shall see in a moment, other co-ordinates

beside altitude and azimuth are needed for a complete description of the

places of the stars on the celestial sphere. Owing to the apparent

revolution of the heavens round the earth, the altitudes and azimuths of

the celestial bodies are continually changing. We shall now study the

causes of these changes.

=5. The Apparent Motion of the Heavens.= We have likened the earth to a

rotating school globe. As such a globe turns, any particular spot on it

is presented in succession toward the various sides of the room. In

precisely the same way any spot on the earth is turned by its rotation

successively toward various parts of the surrounding sky. To understand

the effect of this, a little patient watching of the actual heavens will

be required, but this has the charm of all out-of-doors observation of

nature, and it will be found of fascinating interest as the facts begin

to unfold themselves.

[Illustration:

=The Moon Near the “Crater” Tycho=

Photographed at the Lick Observatory under the direction of E. S.

Holden.

Tycho is the regular oval depression a little below the centre of the

view. The vast depression, 140 miles across, with a row of smaller

craters within, below the centre of the view at the top, is Clavius.

The photograph was made when sundown was approaching on that part of

the moon. Observe the jagged line of advancing night lying across

the rugged surface on the western (left-hand) side.

]

It is best to begin by finding the North Star, or pole star. If you are

living not far from latitude 40° north, which is the median latitude of

the United States, you must, after determining as closely as you can the

situation of the north point, look upward along the meridian in the

north until your eyes are directed to a point about 40° above the

horizon. Forty degrees is somewhat less than half-way from the horizon

to the zenith, which, as we have seen, are separated by an arc of 90°.

At that point you will notice a lone star of what astronomers call the

second magnitude. This is the celebrated North Star. It is the most

useful to man of all the stars, except the sun, and it differs from all

the others in a way presently to be explained. But first it is essential

that you should make no mistake in identifying it. There are certain

landmarks in the sky which make such identification certain. In the

first place, it is always so close to the meridian in the north, that by

naked-eye observation you would probably never suspect that it was not

exactly on the meridian. Then, its altitude is always equal, or very

nearly equal, to the latitude of the place where you happen to be on the

earth, so that if you know your latitude you know how high to carry your

eye above the northern horizon. If you are in latitude 50°, the star

will be at 50° altitude, and if your latitude is 30°, the altitude of

the star will be 30°. Next you will notice that the North Star is

situated at the end of the handle of a kind of dipper-shaped figure

formed by stars, the handle being bent the wrong way. All of the stars

forming this “dipper” are faint, except the two which are farthest from

the North Star, in the outer edge of the bowl, one of which is about as

bright as the North Star itself. Again, if you carry your eye along the

handle to the bowl, and then continue onward about as much farther, you

will be led to another, larger, more conspicuous, and more perfect,

dipper-shaped figure, which is in the famous constellation of Ursa

Major, or the Great Bear. This striking figure is called the Great

Dipper (known in England as The Wain). It contains seven conspicuous

stars, all of which, with one exception, are equal in brightness to the

North Star. Now, look particularly at the two stars which indicate the

outer side of the bowl of this dipper, and you will find that if you

draw an imaginary line through them toward the meridian in the north, it

will lead your eye directly back to the North Star. These two

significant stars are often called The Pointers. With their aid you can

make sure that you have really found the North Star.

Having found it, begin by noting the various groups of stars, or

constellations, in the northern part of the sky, and, as the night wears

on, observe whether any change takes place in their position. To make

our description more definite, we will suppose that the observations

begin at nine o'clock P.M. about the 1st of July. At that hour and date,

and from the middle latitudes of the United States, the Great Dipper is

seen in a south-westerly direction from the North Star, with its handle

pointing overhead. At the same time, on the opposite side of the North

Star, and low in the north-east, appears the remarkable constellation of

Cassiopeia, easily recognisable by a zigzag figure, roughly resembling

the letter W, formed by its five principal stars. Fix the relative

positions of these constellations in the memory, and an hour later, at

10 P.M., look at them again. You will find that they have moved, the

Great Dipper sinking, while Cassiopeia rises. Make a third observation

at 11 P.M., and you will perceive that the motion has continued, The

Pointers having descended in the north-west, until they are on a level

with the North Star, while Cassiopeia has risen to nearly the same level

in the north-east. In the meantime, the North Star has remained

apparently motionless in its original position. If you repeat the

observation at midnight, you will find that the Great Dipper has

descended so far that its centre is on a level with the North Star, and

that Cassiopeia has proportionally risen in the north-east. It is just

as if the two constellations were attached to the ends of a rod pivoted

at the centre upon the North Star and twirling about it.

In the meantime you will have noticed that the figure of the “Little

Dipper,” attached to the North Star, which had its bowl toward the

zenith at 9 P.M., has swung round so that at midnight it is extended

toward the south-west. Thus, you will perceive that the North Star is

like a hub round which the heavens appear to turn, carrying the other

stars with them.

To convince yourself that this motion is common to the stars in all

parts of the sky, you should also watch the conduct of those which pass

overhead, and those which are in the southern quarter of the heavens.

For instance, at 9 P.M. (same date), you will see near the zenith a

beautiful coronet which makes a striking appearance although all but one

of its stars are relatively faint. This is the constellation Corona

Borealis, or the Northern Crown. As the hours pass you will see the

Crown swing slowly westward, descending gradually toward the horizon,

and if you persevere in your observations until about 5 A.M., you will

see it set in the north-west. The curve that it describes is concentric

with those followed by the Great Dipper and Cassiopeia, but, being

farther from the North Star than they are, and at a distance greater

than the altitude of the North Star, it sinks below the horizon before

it can arrive at a point directly underneath that star. Then take a star

far in the south. At 9 o'clock, you will perceive the bright reddish

star Antares, in the constellation Scorpio, rather low in the south and

considerably east of the meridian. Hour after hour it will move

westward, in a curve larger than that of the Northern Crown, but still

concentric with it. A little before 10 P.M., it will cross the meridian,

and between 1 and 2 A.M., it will sink beneath the horizon at a point

south of west.

So, no matter in what part of the heavens you watch the stars, you will

see not only that they move from east to west, but that this motion is

performed in curves concentric round the North Star, which alone appears

to maintain its place unchanged. Along the eastern horizon you will

perceive stars continually rising; in the middle of the sky you will see

others continually crossing the meridian—a majestic march of

constellations,—and along the western horizon you will find still others

continually setting. If you could watch the stars uninterruptedly

throughout the twenty-four hours (if daylight did not hide them from

sight during half that period), you would perceive that they go entirely

round the celestial sphere, or rather that it goes round with them, and

that at the end of twenty-four hours they return to their original

positions. But you can do this just as well by looking at them on two

successive nights, when you will find that at the same hour on the

second night they are back again, practically in the places where you

saw them on the first night.

Of course, what happens on a July night happens on any other night of

the year. We have taken a particular date merely in order to make the

description clearer. It is only necessary to find the North Star, the

Great Dipper, and Cassiopeia, and you can observe the apparent

revolution of the heavens at any time of the year. These constellations,

being so near the North Star that they never go entirely below the

horizon in middle northern latitudes, are always visible on one side or

another of the North Star.

Now, call upon your imagination to deal with what you have been

observing, and you will have no difficulty in explaining what all this

apparent motion of the stars means. You already know that the heavens

form a sphere surrounding the earth. You have simply to suppose the

North Star to be situated at, or close to, the north end, or north pole,

of an imaginary axle, or axis, round which the celestial sphere seems to

turn, and instantly the whole series of phenomena will fall into order,

and the explanation will stare you in the face. That explanation is that

the motion of all the stars in concentric circles round the North Star

is due to an apparent revolution of the whole celestial sphere, like a

huge hollow ball, about an axis, the position of one of whose poles is

graphically indicated in the sky by the North Star. The circles in which

the stars seem to move are perpendicular to this axis, and inclined to

the horizon at an angle depending upon the altitude of the North Star at

the place on the earth where the observations are made.

Another important fact demands our attention, although the thoughtful

reader will already have guessed it—the north pole of the celestial

sphere, whose position in the sky is closely indicated by the North

Star, is situated directly over the north pole of the earth. This

follows from the fact that the apparent revolution of the celestial

sphere is due to the real rotation of the earth. You can see that the

two poles, that of the earth and that of the heavens, must necessarily

coincide, by taking a school globe and imagining that you are an

intelligent little being dwelling on its surface. As the globe turned on

its axis you would see the walls of the room revolving round you, and

the poles of the apparent axis round which the room turned, would,

evidently, be directly over the corresponding poles of the globe itself.

Another thing which you could make clear by this experiment is that, as

the poles of the celestial sphere are over the earth's poles, so the

celestial equator, or equator of the heavens, must be directly over the

equator of the earth.

We can determine the location of the poles of the heavens by watching

the revolution of the stars around them, and we can fix the position of

the circle of the equator of the heavens, by drawing an imaginary line

round the celestial sphere, half-way between the two poles. We have

spoken specifically only of the north pole, but, of course, there is a

corresponding south pole situated over the south pole of the earth, but

whose position is invisible from the northern hemisphere. It happens

that the place of the south celestial pole is not indicated to the eye,

like that of the northern, by a conspicuous star.

[Illustration:

=Drawing of Jupiter=

]

[Illustration:

=Drawing of Jupiter=

Note the change of details between the two drawings, made at different

times. Similar changes are continually occurring.

]

=6. Locating the Stars on the Celestial Sphere.= Having found the poles

and the equator of the celestial sphere, we begin to see how it is

possible to make a map, or globe, of the heavens just as we do of the

earth, on which the objects that they contain may be represented in

their proper positions. When we wish to describe the location of an

object on the earth, a city for instance, we have to refer to a system

of imaginary circles, drawn round the earth and based upon the equator

and the poles. These circles enable us to fix the place of any point on

the earth with accuracy. One set of circles called parallels of latitude

are drawn east and west round the globe parallel to the equator, and

becoming smaller and smaller until the smallest runs close round their

common central point, which is one of the poles. Each pole of the earth

is the centre of such a set of circles all parallel to the equator.

Since each circle is unvarying in its distance from the equator, all

places which are situated anywhere on that circle have the same

latitude, or distance from the equator, either north or south.

But to know the latitude of any place on the earth is not sufficient; we

must also know what is called its longitude, or its angular distance

east or west of some chosen point on the equator. This knowledge is

obtained with the aid of another set of circles drawn north-and-south

round the earth, and all meeting and crossing at the poles. These are

called meridians of longitude. In order to make use of them we must, as

already intimated, select some particular meridian whose crossing point

on the equator will serve as a place of beginning. By common consent of

the civilised world, the meridian which passes through the observatory

at Greenwich, near London, has been chosen for this purpose. It is, like

all the meridians, perpendicular to the equator, and it is called the

prime meridian of the earth.

In locating any place on the earth, then, we ascertain by means of the

parallel of latitude passing through it how far in degrees, it is north

or south of the equator, and by means of its meridian of longitude how

far it is east or west of the prime meridian, or meridian of Greenwich.

These two things being known, we have the exact location of the place on

the earth. Let us now see how a similar system is applied to ascertain

the location of a heavenly body on the celestial sphere.

We have observed that the poles of the heavens correspond in position,

or direction, with those of the earth, and that the equator of the

heavens runs round the sky directly over the earth's equator. It follows

that we can divide the celestial sphere just as we do the surface of the

earth by means of parallels and meridians, corresponding to the similar

circles of the earth. On the earth, distance from the equator is called

latitude, and distance from the prime meridian, longitude. In the

heavens, distance from the equator is called declination, and distance

from the prime meridian, right ascension; but they are essentially the

same things as latitude and longitude, and are measured virtually in the

same way. In place of parallels of latitude, we have on the celestial

sphere circles drawn parallel to the equator and centring about the

celestial poles, which are called parallels of declination, and in place

of meridians of longitude, we have circles perpendicular to the equator,

and drawn through the celestial poles, which are called hour circles.

The origin of this name will be explained in a moment. For the present

it is only necessary to fix firmly in the mind the fact that these two

systems of circles, one on the earth and the other in the heavens, are

fundamentally identical.

Just as on the earth geographers have chosen a particular place, viz.

Greenwich, to fix the location of the terrestrial prime meridian, so

astronomers have agreed upon a particular point in the heavens which

serves to determine the location of the celestial prime meridian. This

point, which lies on the celestial equator, is known as the vernal

equinox. We shall explain its origin after having indicated its use. The

hour circle which passes through the vernal equinox is the prime

meridian of the heavens, and the vernal equinox itself is sometimes

called the “Greenwich of the Sky.”

If, now, we wish to ascertain the exact location of a star on the

celestial sphere, as we would that of New York, London, or Paris, on the

earth, we measure along the hour circle running through it, its

declination, or distance from the celestial equator, and then, along its

parallel of declination, we measure its right ascension, or distance

from the vernal equinox. Having these two co-ordinates, we possess all

that is necessary to enable us to describe the position of the star, so

that someone else looking for it, may find it in the sky, as a navigator

finds some lone island in the sea by knowing its latitude and longitude.

Declination, as we have seen, is simply another name for latitude, but

right ascension, which corresponds to longitude, needs a little

additional explanation. It differs from longitude, first, in that,

instead of being reckoned both east and west from the prime meridian, it

is reckoned only toward the east, the reckoning being continued

uninterruptedly entirely round the circle of the equator; and, second,

in that it is usually counted not in degrees, minutes, and seconds of

arc, but in hours, minutes, and seconds of time. The reason for this is

that, since the celestial sphere makes one complete revolution in

twenty-four hours, it is convenient to divide the circuit into

twenty-four equal parts, each corresponding to the distance through

which the heavens appear to turn in one hour. This explains the origin

of the term hour circles applied to the celestial meridians, which, by

intersecting the equator, divide it into twenty-four equal parts, each

part corresponding to an hour of time. In expressing right ascension in

time, the Roman numerals—I, II, III, IV, V, VI, VII, VIII, IX, X, XI,

XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX, XXI, XXII, XXIII,

XXIV—are employed for the hours, and the letters _m_ and _s_

respectively for the minutes and seconds. Since there are 360° in every

circle, it is plain that one hour of right ascension corresponds to 15°.

So, too, one minute of right ascension corresponds to 15′, and one

second to 15″. It will be found useful to memorise these relations.

[Illustration:

_Fig. 3. Right Ascension and Declination._

The plane of the horizon, with the north, south, east, and west

points, and the zenith, are represented as in Fig. 2.

P and P′ are the poles of the celestial sphere, the dotted line

connecting them representing the direction of the axis, both of

celestial sphere and the earth.

The circle Eq Eq′ is the equator.

V is the vernal equinox, or the point on the equator whence right

ascension is reckoned round toward the east.

The circle passing through s, parallel to the equator, is a

declination circle.

The circle P s P′ is the hour circle of the star s.

The arc of this hour circle contained between s and the point where it

meets the equator is the star's declination. Its right ascension is

measured by the arc of the equator contained between V and the point

where its hour circle meets the equator, or by the angle V P s.

The hour circle P V P′, passing through the vernal equinox, is the

equinoctial colure. When this has moved up to coincidence with the

meridian, N Z S, it will be astronomical noon.

]

=7. Effects Produced by Changing the Observer's Place on the Earth.= The

reader will recall that in Sect. 4 we described another system of

circles for determining the places of stars, a system based on the

horizon and the zenith. This horizon-zenith system takes no account of

the changes produced by the apparent motion of the heavens, and

consequently it is not applicable to determining the absolute positions

of the stars on the celestial sphere. It simply shows their positions in

the visible half of the sky, as seen at some particular time from some

definite point on the earth. In order to show the changing relations of

this system to that which we have just been describing, let us consider

the effects produced by shifting our place of observation on the earth.

Since the zenith is the point overhead and the nadir the point

underfoot, and the horizon is a great circle drawn exactly half-way

between the zenith and the nadir, it is evident, upon a moment's

consideration, that every place on the earth has its own zenith and its

own horizon. It is also clear that every place must have its own

meridian, because the meridian is a north-and-south line running

directly over the observer's head. You can see how this is, if you

reflect that for an observer situated on the other side of the earth

what is overhead for you will be underfoot for him, and _vice versa_.

Thus the direction of our zenith is the direction of the nadir for our

antipodes, and the direction of their zenith is the direction of our

nadir. They see the half of the sky which is invisible to us, and we the

half which is invisible to them.

Now, suppose that we should go to the north pole. The celestial north

pole would then be in our zenith, and the equator would correspond with

the horizon. Thus, for an observer at the north pole the two systems of

circles that we have described would fall into coincidence. The zenith

would correspond with the pole of the heavens; the horizon would

correspond with the celestial equator; the vertical circles would

correspond with the hour circles; and the altitude circles would

correspond with the circles of declination. The North Star, being close

to the pole of the heavens, would appear directly overhead. Being at the

zenith, its altitude would be 90° (see Sect. 4). Peary, if he had

visited the pole during the polar night, would have seen the North Star

overhead, and it would have enabled him with relatively little trouble

to determine his exact place on the earth, or, in other words, the exact

location of the north terrestrial pole. With the pole star in the

zenith, it is evident that the other stars would be seen revolving round

it in circles parallel to the horizon. All the stars situated north of

the celestial equator would be simultaneously and continuously visible.

None of them would either rise or set, but all, in the course of

twenty-four hours, would appear to make a complete circuit horizontally

round the sky. This polar presentation of the celestial sphere is called

the parallel sphere, because the stars appear to move parallel to the

horizon. No man has yet beheld the nocturnal phenomena of the parallel

sphere, but if in the future some explorer should visit one of the

earth's poles during the polar night, he would behold the spectacle in

all its strange splendour.

[Illustration:

=Jupiter=

Photographed at the Lick Observatory.

Observe on the left the Great Red Spot, which first appeared in 1878.

]

Next, suppose that you are somewhere on the earth's equator. Since the

equator is everywhere 90°, or one quarter of a circle, from each pole,

it is evident that looking at the sky from the equator you would see the

two poles (if there was anything to mark their places) lying on the

horizon one exactly in the north and the other exactly in the south. The

celestial equator would correspond with the prime vertical, passing east

and west directly over your head, and all the stars would rise and set

perpendicularly to the horizon, each describing a semicircle in the sky

in the course of twelve hours. During the other twelve hours, the same

stars would be below the horizon. Stars situated near either of the

poles would describe little semi-circles near the north or the south

point; those farther away would describe larger semi-circles; those

close to the celestial equator would describe semi-circles passing

overhead. But all, no matter where situated, would describe their

visible courses in the same period of time. This equatorial presentation

of the celestial sphere is called the right sphere, because the stars

rise and set at a right angle to the plane of the horizon. Comparing it

with the system of circles on which right ascension and declination are

based, we see that, as the prime vertical corresponds with the celestial

equator, so the horizon must represent an hour circle. The meridian also

represents an hour circle. It may require a little thought to make this

clear, but it will be a good exercise.

Finally, if you are somewhere between the equator and one of the poles,

which is the actual situation of the vast majority of mankind, you see

either the north or the south pole of the heavens elevated to an

altitude corresponding with your latitude, and the stars apparently

revolving round it in circles inclined to the horizon at an angle

depending upon the latitude. The nearer you are to the equator, the

steeper this angle will be. This ordinary presentation of the celestial

sphere is called the oblique sphere. Its horizon does not correspond

with either the equator or the prime vertical, and its zenith and nadir

lie at points situated between the celestial poles and the celestial

equator.

=8. The Astronomical Clock and the Ecliptic.= It will be remembered that

the meridian of any place on the earth is a straight north and south

line running through the zenith and perpendicular to the horizon. More

strictly speaking, the meridian is a circle passing from north to south

directly overhead and corresponding exactly with the meridian of

longitude of the place of observation. Now, let us consider the hour

circles on the celestial sphere. They are drawn in the same way as the

meridians on the earth. But the celestial sphere appears to revolve

round the earth, and as it does so it must carry the hour circles with

it, since they are fixed in position upon its surface. Fix your

attention upon the first of these hour circles, _i. e._, the one which

runs through the vernal equinox. Its right ascension is called 0 hours,

because it is the starting point. Suppose that at some time we find the

vernal equinox exactly in the south; then the 0 hour circle, or the

prime meridian of the heavens, will, at that instant, coincide with the

meridian of the place of observation. But one hour later, in consequence

of the motion of the heavens, the vernal equinox, together with the

circle of 0 hours, will be 15°, or one hour of right ascension, west of

the meridian, and the hour circle marked I will have come up to, and for

an instant will be blended with, the meridian. An hour later still, the

circle of II hours right ascension will have taken its place on the

meridian, while the vernal equinox and the circle of 0 hours will be II

hours, or 30°, west of the meridian. And so on, throughout the entire

circuit of the sky.

What has just been said makes it evident that the apparent motion of the

heavens resembles the movement of a clock, the vernal equinox, or the

circle of 0 hours, serving as a hand, or pointer, on the dial.

Astronomers use it in exactly that way, for astronomical clocks are made

with dials divided into twenty-four hour spaces, and the time reckoning

runs continuously from 0 hours to XXIV hours. The “astronomical day”

begins when the vernal equinox is on the meridian. At that instant the

hands of the astronomical clock mark 0 hours, 0 minutes, 0 seconds. Thus

the clock follows the motion of the heavens, and the astronomer can tell

by simply glancing at the dial, and without looking at the sky, where

the vernal equinox is, and what is the right ascension of any body which

may at that moment be on the meridian.

We must now explain a little more fully what the vernal equinox is, and

why it has been chosen as the “Greenwich of the Sky.” Its position is

not marked by any star, but is determined by means of the intersecting

circles that we have described. There is one other such circle, that we

have not yet mentioned, which bears a peculiar relation to the vernal

equinox. This is the ecliptic. Just as the daily, or diurnal, rotation

of the earth on its axis causes the whole celestial sphere to appear to

make one revolution every day, so the yearly or annual revolution of the

earth in its orbit about the sun causes the sun to appear to make one

revolution through the sky every year. As the earth moves onward in its

orbit, the sun seems to move in the opposite direction. Inasmuch as

there are 360° in a complete circle and 365 days in a year, the apparent

motion of the sun amounts to nearly 1° per day, or 30° per month. In

twelve months, then, the sun comes back again to the place in the sky

which it occupied at the beginning of the year. Since the motion of the

earth in its orbit is from west to east (the same as that of its

rotation on its axis), it follows that the direction of the sun's

apparent annual motion in the sky is from east to west (like its daily

motion). Thus, while _in fact_ the earth pursues a path, or orbit, round

the sun, the sun _seems_ to pursue a path round the earth. This apparent

path of the sun, projected against the background of the sky, is called

the ecliptic. The name arises from the fact that eclipses only occur

when the moon is in or near the plane of the sun's apparent path.

As the apparent motion of the sun round the ecliptic is caused by the

real motion of the earth round the sun, we may regard the ecliptic as a

circle marking the intersection of the plane of the earth's orbit with

the celestial sphere. In other words, if we were situated on the sun

instead of on the earth, we would see the earth travelling round the sky

in the circle of the ecliptic. We must keep this fact, that the ecliptic

indicates the plane of the earth's orbit, firmly in mind, in order to

understand what follows.

The ecliptic is not coincident with the celestial equator, for the

following reason: The axis of the earth's daily rotation is not parallel

to, or does not point in the same direction as, the axis of its yearly

revolution round the sun. As the axis of rotation is perpendicular to

the equator, so the axis of the yearly revolution is perpendicular to

the ecliptic, and since these two axes are inclined to one another, it

results that the equator and the ecliptic must lie in different planes.

The inclination of the plane of the ecliptic to that of the equator

amounts to about 23½°.

As it is very important to have a clear conception of this subject, we

may illustrate it in this way: Take a ball to represent the earth, and

around it draw a circle to represent the equator. Then, through the

centre of the ball, and at right angles to its equator, put a long pin

to represent the axis. Set it afloat in a tub of water, weighting it so

that it will be half submerged, and placing it in such a position that

the pin will be not upright but inclined at a considerable angle from

the vertical. Now, imagine that the sun is situated in the centre of the

tub, and cause the ball to circle slowly round it, while maintaining the

pin always in the same position. Then the surface of the water will

represent the plane of the ecliptic, or plane of the earth's orbit, and

you will see that, in consequence of the inclination of the pin, the

plane of the equator does not coincide with that of the ecliptic (or the

surface of the water), but is tipped with regard to it in such a manner

that one half of the equator is below and the other half above it.

Instead of actually trying this experiment, it will be a useful exercise

of the imagination to represent it to the mind's eye just as if it were

tried.

We have said that the inclination of the equator to the ecliptic amounts

to 23½°, and this angle should be memorised. Now, since both the

ecliptic and the equator are great circles of the celestial sphere, _i.

e._, circles whose planes cut through the centre of the sphere, they

must intersect one another at two opposite points. In the experiment

just described, these two points lie on opposite sides of the ball,

where the equator cuts the level of the water. These points of

intersection of the equator and the ecliptic on the celestial sphere are

called the equinoxes, or equinoctial points, because when the sun

appears at either of those points it is perpendicular over the equator,

and when it is in that position day and night are of equal length all

over the earth. (Equinox is from two Latin words meaning “equal night.”)

[Illustration:

=Saturn=

From a drawing by Trouvelot.

]

[Illustration:

=Saturn=

Photographed at the Lick Observatory.

]

We shall have more to say about the equinoxes later, but for the present

it is sufficient to remark that one of these points—that one where the

sun is about the 21st of March, which is the beginning of astronomical

spring—is the “Greenwich of the Sky,” or the vernal equinox. The other,

opposite, point is called the autumnal equinox, because the sun arrives

there about the 23d of September, the beginning of astronomical autumn.

The vernal equinox, as we have already seen, serves as a pointer on the

dial of the sky. When it crosses the meridian of any place it is

astronomical noon at that place. Its position in the sky is not marked

by any particular star, but it is situated in the constellation Pisces,

and lies exactly at the crossing point of the celestial equator and the

ecliptic. The hour circle, running through this point, and through its

opposite, the autumnal equinox, is the prime meridian of the heavens,

called the equinoctial colure. The hour circle at right angles to the

equinoctial colure, _i. e._, bearing to it the same relation that the

prime vertical does to the meridian (see Sect. 4), is called the

solstitial colure. This latter circle cuts the ecliptic at two opposite

points, called the solstices, which lie half-way between the equinoxes.

Since the ecliptic is inclined 23½° to the plane of the equator, and

since the solstices lie half-way between the two crossing points of the

ecliptic and the equator, it is evident that the solstices must be

situated 23½° from the equator, one above and the other below, or one

north and the other south. The northern one is called the summer

solstice, because the sun arrives there at the beginning of astronomical

summer, about the 22d of June, and the southern one is called the winter

solstice, because the sun arrives there at the beginning of the

astronomical winter, about the 22d of December. The name solstice comes

from two Latin words meaning “the standing still of the sun,” because

when it is at the solstitial points its apparent course through the sky

is for several days nearly horizontal and its declination changes very

slowly.

Now, just as there are two opposite points in the sky at equal distances

from the equator, which mark the poles of the imaginary axis about which

the celestial sphere makes its diurnal revolution, so there are two

opposite points at equal distances from the ecliptic which mark the

poles of the imaginary axis about which the yearly revolution of the sun

takes place. These are called the poles of the ecliptic, and they are

situated 23½° from the celestial poles—a distance necessarily

corresponding with the inclination of the ecliptic to the equator. The

northern pole of the ecliptic is in the constellation Draco, which you

may see any night circling round the North Star, together with the Great

Dipper and Cassiopeia.

=9. Celestial Latitude and Longitude.= We have seen that the celestial

sphere is marked with imaginary circles resembling the circles of

latitude and longitude on the earth, and that in both cases the circles

are used for a similar purpose, viz., to determine the location of

objects, in one case on the globe of the earth and in the other on the

sphere of the heavens. It has also been explained that what corresponds

to latitude on the celestial sphere is called declination, and what

corresponds to longitude is called right ascension. It happens, however,

that these same terms, latitude and longitude, are also employed in

astronomy. But, unfortunately, they are based upon a different set of

circles from that which has been described, and they do not correspond

in the way that right ascension and declination do to terrestrial

longitude and latitude. A few words must therefore be devoted to

celestial latitude and longitude, as distinguished from declination and

right ascension.

Celestial latitude and longitude then, instead of being based upon the

equator and the poles, are based upon the ecliptic and the poles of the

ecliptic. Celestial latitude means distance north or south of the

ecliptic (not of the equator), and celestial longitude means distance

from the vernal equinox reckoned along the ecliptic (not along the

equator). Celestial longitude runs, the same as right ascension, from

west toward east, but it is reckoned in degrees instead of hours.

Celestial latitude is measured the same as declination, but along

circles running through the poles of the ecliptic instead of the

celestial poles, and drawn perpendicular to the ecliptic instead of to

the equator. Circles of celestial latitude are drawn parallel to the

ecliptic and centring round the poles of the ecliptic, and meridians of

celestial longitude are drawn through the poles of the ecliptic and

perpendicular to the ecliptic itself. The meridian of celestial

longitude that passes through the two equinoxes is the ecliptic prime

meridian. This intersects the equinoctial colure at the equinoctial

points, making with it an angle of 23½°. The solstitial colure, which it

will be remembered runs round the celestial sphere half-way between the

equinoxes, is perpendicular to the ecliptic as well as to the equator,

and so is common to the two systems of circles. It passes alike through

the celestial poles and the poles of the ecliptic. It will also be

observed that the vernal equinox is common to the two systems of

co-ordinates, because it lies at one of the intersections of the

ecliptic and the equator. In passing from one system to the other, the

astronomer employs the methods of spherical trigonometry.

[Illustration:

_Fig. 4. The Ecliptic and Celestial Latitude and Longitude._

C, as in the other figures, is the place of the observer and Z is the

zenith, but to avoid complication of details the circle of the

horizon is not drawn, only the north-and-south line, N C S, being

shown.

Eq Eq′ is the equator.

Ec Ec′ is the ecliptic.

P and P′ are the celestial poles.

p and p′ are the poles of the ecliptic.

Na is the nadir.

V is the vernal equinox, and A the autumnal equinox.

The circle through s, parallel to the ecliptic, is a latitude circle.

The circle p s p' is the ecliptic meridian of the star s.

The circle P V P′ A is the equinoctial colure.

The circle p V p′ A is the prime ecliptic meridian.

The arc of the ecliptic meridian contained between the ecliptic and s

measures the star's latitude.

The arc of the ecliptic contained between V and the point where the

ecliptic meridian p s p′ meets the ecliptic (or the angle V p s)

measures the star's longitude east from V, the vernal equinox.

]

=10. The Zodiac and the Precession of the Equinoxes.= The next thing

with which we must make acquaintance is the zodiac. We have learned that

the ecliptic is a great circle of the celestial sphere inclined at an

angle of 23½° to the equator, and crossing the latter at two opposite

points called the equinoxes, and that the sun in its annual journey

round the sky follows the circle of the ecliptic. Consequently, the

place which the sun occupies at any time must be somewhere on the course

of the ecliptic. The fact has been mentioned that as seen from the sun

the earth would appear to travel round the ecliptic, whence the ecliptic

may be regarded as the projection of the earth's orbit, or path, against

the background of the heavens. But, besides the earth there are seven

other large planets, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and

Neptune, which, like it, revolve round the sun, some nearer and some

farther away. Now, the orbits of all of these planets lie in planes

nearly coincident with that of the earth's orbit. None of them is

inclined more than 7° from the ecliptic and most of them are inclined

only one or two degrees. Consequently, as we watch these planets moving

slowly round in their orbits we find that they are always quite close to

the circle of the ecliptic. This fact shows that the solar system, _i.

e._, the sun and its attendant planets, occupies a disk-shaped area in

space, the outlines of which would be like those of a very thin round

cheese, with the sun in the centre. The ecliptic indicates the median

plane of this imaginary disk. The moon, too, travels nearly in this

common plane, its orbit round the earth being inclined only a little

more than 5° to the ecliptic.

Even the early astronomers noticed these facts, and in ancient times

they gave to the apparent road round the sky in which the sun and

planets travel, in tracks relatively as close together as the parallel

marks of wheels on a highway, the name zodiac. They assigned to it a

certain arbitrary width, sufficient to include the orbits of all the

planets known to them. This width is 8° on each side of the circle of

the ecliptic, or 16° in all. They also divided the ring of the zodiac

into twelve equal parts, corresponding with the number of months in a

year, and each part was called a sign of the zodiac. Since there are

360° in a circle, each sign of the zodiac has a length of just 30°. To

indicate the course of the zodiac to the eye, its inventors observed the

constellations lying along it, assigning one constellation to each sign.

Beginning at the vernal equinox, and running round eastward, they gave

to these zodiacal constellations, as well as to the corresponding signs,

names drawn from fancy resemblances of the figures formed by the stars

to men, animals, or other objects. The first sign and constellation were

called Aries, the Ram, indicated by the symbol ♈︎; the second, Taurus,

the Bull, ♉︎; the third, Gemini, the Twins, ♊︎; the fourth, Cancer, the

Crab, ♋︎; the fifth, Leo, the Lion, ♌︎; the sixth, Virgo, the Virgin,

♍︎; the seventh, Libra, the Balance, ♎︎; the eighth, Scorpio, the

Scorpion, ♏︎; the ninth, Sagittarius, the Archer, ♐︎; the tenth,

Capricornus, the Goat, ♑︎; the eleventh, Aquarius, the Water-Bearer, ♒︎;

and the twelfth, Pisces, the Fishes, ♓︎. The name zodiac comes from a

Greek word for animal, since most of the imaginary figures formed by the

stars of the zodiacal constellations are those of animals. The signs and

their corresponding constellations being supposed fixed in the sky, the

planets, together with the sun and the moon, were observed to run

through them in succession from west to east.

When this system was invented, the signs and their constellations

coincided in position, but in the course of time it was found that they

were drifting apart, the signs, whose starting point remained the vernal

equinox, backing westward through the sky until they became disjoined

from their proper constellations. At present the sign Aries is found in

the constellation next west of its original position, viz., Pisces, and

so on round the entire circle. This motion, as already intimated,

carries the equinoxes along with the signs, so that the vernal equinox,

which was once at the beginning of the constellation Aries (as it still

is at the beginning, or “first point,” of the _sign_ Aries), is now

found in the constellation Pisces.

To explain the shifting of the signs of the zodiac on the face of the

sky we must consider the phenomenon known as the precession of the

equinoxes, which is one of the most interesting things in astronomy. Let

us refer again to the fact that the axis of the earth's daily rotation

is inclined 23½° from a perpendicular to the plane of its yearly

revolution round the sun, from which it results that the ecliptic is

tipped at the same angle to the plane of the equator. Thus the sun,

moving in the ecliptic, appears half the year above (or north of) the

equator, and half the year below (or south of) it, the crossing points

being the two equinoxes. Now, this inclination of the earth's axis is

the key to the explanation we are seeking. The direction in which the

axis lies in space is a _fixed_ direction, which can be changed only by

some outside force interfering. What we mean by this will become clearer

if we think of the earth's axis as resembling the peg of a top, or the

axis of a gyroscope. When a top is spinning smoothly, with its peg

vertical, the peg will remain vertical as long as the spin is not

diminished, and no outside force interferes. So, too, the axis of the

spinning-wheel of a gyroscope keeps pointing in the same direction so

persistently that the wheel is kept from falling. If it is so mounted

that it is free to move in any direction, and if then you take the

instrument in your hand and turn round with it, the axis will adjust

itself in such a manner as to retain its original direction in space.

This tendency of a rotating body to keep its axis of rotation fixed

applies equally to the earth, whose axis, also, maintains a constant

direction in space, except for a slow change produced by outside forces,

which change constitutes the phenomenon of the precession of the

equinoxes.

We cannot too often recall the fact that the axis of the earth is

coincident in direction with that of the celestial sphere, so that the

earth's poles are situated directly under the celestial poles. But the

poles of the ecliptic are 23½° aside from the celestial poles. If the

direction of the earth's axis and with it that of the celestial sphere,

did not change at all, then the celestial poles and the poles of the

ecliptic would always retain the same relative positions in the sky;

but, in fact, an exterior force, acting upon the earth, causes a gradual

change in the direction of its axis, and in consequence of this change

the celestial poles, whose position depends upon that of the earth's

poles, have a slow motion of revolution about the poles of the ecliptic,

in a circle of 23½° radius. The force which produces this effect is the

attraction of the sun and the moon upon the protuberant part of the

earth round its equator. If the earth were a perfect sphere, this force

could not act, or would not exist, but since the earth is an oblate

spheroid, slightly flattened at the poles, and bulged round the equator,

the attraction acts upon the equatorial protuberance in such a way as to

strive to pull the earth's axis into an upright position with respect to

the plane of the ecliptic. But, in consequence of its spinning motion,

the earth resists this pull, and tries, so to speak, to keep the

inclination of its axis unchanged. The result is that the axis swings

slowly round while maintaining nearly the same inclination to the plane

of the ecliptic.

Here, again, we may employ the illustration of a top. If the peg of the

top is tipped a little aside, so that the attraction of gravitation

would cause the top to fall flat on the table if it were not spinning,

it will, as long as it continues to spin, swing round and round in a

circle instead of falling. We cannot enter into a mathematical

explanation of this phenomenon here, but the reader will find a clear

popular account of the whole matter in Prof. John Perry's little book on

_Spinning Tops_. It is sufficient here to say that the attraction of

gravitation, tending to make the top fall, but really causing the peg to

turn round and round, resembles, in its effect, the attraction of the

sun and the moon upon the equatorial protuberance of the earth, which

makes the earth's axis turn round in space.

[Illustration:

=The Milky Way about Chi Cygni=

Photographed at the Lick Observatory by E. E. Barnard, with the

six-inch Willard lens.

Observe the cloud-like forms.

]

Now, as we have said, this slow swinging round of the axis of the earth

produces the so-called precession of the equinoxes. In a period of about

25,800 years, the axis makes one complete swing round, so that in that

space of time the celestial poles describe a revolution about the poles

of the ecliptic, which remain fixed. But since the equator is a circle

situated half-way between the poles, it is evident that it must turn

also. To illustrate this, take a round flat disk of tin, or pasteboard,

to represent the equator and its plane, and perpendicularly through its

centre run a straight rod to represent the axis. Put one end of the axis

on the table, and, holding it at a fixed inclination, turn the upper end

round in a circle. You will see that as the axis thus revolves, the disk

revolves with it, and if you imagine a plane, parallel to the surface of

the table, passing through the centre of the disk at the point where the

rod pierces it, you will perceive that the two opposite points, where

the edge of the disk intersects this imaginary plane, revolve with the

disk. In one position of the axis, for instance, these points may lie in

the direction of the north-and-south sides of the room. When you have

revolved the axis, and with it the disk, one quarter way round, the

points will lie toward the east and west sides of the room. When you

have produced a half revolution they will once more lie toward the

north-and-south, but now the direction of the slope of the disk will be

the reverse of that which it had at the beginning. Finally, when the

revolution is completed, the two points will again lie north-and-south

and the slope of the disk will be in the same direction as at the start.

In this illustration the disk stands for the plane of the celestial

equator, the rod for the axis of the celestial sphere, the imaginary

plane parallel to the surface of the table for the plane of the

ecliptic, and the two opposite points where this plane is intersected by

the edge of the disk for the equinoxes. The motion of these points as

the inclined disk revolves represents the precession of the equinoxes.

This term means that the direction of the motion of the equinoxes, as

they shift their place on the ecliptic, is such that they seem to

precess, or move forward, as if to meet the sun in its annual journey

round the ecliptic. The direction is from east to west, and thus the

zodiacal signs are carried farther and farther westward from the

constellations originally associated with them; for these signs, as we

have said, are so arranged that they begin at the vernal equinox, and if

the equinox moves, the whole system of signs must move with it. The

amount of the motion is about 50″.2 per year, and since there are

1,296,000″ in a circle, simple division shows that the time required for

one complete revolution of the equinoxes must be, as already stated in

reference to the poles, about 25,800 years. A little over 2000 years ago

the signs and the constellations were in accord; it follows, then, that

about 23,800 years in the future, they will be in accord again. In the

meanwhile the signs will have backed entirely round the circle of the

ecliptic.

The attentive reader will perceive that the precession of the equinoxes,

with its attendant revolution of the celestial poles round the poles of

the ecliptic, must affect the position of the North Star. We have

already said that that star only _happens_ to occupy its present

commanding position in the sky. The star itself is motionless, or

practically so, with regard to the earth, and it is the north pole that

changes its place. At the present time the pole is about 1° 10, from the

North Star, in the direction of the Great Dipper, and it is slowly

drawing nearer so that in about 200 years it will be less than half a

degree from the star. After that the precessional motion will carry the

pole in a circle departing farther and farther from the star, until the

latter will have entirely lost its importance as a guide to the position

of the pole. It happens, however, that several other conspicuous stars

lie near this circle. One of these is Thuban, or Alpha Draconis (not now

as bright as it once was), and this star at the time when it served as

an indicator of the place of the pole, some 4600 years ago, was

connected with a very romantic chapter in the history of astronomy. In

the great pyramid of Cheops in Egypt, there is a long passage leading

straight toward the north from a chamber cut deep in the rock under the

centre of the pyramid, and the upward slope of this passage is such that

it is believed to have been employed by the Egyptian astronomer-priests

as a kind of telescope-tube for viewing the then pole star, and

observing the times of its passage over the meridian—for even the North

Star, since it is not _exactly_ at the pole, revolves every twenty-four

hours in a tiny circle about it, and consequently crosses the meridian

twice a day, once above and once beneath the true pole.

About 11,500 years in the future, the extremely brilliant star Vega, or

Alpha Lyræ, will serve as a pole star, although it will not be as near

the pole as the North Star now is. At that time the North Star will be

nearly 50° from the pole. In about 21,000 years the pole will have come

round again to the neighbourhood of Alpha Draconis, the star of the

pyramid, and in about 25,800 years the North Star will have been

restored to its present prestige as the apparent hub of the heavens.

One curious irregularity in the motion of the earth's poles must be

mentioned in connection with the precession of the equinoxes. This is a

kind of “nodding,” known as nutation. It arises from variation in the

effect of the attraction of the sun and the moon, due to the varying

directions in which the attraction is exercised. As far as the sun is

concerned, the precession is slower near the time of the equinoxes than

in other parts of the year; in other words, it is most rapid in

mid-summer and mid-winter when one or the other of the poles is turned

sunward. A similar, but much larger, change takes place in the effect of

the moon's attraction owing to the inclination of her orbit to the

ecliptic. During about nine and a half years, or half the period of

revolution of her nodes (see Part III, Section 4), the moon tends to

hasten the precession, and during the next nine and a half years to

retard it. The general effect of the combination of these irregularities

is to cause the earth's poles to describe a slightly waving curve

instead of a smooth circle round the poles of the ecliptic. There are

about 1400 of these “waves,” or “nods,” in the motion of the poles in

the course of their 26,000-year circuit. In accurate observation the

astronomer is compelled to take account of the effects of nutation upon

the apparent places of the stars.

A very remarkable general consequence of the change in the direction of

the earth's axis will be mentioned when we come to deal with the

seasons.

[Illustration:

=The Great Southern Star-Cluster ω Centauri=

Photographed by S. I. Bailey at the South American Station of Harvard

Observatory.

Note the streaming of small stars around the cluster. The cluster

itself is globular and its stars are too numerous to be counted, or

even to be

separately distinguished in the central part.

]

------------------------------------------------------------------------

PART II.

THE EARTH.

------------------------------------------------------------------------

PART II.

THE EARTH.

=1. Nature, Shape, and Size of the Earth.= The situation of the earth in

the universe has been briefly described in Part I; it remains now to see

what the earth is in itself, and what are some of the principal

phenomena connected with it as a celestial body inhabited by observant

and reasoning beings.

We know by ordinary experience that the earth is composed of rock, sand,

soil, etc., and generally covered, where there is no running or standing

water in the form of rivers, lakes, or seas, with vegetation, such as

trees and grass. Further experience teaches us that the earth is very

large, and that its surface is divided into wide areas of land and of

water. The largest bodies of water, the oceans, taken all together,

cover about 72 per cent., or nearly three-quarters of the entire surface

of the earth. Investigations carried as far down as we can go show that

the interior of the earth consists of various kinds of rock, in which

are contained many different kinds of metals. While there is reason for

thinking that a high degree of temperature prevails deep in the earth,

yet it appears evident, for other reasons, that, taken as a whole, it is

solid and very rigid throughout. By methods, the history and description

of which we have not here sufficient space to give, it has been proved

that the earth is, in form, a globe, or more strictly an ellipsoid,

slightly drawn in at the poles and swollen round the equator. The polar

diameter is 7899 miles, and the equatorial diameter 7926 miles, the

difference amounting to only 27 miles. Thus, for ordinary purposes, we

may regard the earth as being a true sphere. The level of its surface,

however, is varied by hills and mountains, which, though insignificant

in comparison with the size of the whole earth, are enormous when

compared with the structures of human hands. The loftiest known mountain

on the earth, Mt. Everest in the Himalayas, has an elevation of 29,000

feet above sea-level, and the deepest known depression of the ocean

bottom, near the island of Guam in the Pacific, sinks 31,614 feet below

sea-level. Thus, the apex of the highest mountain is about eleven and a

half miles in vertical elevation above the bottom of the deepest pit of

the sea—a distance very considerably less than half the difference

between the equatorial and polar diameters of the earth.

It is believed that at the beginning of its history the earth was a

molten mass, or perhaps a mass of hot gases and vapours like the sun,

and that it assumed its present shape in obedience to mechanical laws,

as it cooled off. The rotation caused it to swell round the equator and

draw in at the poles.

The outer part of the earth is called its crust, and geology shows that

this has been subject to violent changes, such as upheavals and

subsidences, and that in many places sea and land have interchanged

places, probably more than once. Geology also shows that the rocks of

the earth's crust are filled with the remains, or fossils, of plants and

animals differing from those now existing, though related to them, and

that many of these must have lived millions of years ago. Thus we see

that the earth bears marks of an immense antiquity, and that it was

probably inhabited during vast ages before the race of man had been

developed. The origin of life upon the earth is unknown.

=2. The Attraction of Gravitation.= Among the phenomena of life upon the

earth, which are so familiar that only thoughtful persons see anything

to wonder at in them, is what we call the “weight” of bodies. Every

person feels that he is held down to the ground by his weight, and he

knows that if he drops a heavy body it will fall straight toward the

ground. But what is this weight which causes everything either to rest

upon the earth or to fall back to it if lifted up and dropped? The

answer to this question involves a principle, or “law,” which affects

the whole universe, and makes it what we see it. This principle is one

of the great foundation stones of astronomy. It is called the law of

gravitation, the word gravitation being derived from the Latin _gravis_,

“heavy.” Briefly stated, the law is that every body, or every particle

of matter, attracts, or strives to draw to itself, every other body, or

particle of matter. This force is called the attraction of gravitation.

A large body possesses more attractive force than a small one, in

proportion to the mass, or quantity of matter, that it contains. The

earth, being extremely large, holds all bodies on its surface with a

force proportionate to its great mass. This explains why we possess what

we call weight, which is simply the effect of the attraction of the

earth upon our bodies. A large body is heavier, or drawn with more force

by the earth, than a small one (composed of the same kind of matter),

because it has a greater mass. The body really attracts the earth as

much as the earth attracts the body, but the amount of motion caused by

the attraction is proportional to the respective masses of the

attracting bodies, and since the mass of the earth is almost infinitely

great in comparison with that of any body that we can handle, the motion

which the latter imparts to the earth is imperceptible, and it is the

small body only that is seen to move under the force of the attraction.

Now we are going to see how vastly important in its effects is the fact

that the earth is spherical in form. Sir Isaac Newton, who first worked

out mathematically the law of gravitation, proved that a spherical body

attracts, and is attracted, as if its entire mass were concentrated in a

point at its centre. From this it follows that the attraction of the

earth is exercised just as if the whole attractive force emanated from a

middle point, and, that being so, the effect of the attraction is to

draw bodies from all sides toward the centre of the earth. This explains

why people on the opposite side of the earth, or under our feet, as we

say, experience the same attractive force, or have the same weight, that

we do. All round the earth, no matter where they may be situated,

objects are drawn toward the centre. If at any point on the earth you

suspend a plumb-line, and then, going one quarter way round, suspend

another plumb-line, each of the lines will be vertical at the place

where it hangs, and yet, the directions of the two lines will be at

right angles to one another, since both point toward the centre of the

earth.

Knowing the manner in which the earth attracts, we have the means of

determining its entire mass, or, as it is sometimes called, the weight

of the earth. The principle on which this is done is easily

understood, Suppose, for instance, that a small ball of lead, of known

weight, is brought near a large ball, and delicately suspended in such

a way that, by microscopic observation, the movement imparted by the

attraction of the large ball can be measured. The force required to

produce this movement can be compared with the force of the earth's

attraction which produces the weight of the ball, and thus the ratio

of the mass of the earth to that of the ball is determined. The total

mass of the earth has been found to be equivalent to a “weight” of

about 6,500,000,000,000,000,000,000 tons. The mean density of the

earth compared with that of water is found to be about 5½, that is to

say, the earth weighs 5½ times as much as a globe of water of equal

size.

Newton did not stop with showing the manner of the earth's attraction

upon bodies on or near its surface; he proved that the earth attracted

the moon also, and thus retained it in its orbit. To understand this we

must notice another fact concerning the manner in which gravitation

acts. Its force varies with distance. Experiment followed by

mathematical demonstration, has proved that the variation of the

attraction is inversely proportional to the square of the distance. This

simply means that if the distance between the two bodies concerned is

doubled, the force of attraction will be diminished four times, 4 being

the square of 2; and that if the distance is halved, the force will be

increased fourfold. Increase the distance three times, and the force

diminishes nine times; diminish the distance three times, and the force

increases nine times, because 9 is the square of 3, and, as we have

said, the force varies inversely, or contrarily, to the change of

distance. Knowing this, Newton computed what the force of the earth's

attraction must be on the moon, and he found that it was just sufficient

to keep the latter moving round and round the earth. But why does not

the moon fall directly to the earth? Because the moon had originally

another motion across the direction of the earth's attraction. How it

got this motion is a question into which we cannot here enter, but, if

it were not attracted by the earth (or by the sun), the moon would

travel in a straight line through space, like a stone escaping from a

sling. The force of the attraction is just sufficient to make the moon

move in an orbital path about the earth.

[Illustration:

_Fig. 5. How the Earth Controls the Moon._

Let C be the centre of the earth and M that of the moon. Suppose the

moon to be moving in a straight line at such a velocity that it

will, if not interfered with, go to A in one day. Now suppose the

attraction of the earth to act upon it. That attraction will draw it

to M′. Again suppose that at M′ the moon were suddenly released from

the earth's attraction; it would then shoot straight ahead to B in

the course of the next day. But, in fact, the earth's attraction

acts continually, and in the second day the moon is drawn to M″. In

other words the moon is all the time falling away from the straight

line that it would pursue but for the earth's attraction, and yet it

does not get nearer the earth but simply travels in an endless curve

round it.

]

The same principle was extended by Newton to explain the motion of the

earth around the sun. The force of the sun's attraction, calculated in

the same way, can be shown to be just sufficient to retain the earth in

its orbit and prevent it from travelling away into space. And so with

all the other planets which revolve round the sun. And this applies

throughout the universe. There are certain so-called double, or binary,

stars, which are so close together that their attraction upon one

another causes them to revolve in orbits about their common centre. In

truth, all the stars attract the earth and the sun, but the force of

this attraction is so slight on account of their immense distance that

we cannot observe its effects. The reader who wishes to pursue this

subject of gravitational attraction should consult more extensive works,

such as Prof. Young's _General Astronomy_, or Sir George Airy's

_Gravitation_.

[Illustration:

=Photograph of a Group of Sun-spots=

Similar groups are frequently seen during periods of sun-spot maximum.

]

=3. The Tides.= The tides in the ocean are a direct result of the

attraction of gravitation. They also involve in an interesting way the

principle that a spherical body, like the earth, attracts and is

attracted as if its entire mass were concentrated at its centre. The

cause of the tides is the difference in the attraction of the sun and

moon upon the body of the earth as a rigid sphere, and upon the water of

the oceans, as a fluid envelope whose particles, while not free to

escape from the earth, are free to move, or slide, among one another in

obedience to varying forces. The difference of the force of attraction

arises from the difference of distance. Since the moon, because of her

relative nearness, is the chief agent in producing tides we shall, at

first, consider her tidal influence alone. The diameter of the earth is,

in round numbers, 8000 miles; therefore, its radius is 4000 miles. From

this it follows that the centre of the earth is 4000 miles farther from

the moon than that side of the earth which is toward her at any time,

and 4000 miles nearer than the side which is away from her.

Consequently, her attraction must be stronger upon the water of the

ocean lying just under her than upon the centre of the earth, and it

must also be stronger upon the centre of the earth than upon the water

of the ocean lying upon the side which is farthest from her. The result

of these differences in the force of the moon's attraction is that the

water directly under her tends away from the centre of the earth, while,

on the other hand, the earth, considered as a solid sphere, tends away

from the water on the side opposite to that where the moon is, and these

combined tendencies cause the water to rise, with regard to its general

level, in two protuberances, situated on opposite sides of the earth.

These we call tides.

[Illustration:

_Fig. 6. The Tidal Force of the Moon._

The solid earth is represented surrounded by a shell of water. The

water on the side toward the moon is more attracted than the centre

of the earth, C; the water on the opposite side is less attracted.

The lines of force from the moon to the parts of the water lying

toward A and B are inclined to the direct line between the centres

of the earth and the moon, and the forces acting along these lines

tend to draw the water in the directions shown by the arrow points.

These are resultants of the horizontal and vertical components of

the moon's attraction at the corresponding points on the earth, and

the force acting along them tends to increase the weight of the

water wherever the lines are inclined more toward the centre of the

earth than toward the moon. On the side opposite the moon the same

effects are produced in reverse, because on that side the general

tendency is to draw the earth away from the water. Consequently if

the earth did not rotate, and if it were surrounded with a complete

shell of water, the latter would be drawn into an ellipsoidal shape,

with the highest points under and opposite to the moon, and the

lowest at the extremities of the diameter lying at right angles to

the direction of

the moon.

]

Some persons, when this statement is made, inquire: “Why, then, does not

the moon take the water entirely away from the earth?” The answer is,

that the effect of the tidal force is simply to diminish very slightly

the weight of the water, or its tendency towards the earth's centre, but

not to destroy, or overmaster, the gravitational control of the earth.

The water retains nearly all its weight, for the tidal force of the moon

diminishes it less than one part in 8,000,000. Still, this slight

diminution is sufficient to cause the water to swell a little above its

general level, at the points where it feels the effect of the tidal

force. On the other hand, around that part of the earth which is

situated half-way between the two tides, or along a diameter at right

angles to the direction of the moon, the latter's attraction _increases_

the weight of the water, _i. e._, its tendency toward the earth's centre

(see Fig. 6). Perhaps this can better be understood, if we imagine the

earth to be entirely liquid. In that case the difference in the force of

the moon's attraction with difference of distance would be manifested in

varying degrees throughout the earth's whole frame, and the result would

be to draw the watery globe out into an ellipsoidal figure, having its

greatest diameter in the line of the moon's attraction, and its smallest

diameter at right angles to that line. The proportions of the ellipsoid

would be such that the forces would be in equilibrium.

Owing to a variety of causes, such as the rotation of the earth on its

axis, which carries the water rapidly round with it; the inertia of the

water, preventing it from instantly responding to the tidal force; the

irregular shape of the oceans, interrupted on all sides by great areas

of land; their varying depth, producing differences of friction, and so

on, the tidal waves do not appear directly under, or directly opposite

to, the moon, and the calculation of the course and height of the actual

tides, at particular points on the earth, becomes one of the most

difficult problems in astronomical physics.

We now turn to consider the effects of the sun's tidal force in

connection with that of the moon. This introduces further complications.

The solar tides are only about two-fifths as high as the lunar tides,

but they suffice to produce notable effects when they are either

combined with, or act in opposition to, the others. They are combined

twice a month—once when the moon is between the earth and the sun, at

the time of new moon; and again when the moon is in opposition to the

sun, at the time of full moon. In these two positions the attractions of

the sun and the moon must, so to speak, act together, with the result

that the tides produced by them blend into a single greater wave. This

combination produces what are called spring tides, the highest of the

month. When, on the other hand, the moon is in a position at right

angles to the direction of the sun, which happens at the lunar phases

named first and last quarters, the solar and the lunar tides have their

crests 90° apart, and, in a sense, act against one another, and then we

have the neap tides, which are the lowest of the month.

Without entering into a demonstration, it may here be stated as a fact

to be memorised, that the tidal force exerted by any celestial body

varies inversely as the _cube_ of the distance. This is the reason why

the sun, although it exceeds the moon in mass more than 25,000,000

times, and is situated only about 400 times as far away from the earth,

exercises comparatively so slight a tidal force on the water of the

ocean. If the tidal force varied as the _square_ of the distance, like

the ordinary effects of gravitation, the tides produced by the sun would

be more than 150 times as high as those produced by the moon, and would

sweep New York, London, and all the seaports of the world to

destruction. In that case it might be possible, by delicate

observations, to detect a tidal effect produced upon the oceans of the

earth by the planet Jupiter.

=4. The Atmosphere.= The solid globe of the earth is enveloped in a

mixture of gases, principally oxygen and nitrogen, which we call the

air, or the atmosphere, and upon whose presence our life and most other

forms of life depend. The atmosphere is retained by the attraction of

the earth, and it rotates together with the earth. If this were not

so—if the atmosphere stood fast while the earth continued to spin within

it—a terrific wind would constantly blow from the east, having a

velocity at the equator of more than a thousand miles an hour.

Exactly how high the atmosphere extends we do not know—it may not have

any definite limits—but we do know that its density rapidly diminishes

with increase of height above the ground, so that above an elevation of

a few miles it becomes so rare that it would not support human life. The

phenomena of meteors, set afire by the friction of their swift rush

through the upper air, prove, however, that there is a perceptible

atmosphere at an elevation of more than a hundred miles.

From an astronomical point of view, the most important effect of the

presence of the atmosphere is its power of refracting light. By

refraction is meant the property possessed by every transparent medium

of bending, under particular circumstances, the rays of light which

enter it out of their original course. The science of physics teaches us

that if a ray of light passes from any transparent medium into another

which is denser, and if the path of this ray is not perpendicular to the

surface of the second medium, it will be turned from its original course

in such a way as to make it more nearly perpendicular. Thus, if a ray of

light passes from air into water at a certain slope to the surface, it

will, upon entering the water, be so changed in direction that the slope

will become steeper. Only if it falls perpendicularly upon the water

will it continue on without change of direction. Conversely a ray

passing from a denser into a rarer medium is bent away from a

perpendicular to the surface of the first medium, or its slope becomes

less. This explains why, if we put a coin in a bowl, with the eye in

such a position that it cannot see the coin over the edge, and then fill

the bowl with water, the coin seems to be lifted up into sight.

Moreover, if any transparent medium increases in density with depth, the

amount of refraction will increase as the ray goes deeper, and the

direction of the ray will be changed from a straight line into a curve,

tending to become more and more perpendicular.