Now all this applies to the atmosphere. If a star is seen in the zenith,

its light falls perpendicularly into the atmosphere and its course is

not deviated, or in other words there is no refraction. But if the star

is somewhere between the zenith and the horizon, its light falls

slopingly into the atmosphere, and is subject to refraction, the amount

of bending increasing with approach to the horizon. Observation shows

that the refraction of the atmosphere, which is zero at the zenith,

increases to about half a degree (and sometimes much more, depending

upon the state of the air), near the horizon. It follows that a

celestial object seen near the horizon will ordinarily appear about half

a degree above its true place. Since the apparent diameters of the sun

and the moon are about half a degree, when they are rising or setting

they can be seen on the horizon before they have really risen above it,

or after they have really sunk below it. Tables of refraction at various

altitudes have been prepared, and they have to be consulted in all exact

observations of the celestial bodies.

[Illustration:

_Fig. 7. Refraction._

Suppose an observer situated at O on the earth. The sun, at S, has

sunk below the level of his horizon, O H, but since the sun sends

out rays in all directions there will be some, such as S A B, which

will strike the atmosphere at A, and the refraction, tending to make

the ray more nearly perpendicular to the surface of the atmosphere,

will, instead of allowing it to go on straight over the observer's

head to B, bend it down along the dotted line A O, and the observer

will see the sun as if it lay in the direction of the dotted line O

A S′, which places the sun apparently above the horizon.

]

=5. Dip of the Horizon.= Another correction which has to be applied in

many observations depends upon the sphericity of the earth. We have

described the rational horizon, and pointed out how it differs from the

sensible horizon. We have also said that at sea the sensible horizon

nearly accords with the rational horizon (see Part I, Sect. 3). But the

accord is not complete, owing to what is called the dip of the horizon.

In fact, the sea horizon lies below the rational horizon by an amount

varying with the elevation of the eye above the surface. Geometry

enables us to determine just what the dip of the horizon must be for any

given elevation of the eye. A rough and ready rule, which may serve for

many purposes, is that the square root of the elevation of the eye in

feet equals the dip of the horizon in minutes of arc, or of angular

measure. The reader will readily see that the dip of the horizon is a

necessary consequence of the rotundity of the earth. It is because of

this that, as a ship recedes at sea her hull first disappears below the

horizon, and then her lower sails, and finally her top-sails. The use of

a telescope does not help the matter, because a telescope only _sees

straight_, and cannot bend the line of sight over the rim of the

horizon. Atmospheric refraction, however, enables us to see an object

which would be hidden by the horizon if there were no air. In

navigation, which, as a science, is an outgrowth of astronomy, these

things have to be carefully taken into account.

[Illustration:

_Fig. 8. Dip of the Horizon._

It is to be remembered that it is the _sensible_ horizon which dips,

and not the _rational_ horizon. The sensible horizon of the observer

at the elevation A dips below the horizontal plane and he sees round

the curved surface as far as a; in other words his skyline is at a.

The observer at the elevation B has a sensible horizon still more

inclined and he sees as far as b. If the observation were made from

an immense height the observer would see practically half round the

earth

just as we see half round the globe of the moon.

]

[Illustration:

Polar Streamers of the Sun, Eclipse of 1889

]

[Illustration:

The Solar Corona at the Eclipse of 1871 From drawings.

]

=6. Aberration.= A few words must be said about the phenomenon known as

aberration of light. This is an apparent displacement of a celestial

object due to the motion of the earth in its orbit. It is customary to

illustrate it by imagining oneself to be in a shower of rain, whose

drops are falling vertically. In such a case, if a person stands fast

the rain will descend perpendicularly upon his head, but if he advances

rapidly in any direction he will feel the drops striking him in the

face, because his own forward motion is compounded with the downward

motion of the rain so that the latter seems to be descending slantingly

toward him. The same thing happens with the light falling from the

stars. As the earth advances in its orbit it seems to meet the light

rays, and they appear to come from a direction ahead of the flying

earth. The result is that, since we see a star in the direction from

which its light seems to come, the star appears in _advance_ of its real

position, or of the position in which we would see it if the earth stood

fast. The amount by which the position of a star is shifted by

aberration depends upon the ratio of the earth's velocity to the

velocity of light. In round numbers this ratio is as 1 to 10,000. The

motion of the earth being in a slightly eccentric ellipse, the stars

describe corresponding, but very tiny, ellipses once every year upon the

background of the sky. But the precise shape of the ellipse depends upon

the position of the star on the celestial sphere. If it is near one of

the poles of the ecliptic, it will describe an annual ellipse which will

be almost a circle, its greater diameter being 41″ of arc. If it is near

the plane of the ecliptic, it will describe a very eccentric ellipse,

but the greater diameter will always be 41″, although the shorter

diameter may be immeasurably small. The effects of aberration have to be

allowed for in all careful astronomical observation either of the sun or

the stars. This is done by reducing the apparent place of the object to

the place it would have if it were seen at the centre of its annual

ellipse.

=7. Time.= Without astronomical observations we could have no accurate

knowledge of time. The basis of the measurement of time is furnished by

the rotation of the earth on its axis. We divide the period which the

earth occupies in making one complete turn into twenty-four equal parts,

or hours. The ascertainment of this period, called a day, depends upon

observations of the stars. Suppose we see a certain star exactly on the

meridian at some moment; just twenty-four hours later that star will

have gone entirely round the sky, and will again appear on the meridian.

The revolving heavens constitute the great clock of clocks, by whose

movements all other clocks are regulated. We know that it is not the

heavens which revolve, but the earth which rotates, but for convenience

we accept the appearance as a substitute for the fact. The rotation of

the earth is so regular that no measurable variation has been found in

two thousand years. We have reasons for thinking that there must be a

very slow and gradual retardation, owing principally to the braking

action of the tides, but it is so slight that we cannot detect it with

any means at present within our command.

In Part I it was shown how the passage across the meridian of the point

in the sky called the vernal equinox serves to indicate the beginning of

the astronomical “day,” but the position of the vernal equinox itself

has to be determined by observations on the stars. By means of a

telescope, so mounted that it can only move up or down, round a

horizontal axis, and with the axis pointing exactly east and west so

that the up and down movements of the telescope tube follow the line of

the meridian, the moment of passage across the meridian of a star at any

altitude can be observed. Observations of this nature are continually

made at all great government observatories, such as the observatory at

Washington or that at Greenwich, and at many others, and by their means

clocks and chronometers are corrected, and a standard of time is

furnished to the whole world.

There are, however, three different ways of reckoning time, or, as it is

usually said, three kinds of time. One is sidereal time, which is

indicated by the passage of stars across the meridian, and which

measures the true period of the earth's rotation; another is apparent

solar time, which is indicated by the passage of the sun across the

meridian; and a third is mean solar time, which is indicated by a

carefully regulated clock, whose errors are corrected by star

observations. This last kind of time is that which is universally used

in ordinary life (the use of sidereal time being confined to astronomy),

so it is necessary to explain what it is and how it differs from

apparent solar time.

[Illustration:

_Fig. 9. Sidereal and Solar Time._

C is the centre of the earth, and O the place of an observer on the

earth's surface.

Suppose the sun at A to be in conjunction with the star S. Then, at

the end of twenty-four sidereal hours, when the earth has made one

turn on its axis and the place O has again come into conjunction

with the star, the sun, in consequence of its yearly motion in the

ecliptic, will have advanced to B, and the earth will have to turn

through the angle A C B before O will overtake the sun and complete

a solar day; wherefore the solar day is longer than the sidereal.

]

In the first place, the reason why sidereal time is not universally and

exclusively used is because, although it measures the true period of the

earth's rotation by the apparent motion of the stars, it does not

exactly accord with the apparent motion of the sun; and, naturally, the

sun, since it is the source of light for the earth, and the cause of the

difference between day and night, is taken for all ordinary purposes, as

the standard indicator of the progress of the hours. The fact that it is

mid-day, or noon, at any place when the sun crosses the meridian of that

place, is a fact of common knowledge, which cannot be ignored. On the

other hand, the vernal equinox, which is the “noon mark” for sidereal

time, is independent of the alternation of day and night, and may be on

the meridian as well at midnight as at mid-day. Before clocks and

watches were perfected, the moment of the sun's passage over the

meridian was determined by means of a gnomon, which shows the instant of

noon by the length of a shadow cast by an upright rod. Since the

apparent course of the sun through the sky is a curve, rising from the

eastern horizon, attaining its greatest elevation where it meets the

meridian, and thence declining to the western horizon, it is evident

that the length of the shadow must be least when the sun is on the

meridian, or at its maximum altitude. The gnomon, or the sun-dial, gives

us apparent solar time. But this differs from sidereal time because, as

we saw in Part I, the sun, in consequence of the earth's motion round

it, moves about one degree eastward every twenty-four hours, and, since

one degree is equal to four minutes of time, the sun rises about four

minutes later, with reference to the stars, every morning. Consequently

it comes four minutes later to the meridian day after day. Or, to put it

in another way, suppose that the sun and a certain star are upon the

meridian at the same instant. The star is fixed in its place in the sky,

but the sun is not fixed; on the contrary it moves about one degree

eastward (the same direction as that of the earth's rotation) in

twenty-four hours. Then, when the rotation of the earth has brought the

star back to the meridian at the end of twenty-four sidereal hours, the

sun, in consequence of its motion, will still be one degree east of the

meridian, and the earth must turn through the space of another degree,

which will take four minutes, before it can have the sun again upon the

meridian. The true distance moved by the sun in twenty-four hours is a

little less than one degree, and the exact time required for the

meridian to overtake it is 3 min. 56.555 sec. Thus, the sidereal day

(period of 24 hours) is nearly four minutes shorter than the solar day.

It would seem, then, that by taking the sun for a guide, and dividing

the period between two of its successive passages over the meridian into

twenty-four hours, we should have a perfect measure of time, without

regard to the stars; in other words, that apparent solar time would be

entirely satisfactory for ordinary use. But, unfortunately, the apparent

eastward motion of the sun is not regular. It is sometimes greater than

the average and sometimes less. This variation is due almost entirely:

first, to the fact that its orbit not being a perfect circle the earth

moves faster when it is near perihelion, and slower when it is near

aphelion; and, second, to the effects of the inclination of the ecliptic

to the equator. In consequence, another measure of solar time is used,

called _mean_ solar time, in which, by imagining a fictitious sun,

moving with perfect regularity through the ecliptic, the discrepancies

are avoided. All ordinary clocks are set to follow this fictitious, or

mean, sun. The result is that clock time does not agree exactly with

sun-dial time, or, what is the same thing, apparent solar time. The

clock is ahead of the real sun at some times of the year, and behind it

at other times. This difference is called the equation of time. Four

times in the year the equation is zero, _i.e._, there is no difference

between the clock and the sun. These times are April 15, June 14, Sept.

1, and Dec. 24. At four other times of the year the difference is at a

maximum, viz. Feb. 11, sun 14 min. 27 sec. behind clock; May 14, sun 3

min. 49 sec. ahead of clock; July 26, sun 6 min. 16 sec. behind clock;

Nov. 2, sun 16 min. 18 sec. ahead of clock. These dates and differences

vary very slightly from year to year.

But, whatever measures of time we may use, it is observation of the

stars that furnishes the means of correcting them.

[Illustration:

=Morehouse's Comet, October 15, 1908=

Photographed at the Yerkes Observatory by E. E. Barnard with the

ten-inch Bruce telescope. Exposure one hour and a half.

Note the detached portions which appeared to separate from the head

and retreat up the line of the tail at enormous velocity.

]

[Illustration:

=Morehouse's Comet, November 15, 1908=

Photographed at the Yerkes Observatory by E. E. Barnard, with the

ten-inch Bruce telescope. Exposure forty minutes.

]

=8. Day and Night.= The period of twenty-four hours required for one

turn of the earth on its axis is called a day, and in astronomical

reckoning it is treated as an undivided whole, the hours being counted

uninterruptedly from 0 to 24; but nature has divided the period into two

very distinct portions, one characterised by the presence and the other

by the absence of the sun. Popularly we speak of the sunlighted portion

as day and of the other as night, and there are no two associated

phenomena in nature more completely in contrast one to the other. The

cause of the contrast between day and night must have been evident to

the earliest human beings who were capable of any thought at all. They

saw that day inevitably began whenever the sun rose above the horizon,

and as inevitably ceased whenever it sank beneath it. In all

literatures, imaginative writers have pictured the despair of primeval

man when he first saw the sun disappear and night come on, and his joy

when he first beheld the sun rise, bringing day back with it. Even his

uninstructed mind could not have been in doubt about the causal

connection of the sun with daylight.

We now know that the cause of the alternate rising and setting of the

sun, and of its apparent motion through the sky, is the rotation of the

earth. Making in our minds a picture of the earth as a turning globe

exposed to the sunbeams, we are able to see that one half of it must

necessarily be illuminated, while the other half is in darkness. We also

see that its rotation causes these two halves gradually to interchange

places so that daylight progresses completely round the earth once in

the course of twenty-four hours. If the earth were not surrounded by an

atmosphere, exactly one half of it would lie in the sunlight and exactly

one half in darkness, but the atmosphere causes the illuminated part

slightly to exceed the unilluminated part. The reason for this is

twofold: first, because the atmosphere, being transparent and extending

to a considerable height above the solid globe, receives rays from the

sun after the latter has sunk below the horizon, and these rays cause a

faint illumination in the sky after the sun as viewed from the surface

of the ground has disappeared; and, second, because the air has the

property of refracting the rays of light, in consequence of which the

sun appears above the horizon both a little time before it has actually

risen and a little time after it has actually set. The faint

illumination at the beginning and the end of the day is called twilight.

Its cause is the reflection of light from the air at a considerable

elevation above the ground. Observation shows that evening twilight

lasts until the sun has sunk about 18° below the western horizon, while

morning twilight begins when the sun is still 18° below the nearest

horizon. The length of time occupied by twilight, or its duration,

depends upon the observer's place on the earth and increases with

distance from the equator. The length of twilight at any particular

place also varies with the seasons.

It will probably have occurred to the reader that, since day and night

are ceaselessly chasing each other round the globe, it must be necessary

to choose some point of beginning, in order to keep the regular

succession of the days of the week. The necessity for this is evident as

soon as we reflect that what is sunrise at one place on the earth, is

sunset for a place situated half-way round, on the other side. To

understand this it will be better, perhaps, to consider the phenomena of

noon at various places. It is noon at any place when the sun is on the

meridian of that place. But we have seen that every place has its own

meridian; consequently, since the sun cannot be on the meridian of more

than one place at a time, each different place (reckoning east and west,

for, of course, all places lying exactly north or south of one another

have the same meridian), must have its own local noontime. Since the sun

appears to move round the earth from east to west, it will arrive at the

meridian of a place lying east of us sooner than at our meridian, and it

will arrive at our meridian sooner than at that of a place lying west of

us. Thus, when it is noon at Greenwich, it is about 7 o'clock A.M., or

five hours before noon, at New York, because the angular distance

westward round the earth's surface from Greenwich to New York is, in

round numbers, 75°, which corresponds with five hours of time, there

being 150 to every hour. At the same moment it will be 5 o'clock P.M.,

or five hours after noon, at Cashmere, because Cashmere lies 75° east of

Greenwich. That is to say, the sun crosses the meridian of Cashmere five

hours before it reaches the meridian of Greenwich, and it crosses the

meridian of Greenwich five hours before it reaches that of New York. At

a place half-way round the circumference of the globe, _i.e._ 180°

either east or west of Greenwich, it will be midnight at the same

instant when it will be mid-day, or noon, at Greenwich. Now let us

consider this for a moment.

[Illustration:

The arrows show the direction in which the earth turns (from west to

east). It is always noon at the place which is directly under the

sun. Call it Sunday noon at Greenwich, at the top of the circle;

then it is 10 A.M. Sunday at a point 30° west and 2 P.M. Sunday at a

point 30° east, and so on. Exactly opposite to the noon point it is

midnight. By common consent we change the name of the day, and the

date, at midnight; consequently it is Sunday midnight just east of

the vertical line at the bottom of the circle and Monday morning

just west of it. If we cross that line going westward we shall pass

directly from Sunday to Monday, and if we cross it going eastward we

shall pass directly from Monday to Sunday. Since, by convention,

this is a fixed line on the earth's surface, the same change will

take place no matter what the hour of the day may be.

]

It is customary to change the name of the day at midnight. Thus at the

stroke of midnight, anywhere, Sunday gives place to Monday. Suppose,

then, that the day when we see the sun on the meridian at Greenwich

happens to be Sunday. Sunday will then be, so to speak, twelve hours old

at Greenwich, because it began there at the preceding midnight. Sunday

will be only seven hours old at New York, where it also began at the

preceding midnight. In California, 45°, or three hours, still farther

west than New York, Sunday will be only four hours old, since the local

time there is only four hours after midnight. Go on over the Pacific

Ocean, until we arrive at a point 180°, or twelve hours, west of

Greenwich. There, evidently, Sunday will just have been born, the

preceding day, Saturday, having expired at the stroke of midnight. Now

if we just step over that line of 180° in what day shall we be? It

cannot be Sunday, because Sunday has just begun on the line itself. It

cannot be Saturday, because that would be counting backward. Evidently

it can be no other than Monday. Let us examine this a little more

closely. It is Sunday noon at Greenwich. We now go round the earth

eastward instead of westward. At 90°, or six hours, east of Greenwich,

we find that it is 6 P.M. Sunday and at 180°, or twelve hours, east of

Greenwich we find that it is Sunday midnight, or in other words Monday

morning. But the line of 180° _east_ of Greenwich coincides with the

line of 180° _west_ of Greenwich, which we formerly approached from the

opposite direction. So we see that we were right in concluding that in

stepping over that line from the east to the west side, we were passing

from Sunday into Monday. It is on that line that each day vanishes and

its successor takes its place. It is the “date-line” for the whole

earth, chosen by the common consent of every civilised nation, just as

we have seen that the meridian of Greenwich is the common reference line

for reckoning longitude. It lies entirely in the Pacific Ocean, hardly

touching any island, and it was chosen for this very reason, because if

it ran over inhabited lands, like Europe or America, it would cause

endless confusion. Situated as it is, it causes no trouble except to sea

captains, and very little to them. If a ship crosses the line going

westward the captain jumps his log-book one day forward. If it is, for

instance, Wednesday noon, east of the line he calls it Thursday noon, as

soon as he has passed over. If he is going eastward he drops back a day

on crossing the line, as from Thursday noon to Wednesday noon. The

date-line theoretically follows the 180th meridian, but, in fact, in

order to avoid certain groups of islands, it bends about a little, while

keeping its general direction from north to south.

=9. The Seasons.= We now recall again what was said in Part I, about the

inclination of the ecliptic, or the apparent path of the sun in the

heavens, to the equator. Because of this inclination, the sun appears

half the year above the equator and the other half below it. When it is

above the equator for people living in the northern hemisphere, it is

below the equator for those living in the southern hemisphere, and _vice

versa_. This is because observers on opposite sides of the plane of the

equator look at it from opposite points of view. For the northern

observer the celestial equator appears south of the zenith; for the

southern observer it appears north of the zenith, its distance from the

zenith, in both cases, increasing with the observer's distance from the

equator of the earth. If he is on the earth's equator, the celestial

equator passes directly _through_ the zenith. For convenience we shall

suppose the observer to be somewhere in the northern hemisphere.

[Illustration:

=Head of the Great Comet of 1861=

From a drawing by Warren De La Rue.

]

[Illustration:

=Halley's Comet, May 5, 1910=

Photographed at the Yerkes Observatory by E E. Barnard, with the

ten-inch Bruce telescope.

This was shortly before the passage of the comet between the earth and

the sun, when some think its tail was thrown over us.

]

Let us begin with that time of the year when the sun arrives at the

vernal equinox. This occurs about the 21st of March. The sun is then

perpendicular over the equator, daylight extends, uninterrupted, from

pole to pole, and day and night (neglecting the effects of twilight and

refraction) are of equal length all over the earth. Everywhere there are

about twelve hours of daylight and twelve hours of darkness. This is the

beginning of the astronomical spring. As time goes on, the motion of the

sun in the ecliptic carries it eastward from the vernal equinox, and, at

the same time, owing to the inclination of the ecliptic, it rises

gradually higher above the equator, increasing its northern declination

slowly, day after day. Immediately the equality of day and night ceases,

and in the northern hemisphere the day becomes gradually longer in

duration than the night, while in the southern hemisphere it becomes

shorter. Moreover, because the sun is now north of the equator, daylight

no longer extends from pole to pole on the earth, but the south pole is

in continual darkness, while the north pole is illuminated.

You can illustrate this, and explain to yourself why the relative length

of day and night changes, and why the sun leaves one pole in darkness

while rising higher over the other, by suspending a small terrestrial

globe with its axis inclined about 23½° from the perpendicular, and

passing a lamp around it in a horizontal plane. At two points only in

its circuit will the lamp be directly over the equator of the globe.

Call one of these points the vernal equinox. You will then see that,

when the lamp is directly over this point, its light illuminates the

globe from pole to pole, but when it has passed round so as to be at a

point higher than the equator, its light no longer reaches the lower

pole, although it passes over the upper one.

[Illustration:

_Fig. 11. The Seasons._

The earth is represented at four successive points in its orbit about

the sun. Since the axis of the earth is virtually unchangeable in

its direction in space (leaving out of account the slow effects of

the precession of the equinoxes), it results that at one time of the

year, the north pole is inclined toward the sun and at the opposite

time of the year away from it. It attains its greatest inclination

sunward at the summer solstice, then the line between day and night

lies 23½° beyond the north pole, so that the whole area within the

arctic circle is in perpetual daylight. The days are longer than the

nights throughout the northern hemisphere, but the day becomes

longer in proportion to the night as the arctic circle is

approached, and beyond that the sun is continually above the

horizon. In the southern hemisphere exactly the reverse occurs. When

the earth has advanced to the autumn equinox, the axis is inclined

neither toward nor away from the sun. The latter is then

perpendicular over the equator and day and night are of equal length

all over the earth. When the earth reaches the winter solstice the

north pole is inclined away from the sun, and now it is summer in

the southern hemisphere. At the vernal equinox again there is no

inclination of the axis either toward or away from the sun, and once

more day and night are everywhere equal. A little study of this

diagram will show why on the equator day and night are always of

equal length.

]

Now, with the lamp thus elevated above the equator, set the globe in

rotation about its axis. You will perceive that all points in the upper

hemisphere are longer in light than in darkness, because the plane

dividing the illuminated and the unilluminated halves of the globe is

inclined to the globe's axis in such a way that it lies beyond the upper

pole as seen from the direction of the lamp. Consequently, the upper

half of the globe above the equator, as it goes round, has more of its

surface illuminated than unilluminated, and, as it turns on its axis,

any point in that upper half, moving round parallel to the equator, is

longer in light than in darkness. You will also observe that the ratio

of length of the light to the darkness is greater the nearer the point

lies to the pole, and that when it is within a certain distance of the

pole, corresponding with the elevation of the lamp above the equator, it

lies in continual light—in other words, within that distance from the

pole night vanishes and daylight is unceasing. At the same time you will

perceive that round the lower pole there is a similar space within which

day has vanished and night is unceasing, and that in the whole of the

lower hemisphere night is longer than day. Exactly on the equator, day

and night are always of equal length.

Endeavour to represent all this clearly to your imagination, before

actually trying the experiment, or consulting a diagram. If you try the

experiment you may, instead of setting the axis of the globe at a slant,

place it upright, and then gradually raise and lower the lamp as it is

carried round the globe, now above and now below the equator.

We return to our description of the actual movements of the sun. As it

rises higher from the equator, not only does the day increase in length

relatively to the night, but the rays of sunlight descend more nearly

perpendicular upon the northern hemisphere. The consequence is that

their heating effect upon the ground and the atmosphere increases and

the temperature rises until, when the sun reaches its greatest northern

declination, about the 22d of June (when it is 23½° north of the

equator), the astronomical summer begins. This point in the sun's course

through the circle of the ecliptic is called the summer solstice (see

Part I, Sect. 8). Having passed the solstice, the sun begins to decline

again toward the equator. For a short time the declination diminishes

slowly because the course of the ecliptic close to the solstice is

nearly parallel to the equator, and in the meantime the temperature in

the northern hemisphere continues to increase, the amount of heat

radiated away during the night being less than that received from the

sun during the day. This condition continues for about six weeks, the

greatest heats of summer falling at the end of July or the beginning of

August, when the sun has already declined far toward the equator, and

the nights have begun notably to lengthen. But the accumulation of heat

during the earlier part of the summer is sufficient to counterbalance

the loss caused by the declension of the sun.

About the 23d of September the sun again crosses the equator, this time

at the autumnal equinox, the beginning of the astronomical autumn, and

after that it sinks lower and lower (while appearing to rise in the

southern hemisphere), until about the 22d of December, when it reaches

its greatest southern declination, 23½°, at the winter solstice, which

marks the beginning of the astronomical winter. It is hardly necessary

to point out that the southern winter corresponds in time with the

northern summer, and _vice versa_. From the winter solstice the sun

turns northward once more, reaching the vernal equinox again on the 21st

of March.

Thus we see that we owe the succession of the seasons entirely to the

inclination of the earth's axis out of a perpendicular to the plane of

the ecliptic. If there were no such inclination there would be climate

but no seasons. There would be no summer heat, except in the

neighbourhood of the equator, while the middle latitudes would have a

moderate temperature the year round. Owing to the effects of refraction,

perpetual day would prevail within a small region round each of the

poles. The sun would be always perpendicular over the equator.

Two things remain to be pointed out with regard to the effect of the

sun's annual motion in the ecliptic. One of these is the circles called

the tropics. These are drawn round the earth parallel to the equator and

at a distance of 23½° from it, one in the northern and the other in the

southern hemisphere. The northern one is called the tropic of Cancer,

because its corresponding circle on the celestial sphere runs through

the zodiacal sign Cancer, and the southern one is called the tropic of

Capricorn for a similar reason. The tropics run through the two

solstices, and mark the apparent _daily_ track of the sun in the sky

when it is at either its greatest northern or its greatest southern

declination. The sun is then perpendicular over one or the other of the

tropics. That part of the earth lying between the tropics is called the

torrid zone, because the sun is always not far from perpendicular over

it, and the heat is very great.

[Illustration:

=The Six-Tailed Comet of 1744=

From a contemporary drawing.

]

The other thing to be mentioned is the polar circles. These are situated

23½° from each pole, just as the tropics are situated a similar distance

on each side of the equator. The northern is called the arctic, and the

southern the antarctic circle. Those parts of the earth which lie

between the tropics and the polar circles are called respectively the

northern and the southern temperate zone. The polar circles mark the

limits of the region round each pole where the sun shines continuously

when it is at one or the other of the solstices. If the reader will

recall the experiment with the globe and the lamp, he will perceive that

these circles correspond with the borders of the circular spaces at each

pole of the globe which are alternately carried into and out of the full

light as the lamp is elevated to its greatest height above the equator

or depressed to its greatest distance below it. At each pole, in turn,

there are six months of continual day followed by six months of

continual night, and when the sun is at one of the solstices it just

touches the horizon on the corresponding polar circle at the hour that

marks midnight on the parts of the earth which lie outside the polar

circles. This is the celebrated phenomenon of the “midnight sun.” At any

point within the polar circle concerned, the sun, at the hour of

midnight approaches the horizon but does not touch it, its midnight

elevation increasing with nearness to the pole, while exactly at the

pole itself the sun simply moves round the sky once in twenty-four hours

in a circle practically parallel to the horizon. It is by observations

on the daily movement of the sun that an explorer seeking one of the

earth's poles during the long polar day is able to determine when he has

actually reached his goal.

The reader will have remarked in these descriptions how frequently the

angle of 23½° turns up, and he should remember that it is, in every

case, due to the same cause, viz., the inclination of the earth's axis

from a perpendicular to the ecliptic.

A very remarkable fact must now be referred to. Although the _angular

distance_ that the sun has to travel in passing first from the vernal

equinox to the autumnal equinox, on the northern side of the equator,

and then back again from the autumnal equinox to the vernal equinox, on

the southern side of the equator, is the same, the _time_ that it

occupies in making these two half stages in its annual journey is _not_

the same. Beginning from the 21st of March and counting the number of

days to the 23d of September, and then beginning from the 23d of

September and counting the number of days to the next 21st of March, you

will find that in an ordinary year the first period is seven days longer

than the second. In other words, the sun is a week longer above the

equator than below it. The reason for this difference is found in the

fact that the orbit of the earth about the sun is not a perfect circle,

but is a slightly elongated ellipse, and the sun, instead of being

situated in the centre, is situated in one of the two foci of the

ellipse, 3,000,000 miles nearer to one end of it than to the other. Now

this elliptical orbit of the earth is so situated that the earth is

nearest to the focus occupied by the sun, or in perihelion, about

December 31st, only a few days after the winter solstice, and farthest

from the sun, or in aphelion, about July 1st, only a few days after the

summer solstice. Thus the earth is nearer the sun during the winter half

of the year, when the sun appears south of the equator, than during the

summer half of the year, when the sun appears north of the equator. Now

the law of gravitation teaches that when the earth is nearer the sun it

must move more rapidly in its orbit than when it is more distant, from

which it follows that the time occupied by the sun in its apparent

passage from the vernal equinox to the autumnal equinox is longer than

that occupied in the passage back from the autumnal to the vernal

equinox.

But while the summer half of the year is longer than the winter half in

the northern hemisphere, the reverse is the case in the southern

hemisphere. There the winter is longer than the summer. Moreover, the

winter of the southern hemisphere occurs when the earth is farthest from

the sun, which accentuates the disadvantage. It has been thought that

the greater quantity of ice about the south pole may be due to this

increased length and severity of the southern winter. It is true that

the southern summer, although shorter, is hotter than the northern, but

while, theoretically, this should restore the balance as a whole, yet it

would appear that the short hot summer does not, in fact, suffice to

arrest the accumulation of ice.

However, the present condition of things as between the two hemispheres

will not continue, but in the course of time will be reversed. The

reader will recall that the precession of the equinoxes causes the axis

of the earth to turn slowly round in space. At present the northern end

of the earth's axis is inclined away from the aphelion and in the

direction of the perihelion point of the orbit, so that the northern

summer occurs when the earth is in the more distant part of its orbit,

and the winter when it is in the nearer part. But the precession swings

the axis round _westward_ from its present position at the rate of 50″.2

per year, while at the same time the position of the orbit itself is

shifted (by the effects of the attraction of the planets) in such a

manner that the aphelion and perihelion points, which are called the

apsides, move round _eastward_ at the rate of 11″.25 per year. The

combination of the precession with the motion of the apsides produces a

revolution at the rate of 61″.45 per year, which in the course of 10,500

years will completely reverse the existing inclination of the axis with

regard to the major diameter of the orbit, so that then the northern

hemisphere will have its summer when the earth is near perihelion and

its winter when it is near aphelion. The winter, then, will, for us, be

long and severe and the summer short though hot.

It has been thought possible that such a state of things may cause, in

our hemisphere, a partial renewal of what is known in geology as a

glacial period. A glacial period in the southern hemisphere would

probably always be less severe than in the northern, because of the

great preponderance of sea over land in the southern half of the globe.

An ocean climate is more equable than a land climate.

=10. The Year, the Calendar, and the Month.= A year is the period of

time required for the earth to make one revolution in its orbit about

the sun. But, as there are three kinds, or measures, of time, so there

are three kinds, or measures, of the year. The first of these is called

the sidereal year, but although, like sidereal time, it measures the

true length of the period in question, it is not suitable for ordinary

use. To understand what is meant by a sidereal year, imagine yourself to

be looking at the earth from the sun, and suppose that at some instant

you should see the earth exactly in conjunction with a star. When,

having gone round the sun, it had come back again to conjunction with

the same star, precisely one revolution would have been performed in its

orbit, and the period elapsed would be a sidereal year. Practically, the

length of the sidereal year is determined by observing when the sun, in

its apparent annual journey round the sky, has come back to conjunction

with some given star.

The second kind of year is called the tropical year, and it is measured

by the period taken by the sun to pass round the sky from one

conjunction with the vernal equinox to the next. This period differs

slightly from the first, because, owing to the precession of the

equinoxes, the vernal equinox is slowly shifting westward, as if to meet

the sun in its annual course, from which it results that the sun

overtakes the equinox a little before it has completed a sidereal year.

The tropical year is about twenty minutes shorter than the sidereal

year. It is, however, more convenient for ordinary purposes, because we

naturally refer the progress of the year to that of the seasons, and, as

we have seen, the seasons depend upon the equinoxes.

But yet the tropical year is not entirely satisfactory as a measure of

time, because the number of days contained in it is not an even one. Its

length is 366 days, 5 hours, 48 minutes, 46 seconds. Accordingly, as the

irregularities of apparent solar time were avoided by the invention of

mean solar time, so the difficulty presented by the tropical year is

gotten rid of, as far as possible, by means of what is called the civil

year, or the calendar year, the average length of which is almost

exactly equal to that of the tropical year. This brings us to the

consideration of the calendar, which is as full of compromises as a

political treaty—but there is no help for it since nature did not see

fit to make the day an exact fraction of the year, or, in other words,

to make the day and the year commensurable quantities of time.

Without going into a history of the reforms that the calendar has

undergone, which would demand a great deal of space, we may simply say

that the basis of the calendar we use to-day was established by Julius

Cæsar, with the aid of the Greek astronomer Sosigenes. This is the

Julian calendar, and the reformed shape in which it exists at present is

called the Gregorian calendar. Cæsar assumed 365¼ days as the true

length of the year, and, in order to get rid of the quarter day, ordered

that it should be left out of account for three years out of every four.

In the fourth year the four quarter days were added together to make one

additional day, which was added to that particular year. Thus the

ordinary years were each 365 days long and every fourth year was 366

days long. This fourth year was called the bissextile year. It was

identical with our leap year. The days of both the ordinary and the leap

years were distributed among the twelve months very much as we

distribute them now.

But Cæsar's assumption of 365¼ days as the length of the year was

erroneous, being about 11 min. 14 sec. longer than the real tropical

year. In the sixteenth century this error had accumulated to such a

degree that the months were becoming seriously disjointed from the

seasons with which they had been customarily associated. In consequence,

Pope Gregory XIII, assisted by the astronomer Clavius, introduced a

slight reform of the Julian calendar. The accumulated days were dropped,

and a new start taken, and the rule for leap year was changed so as to

read that “all years, whose date-number is divisible by four without a

remainder are leap years, unless they are century years (such as 1800,

1900, etc.). The century years are not leap years, unless their date

number is divisible by 400, in which case they are.” And this is the

rule as it prevails to-day, although there is now (1912) serious talk of

undertaking a new revision. But the Gregorian calendar is so nearly

correct that more than 3000 years must elapse before the length of the

year as determined by it will differ by one day from the true tropical

year.

The subject of the reform of the calendar is a very interesting one,

but, together with that of the rules for determining the date of Easter,

its discussion must be sought in more extensive works.

There is one other measure of time, depending upon the motion of a

heavenly body, which must be mentioned. This is the month, or the period

required for the moon to make a revolution round the earth. Here we

encounter again the same difficulty, for the month also is

incommensurable with the year. Then, too, the length of the month varies

according to the way in which it is reckoned. We have, first, a sidereal

revolution of the moon, which is measured by the time taken to pass

round the earth from one conjunction with a star to the next. This is,

on the average, 27 days, 7 hours, 43 minutes, 12 seconds. Next we have a

synodical revolution of the moon, which is measured by the time it takes

in passing from the phase of new moon round to the same phase again.

This seems the most natural measure of a month, because the changing

phases of the moon are its most conspicuous peculiarity. (These will be

explained in Part III.) The length of the month, as thus measured, is,

on the average, 29 days, 12 hours, 44 minutes, 3 seconds. The reason why

the synodical month is so much longer than the sidereal month is because

new moon can occur only when the moon is in conjunction with the sun,

_i.e._ exactly between the earth and the sun, and in the interval

between two new moons the sun moves onward, so that for the second

conjunction the moon must go farther to overtake the sun. It will be

observed that both of the month measures are given in average figures.

This is because the moon's motion is not quite regular, owing partly to

the eccentricity of its orbit and partly to the disturbing effects of

the sun's attraction. The length of the sidereal revolution varies to

the extent of three hours, and that of the synodical revolution to the

extent of thirteen hours.

But, whichever measure of the month we take, it is incommensurate with

the year, _i.e._ there is not an even number of months in a year. In

ancient times ceaseless efforts were made to adjust the months to the

measure of the year, but we have practically given up the attempt, and

in our calendar the lunar months shift along as they will, while the

ordinary months are periods of a certain number of days, having no

relation to the movements of the moon.

It has been thought that the period called a week, which has been used

from time immemorial, may have originated from the fact that the

interval from new moon to the first quarter and from first quarter to

full moon, etc., is very nearly seven days. But the week is as

incorrigible as all its sisters in the discordant family of time, and

there is no more difficult problem for human ingenuity than that of

inventing a system of reckoning, in which the days, the weeks, the

months, and the years shall be adjusted to the closest possible harmony.

[Illustration:

=Spiral Nebula in Ursa Major (M 101)=

Photographed at the Lick Observatory by J. E. Keeler, with the

Crossley reflector. Exposure four hours.

Note the appearance of swift revolution, as if the nebula were

throwing itself to pieces like a spinning pin-wheel.

]

[Illustration:

=The Whirlpool Nebula in Canes Venatici=

Photographed at the Lick Observatory by J. E. Keeler, with the

Crossley reflector. Exposure four hours.

Note the “beading” of the arms of the whirling nebula.

]

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

PART III.

THE SOLAR SYSTEM.

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

PART III.

THE SOLAR SYSTEM.

=1. The Sun.= By the term solar system is meant the sun together with

the system of bodies (planets, asteroids, comets and meteors) revolving

round it. The sun, being a star, every other star, for all that we can

tell, may be the ruler of a similar system. In fact, we _know_ that a

few stars have huge dark bodies revolving round them, which may be

likened to gigantic planets. The reason why the sun is the common centre

round which the other members of the solar system move, is because it

vastly exceeds all of them put together in mass, or quantity of matter,

and the power of any body to set another body in motion by its

attractive force depends upon mass. If a great body and a small body

attract each other, both will move, but the motion of the small body

will be so much more than that of the great one that the latter will

seem, relatively, to stand fast while the small one moves. Then, if the

small body had originally a motion across the direction in which the

great body attracts it, the result of the combination will be to cause

the small body to revolve in an orbit (more or less elliptical according

to the direction and velocity of its original motion) about the great

body. If the difference of mass is very great, the large body will

remain virtually immovable. This is the case with the sun and its

planets. The sun has 332,000 times as much mass (or, we may say, is

332,000 times as heavy) as the earth. It has a little more than a

thousand times as much mass as its largest planet, Jupiter. It has

millions of times as much as the greatest comet. The consequence is that

all of these bodies revolve around the sun, in orbits of various degrees

of eccentricity, while the sun itself remains practically immovable, or

just swaying a little this way and that, like a huntsman holding his

dogs in leash.

The distance of the sun from the earth—about 93,000,000 miles—has been

determined by methods which will be briefly explained in the next

section. Knowing its distance, it is easy to calculate its size, since

the apparent diameter of all objects varies directly with their

distance. The diameter of the sun is thus found to be about 866,400

miles, or nearly 110 times that of the earth. In bulk it exceeds the

earth about 1,300,000 times, but its mass, or quantity of matter, is

only 332,000 times the earth's, because its average density is but one

quarter that of the earth. This arises from the fact that the earth is a

solid, compact body, while the sun is a body composed of gases and

vapours (though in a very compressed state). It is the high temperature

of the sun which maintains it in this state. Its temperature has been

calculated at about 16,000° Fahrenheit, but various estimates differ

rather widely. At any rate, it is so hot that the most refractory

substances known to us would be reduced to the state of vapour, if

removed to the sun. The quantity of heat received upon the earth from

the sun can only be expressed in terms of the mechanical equivalent of

heat. The unit of heat in engineering is the calorie, which means the

amount of heat required to raise the temperature of one kilogram of

water (2.2 pounds) one degree Centigrade (1°.8 Fahrenheit). Now

observation shows that the sun furnishes 30 of these calories per minute

upon every square metre (about 1.2 square yard) of the earth's surface.

Perhaps there is no better illustration of what this means than Prof.

Young's statement, that “the heat annually received on each square foot

of the earth's surface, if employed in a perfect heat engine, would be

able to hoist about a hundred tons to the height of a mile.” Or take

Prof. Todd's illustration of the mechanical power of the sunbeams: “If

we measure off a space five feet square, the energy of the sun's rays

when falling vertically upon it is equivalent to one horse power.”

Astronomers ordinarily reckon the solar constant in “small calories,”

which are but the thousandth part of the engineer's calorie, and the

latest results of the Smithsonian Institution observations indicate that

the solar constant is about 1.95 of these small calories per square

centimeter per second. About 30 per cent. must be deducted for

atmospheric absorption.

Heat, like gravitation and like light, varies inversely in intensity

with the square of the distance; hence, if the earth were twice as near

as it is to the sun it would receive four times as much heat and four

times as much light, and if it were twice as far away it would receive

only one quarter as much. This shows how important it is for a planet

not to be too near, or too far from, the sun. The earth would be

vapourised if it were carried within a quarter of a million miles of the

sun.

The sun rotates on an axis inclined about 7½° from a perpendicular to

the plane of the ecliptic. The average period of its rotation is about

25⅓ days—we say “average” because, not being a solid body, different

parts of its surface turn at different rates. It rotates faster at the

equator than at latitudes north-and-south of the equator, the velocity

decreasing toward the poles. The period of rotation at the equator is

about 25 days, and at 40° north or south of the equator it is about 27

days. The direction of rotation is the same as that of the earth's.

The surface of the sun, when viewed with a telescope, is often seen more

or less spotted. The spots are black, or dusky, and frequently of very

irregular shapes, although many of them are nearly circular. Generally

they appear in groups drawn out in the direction of the solar rotation.

Some of these groups cover areas of many millions of square miles,

although the sun is so immense that even then they appear to the naked

eye (guarded by a dark glass) only as small dark spots on its surface.

The centres of sun-spots, are the darkest parts. Generally around the

borders of the spots the surface seems to be more or less heaped up.

Often, in large sun-spots, immense promontories, very brilliant, project

over the dark interior, and many of these are prolonged into bridges of

light, apparently traversing the chasms beneath. Constant changes of

shape and arrangement take place, and there are few more astonishing

telescopic objects than a great sun-spot.

[Illustration:

=“Tress Nebula” (N. G. C. 6992) in Cygnus=

Photographed at the Yerkes Observatory by G. W. Ritchey, with the

two-foot reflector.

Observe the strangely twisted look of this long curved nebula; also

the curious curves composed of minute stars near it.

]

The spots are not always visible in equal numbers, and in some years but

few are seen, and they are small. It has been found that they occur in

periods, averaging about eleven years from maximum to minimum, although

the length of the period is very irregular. It has also been observed

that when the first spots of a new period appear, they are generally

seen some 30° from the equator, either toward the north or toward the

south, and that as the period progresses the spots increase in size, and

seem to draw toward the equator, the last spots of the period being seen

quite close to the equator, on one side or the other. The duration of

individual spots is variable; some last but a day or two, and others

continue for weeks, sometimes being carried out of view by the rotation

of the sun and brought into view again from the other side.

The surface of the sun in the neighbourhood of groups of spots is

frequently marked by large areas covered with crinkled bright lines and

patches, which are called faculæ. These, which are the brightest parts

of the sun, appear to be elevated above the general level.

As to the cause and nature of sun-spots much remains to be learned. In

1908, Prof. George E. Hale, by means of an instrument called the

spectro-heliograph, which selects out of the total radiation of the

solar disk light peculiar to certain elements, and thus permits the use

of that light alone in photographing the sun, demonstrated that

sun-spots probably arise from vortices, or whirling storms, and that

these vortices produce strong magnetic fields in the sun-spots. The

phenomenon may be regarded, says Prof. Hale, as somewhat analogous to a

tornado or waterspout on the earth. The whirling trombe becomes wider at

the top, carrying the gases from below upward. At the centre of the

storm the rapid rotation produces an expansion which cools the gases and

causes the appearance of a comparatively dark cloud, which we see as the

sun-spot. The vortices whirl in opposite directions on opposite sides of

the sun's equator, thus obeying the same law that governs the rotation

of cyclones on the earth.

It has long been a question whether the condition of the sun as

manifested by the spots upon its surface has an influence upon the

meteorology of the earth. It is known that the sun-spot period coincides

closely with periodical changes in the earth's magnetism, and great

outbursts on the sun have frequently been immediately followed by

violent magnetic storms and brilliant displays of the aurora borealis on

the earth.

The sun undoubtedly exercises other influences upon the earth than those

familiar to us under the names of gravitation, light, and heat; but the

nature of these other influences is not yet fully understood.

The brilliant white surface of the sun is called the photosphere. It has

been likened to a shell of intensely hot clouds, consisting of

substances which are entirely vaporous within the body of the sun. Above

the photosphere lies an envelope, estimated to be from 5000 to 10,000

miles thick, known as the chromosphere. It consists mainly of hydrogen

and helium, and when seen during a total eclipse, when the globe of the

sun is concealed behind the moon, it presents a brilliant scarlet

colour. Above this are frequently seen splendid red flame-like objects,

named prominences. They are of two varieties—one cloud-like in

appearance, and the other resembling spikes, or trees with spreading

tops,—but often their forms are infinitely varied. The latter, the

so-called eruptive prominences, exhibit rapid motion away from the sun's

surface, as if they consisted of matter which has been ejected by

explosion. Occasionally these objects have been seen to grow to a height

of several hundred thousand miles, with velocities of two or three

hundred miles per second.

The sun has still another envelope, of changing form,—the corona. This

apparently consists of rare gaseous matter, whose characteristic

constituent is an element unknown on the earth, called coronium. The

corona appears in the form of a luminous halo, surrounding the hidden

sun during a total eclipse, and it often extends outward several million

miles. Its shape varies in accordance with the sun-spot period. It has a

different appearance and outline at a time of maximum sun-spots from

those which it presents at a minimum. There are many things about the

corona which suggest the play of electric and magnetic forces. The

corona, although evidently always existing, is never seen except during

the few minutes of complete obscuration of the sun that occurs in a

total eclipse. This is because its light is not sufficiently intense to

render it visible, when the atmosphere around the observer is

illuminated by the direct rays of sunlight.

=2. Parallax.= We now return to the question of the sun's distance from

the earth, which we treat in a separate section, because thus it is

possible to present, at a single view, the entire subject of the

measurement of the distances of the heavenly bodies. The common basis of

all such measurements is furnished by what is called parallax, which may

be defined as the difference of direction of an object when viewed

alternately from two separate points. The simplest example of parallax

is found in looking at an object first with one eye and then with the

other without, in the meantime, altering the position of the head.

Suppose you sit in front of a window through which you can see the wall

of a house on the opposite side of the street. Choose one of the

vertical bars of the window-sash, and, closing the left eye, look at the

bar with the right and note where it seems to be projected against the

wall. Then close the right eye and open the left, and you will observe

that the place of projection of the bar has shifted toward the right.

This change of direction is due to parallax and its amount depends both

upon the distance between the eyes and upon the distance of the window

from the observer. To see how this principle is applied by the

astronomer, let us suppose that we wish to ascertain the distance of the

moon. The moon is so far away that the distance between the eyes is

infinitesimal in comparison, so that no parallactic shift in its

direction is apparent on viewing it alternately with the two eyes. But

by making the observations from widely separated points on the earth we

can produce a parallactic shifting of the moon's position which will be

easily measurable.

Let one of the points of observation be in the northern hemisphere and

the other in the southern, thousands of miles apart. The two observers

might then be compared to the eyes of an enormous head, each of which

sees the moon in a measurably different direction. If the northern

observer carefully ascertains the angular distance of the moon from his

zenith, and the southern observer does the same with regard to _his_

zenith, as indicated in Fig. 12, they can, by a combination of their

measurements, construct a quadrilateral A C B M, of which all the angles

may be ascertained from the two measurements, while the length of the

sides A C and B C is already known, since they are each equal to the

radius of the earth. With these data it is easy, by the rules of plane

trigonometry, to calculate the length of the other sides, and also the

length of the straight line from the centre of the earth to the moon. In

all such cases the distance between the points of observation is called

the base-line, whose length is known to start with, while the angles

formed by the lines of direction at the opposite ends of the base-line

are ascertained by measurement.

[Illustration:

_Fig. 12. Parallax of the Moon._

Let C be the centre of the earth, A and B the stations of two

observers, one in the northern, the other in the southern

hemisphere, and M the moon. The lines C A Z and C B Z′ indicate the

direction of the zenith at A and B respectively. Subtracting the

measured angles at A and B each from 180° gives the inside angles at

those points. The angle at C is equal to the sum of the latitudes of

A and B since they are on opposite sides of the equator. With three

angles known, the fourth, at M, is found by simply subtracting their

sum from 360°.

]

[Illustration:

=The Great Andromeda Nebula=

Photographed at the Yerkes Observatory by G. W. Ritchey, with the

two-foot reflector.

Observe the vast spiral, or elliptic, rings surrounding the central

condensation and the appearance of breaking up and re-shaping into

smaller masses which some of the rings present.

]

In the case of the sun the distance concerned is so great (about 400

times that of the moon) that the parallax produced by viewing it from

different points on the earth is too small to be certainly measured, and

a modification of the method has to be employed. One such modification,

which has been much used, depends upon the fact that the planet Venus,

being nearer the sun than the earth is, appears, at certain times,

passing directly over the face of the sun. This is called a transit of

Venus. During a transit, Venus is between three and four times nearer

the earth than the sun is, and consequently its parallactic

displacement, when viewed from widely separated points on the earth, is

much greater than that of the sun. One of the ways in which the

astronomer takes advantage of this fact is shown in Fig. 13. Let A and B

be two points on opposite sides of the earth, but both somewhere near

the equator. As Venus swings along in its orbit to pass between the

earth and the sun, it will manifestly be seen just touching the sun's

edge sooner from A than from B. The observer at A notes with extreme

accuracy the exact moment when he sees Venus apparently touch the sun.

Several minutes later, the observer at B will see the same phenomenon,

and he also notes accurately the time of the apparent contact. Now,

since we know from ordinary observation the time that Venus requires to

make one complete circuit of its orbit, we can, by simple proportion,

calculate, from the time that it takes to pass from v to v^1, the

angular distance between the lines A S and B S, or in other words the

size of the angle at S, which is equal to the parallactic displacement

of the sun, as seen from opposite ends of the earth's diameter. Knowing,

to begin with, the distance between A and B, we have the means of

determining the length of all the other lines in the triangle, and hence

the distance of the sun. This process is known as Delisle's method.

There is another method, called Halley's, but in a brief treatise of

this kind we cannot enter into a description of it. It suffices to say

that both depend upon the same fundamental principles.

[Illustration:

_Fig. 13. Parallax of the Sun from Transit of Venus_.

(For description see text.)

]

It must be added, however, that other ways of measuring the sun's

distance than are afforded by transits of Venus have been developed. One

of these depends upon observation of the asteroid Eros, which

periodically approaches much nearer to the earth than Venus ever does.

By observing the parallax of Eros, when it is nearest the earth, its

distance can be ascertained, and that being known the distance of the

sun is immediately deducible from it, because, by the third law of

Kepler (to be explained later), the _relative_ distances of all the

planets from the sun are proportional to their periods of revolution, so

that if we know any one of the distances in miles we can calculate all

the others. It is important here to state the angular amount of the

sun's parallax, since it is a quantity which is continually referred to

in books on astronomy. According to the latest determination, based on

observations of Eros, the solar parallax is 8″.807, which corresponds,

in round numbers, to a distance of 92,800,000 miles. A mean parallax of

8″.796 is given by Mr. C. G. Abbot, based on a combination of results

from a number of different methods, and this corresponds to a distance

of 92,930,000 miles. To the astronomer, who seeks extreme exactness, the

slightest difference is important. It should be noted that the figures

8″.807 or 8″.796 represent the parallactic displacement of the sun, as

seen not from the opposite ends of the earth's entire diameter, but from

opposite ends of its radius, or semi-diameter. Accordingly it is equal

to half of the angle at S in Fig. 13. It is for convenience of

calculation that, in such cases, the astronomer employs the

semi-diameter, instead of the whole diameter for his base-line.

The case of the stars must next be considered, and now we find that the

distances involved are so enormous that the diameter, or semi-diameter,

of the earth is altogether too insignificant a quantity to afford an

available base-line for the measurement. We should have remained forever

ignorant of star distances but for the effects produced by the earth's

change of place due to its annual revolution round the sun. The mean

diameter of the earth's orbit is about 186,000,000 miles, and we are

able to make use of this immense distance as a base-line for

ascertaining the parallax of a star. Suppose, for instance, that the

direction of a star in the sky is observed on the 1st of January, and

again on the 1st of July. In the meantime, the earth will have passed

from one end of the base-line just described to the other, and unless

the star observed is extremely remote, a careful comparison of the two

measurements of direction will reveal a perceptible parallax, from which

the actual distance of the star in question can be deduced.

It is to be observed that if all the stars were equally distant this

method would fail, because then there would be no “background” against

which the shift of place could be observed; all of the stars would shift

together. But, in fact, the vast majority of the stars are so remote

that even a base-line of 186,000,000 miles is insufficient to produce a

measurable shift in their direction. It is only the distances of the

nearer stars which we can measure, and for them the multitude of more

remote ones serves, like the wall of the house in the experiment with

the window-bar, as a background on which the shift of place can be

noted. Just as in calculations of the sun's parallax the semi-diameter

of the earth is chosen for a base-line, so in the case of the stars the

semi-diameter of the earth's orbit, amounting to 93,000,000 miles, forms

the basis. Measured in this way the parallaxes of the nearest stars come

out in tenths, or hundredths, of a second of arc, or angular

measurement. Thus the parallax of Alpha Centauri, the nearest known

star, is about 0″.75, corresponding to a distance of about

26,000,000,000,000 miles. Now 0″.75 is a quantity inappreciable to the

naked eye, and only to be measured with delicate instruments, and yet

this almost invisible shift of direction is all that is produced by

viewing the nearest star in the sky from the opposite ends of a

base-line 93,000,000 miles long!

=3. Spectroscopic Analysis.= We have next to deal with the constitution

of the sun, or the nature of the substances of which it consists, and

for this purpose we must first understand the operation of the

spectroscope, in many respects the most wonderful instrument that man

has invented. It has given birth to the “chemistry of the sun” and the

“chemistry of the stars,” for by its aid we can be as certain of the

nature of many of the substances of which they are made as we could be

by actually visiting them.

[Illustration:

_Fig. 14. Spectrum Analysis._

The red is least turned by the prism from its original course and the

violet most. If between the prism and the screen on which the

spectrum falls there were interposed a gas of any kind that gas

would absorb from the coloured rays passing through it the exact

waves of light with which it would itself shine if it were made

luminous by heat. It would not take out an entire section, or

colour, from the spectrum, but only a small part of one or more of

the colours, and the absence of these parts would be indicated on

the screen by narrow black lines situated in various places; and

these lines, in number and in situation, would differ with every

different kind of gas that was interposed. If several kinds were

interposed simultaneously they would all pick out their own peculiar

rays from the light, and thus the spectrum would be crossed by a

large number of dark lines, by the aid of which the nature of the

various gases that produced them could be told. The effect would be

the same if the gases were interposed in the path of the white light

before it enters the prism;—and this, in fact, is what happens when

the spectrum of the sun, or a star, is examined—the absorption has

already occurred at the surface of the luminous body before the

light comes to the earth.

]

Fundamentally, spectroscopic analysis depends upon the principle of

refraction, of which we have spoken in connection with the atmosphere.

Although the most powerful spectroscopes are now made on a different

plan, the working of the instrument can best be comprehended by

considering it in the form in which it was first invented, and in which

it is still most often used. In its simplest form the spectroscope

consists of a three-angle prism of glass, through which a ray of light

is sent from the sun, star, or other luminous object to be examined.

Glass, like air or water, has the property of refracting, or bending,

all rays of light that enter it in an inclined direction. In passing

through two of the opposite-sloping sides of a prism, the ray is twice

bent, once on entering and again on leaving, in accordance with the

principle that we have already mentioned (see Part II, Sect. 4). Still,

merely bending the ray out of its original course would have no

important result but for another associated phenomenon, known as

dispersion. To explain dispersion we must recall the familiar fact that

white light consists of a number of coloured components which, when

united, make white. It is usual to speak of these primary, or prismatic,

colours, as seven in number. These are red, orange, yellow, green, blue,

indigo, and violet. Physicists now assign a different list of primary

colours, but these, being generally familiar, will best serve our

purpose. Without going into an explanation of the reasons, it will

suffice to say that the waves of light producing these fundamental

colours are not all equally affected by refraction. The red is least,

and the violet most, bent out of its course in passing through the

prism, the other colours being bent more and more in proportion to their

distance from the red. It follows that the ray, or beam, of light, which

was white when it entered the prism, becomes divided or dispersed during

its passage into a brush of seven different hues. Thus the prism may be

said to analyse the light into its fundamental colours, making them

separately visible. This, as a scientific fact, dates from the time of

Newton. But Newton did not dream of the further magic that lay in the

prism.

It was noticed as early as 1801 that, when the light of the sun was

dispersed in the way we have described, not only did the seven primary

colours make their appearance, but across the ribbon-like band, called

the spectrum, that was thus formed, ran a number of thin black lines,

like narrow gaps in the band. The position of these lines was carefully

studied by a German astronomer, Fraunhofer, in 1814, and they still bear

the name of Fraunhofer lines. But the full explanation of them did not

come until 1858 when, with their aid, Kirschoff laid the foundations of

spectrum analysis.

This analysis is based upon the fact that the Fraunhofer lines are

visual indications of the existence of certain substances in the sun. To

explain this we must know three fundamental facts:

1st: Every incandescent body that is either solid or liquid (or, if it

consists of gases, is under high pressure) shines with compound white

light, which, when dispersed by prisms, gives a _continuous_ coloured

band, or spectrum.

2d: Every elementary substance when in the gaseous state, and under low

pressure, if brought to incandescence by heat, shines with light which,

when dispersed, gives a _discontinuous_ spectrum, made up of separate

bright lines; and each different element possesses its own peculiar

spectral lines, never coinciding in position with the lines of any other

element.

3d: If the light from a body giving a continuous spectrum is caused to

pass through a gas which is at a lower temperature, the gas will absorb

precisely those light waves, of which its own spectrum is composed and

will leave in the spectrum of the body a series of dark lines, or gaps,

whose number and position indicate the nature of the gas whose

absorptive action has produced them.

Now, to apply these principles to the sun we have only to remember that

it is a globe of gaseous substances, which are under great pressure,

owing to the immense force of the sun's gravitation. Consequently it

gives a continuous spectrum. But, at the same time, it is surrounded

with gaseous envelopes, which are not as much compressed as the internal

gases are, and which are at a lower temperature because they come in

contact with the cold of surrounding space. The light from the body of

the sun must necessarily pass through these envelopes, and each of the

gases of which they consist absorbs from the passing sunlight its own

peculiar rays, with the result that the spectrum of the sun is seen

crossed with a great number of black lines—the Fraunhofer lines.

It will be remarked that the evidence which the Fraunhofer lines afford

concerning the composition of the sun applies, strictly, only to the

outer portion, or to the envelopes of gaseous matter that surround the

interior globe. But since there is every reason to believe that the

entire body of the sun is in a gaseous state, notwithstanding the

internal pressure, and since we see that there is a continual

circulation going on between the inner and outer portions, it is logical

to conclude that essentially the same elements exist under varying

conditions in all parts of the sun.

In this way, then, we have learned the composition of the sun, and we

find that it consists of virtually the same elementary substances found

upon the earth, but existing there in a gaseous or vaporous state. Among

the elements which have been positively identified in the sun by means

of their characteristic spectral lines are iron, calcium, sodium,

aluminum, copper, zinc, silver, lead, potassium, nickel, tin, silicon,

manganese, magnesium, cobalt, hydrogen, and at least twenty others which

are likewise found upon the earth. Some elementary substances known on

the earth, such as gold and oxygen, have not yet been certainly found in

the sun, but there is every reason to believe that they all exist there,

though perhaps under conditions which render their detection difficult

or impossible. Helium was recognised as an element in the sun, by giving

spectral lines different from any known substance, and it received its

name “sun-metal,” long before it was discovered on the earth. We have

seen that there is at least one element in the sun, coronium, which, as

far as we know, does not exist at all upon the earth, and it is not

improbable that there may be others which have no counterparts on the

earth.

The same kind of analysis applies to the stars, no matter how far away

they may be, so long as they give sufficient light to form a spectrum.

And in this way it has been found that the stars differ somewhat from

the sun and from one another in their composition, and thus a

classification of the stars has been made, and it has been possible to

draw conclusions concerning their relative age, which show that some

stars are comparatively younger than the sun, others older, and others

so far advanced in age, or evolution, that they are drawing near

extinction. Many dark bodies also exist among the stars, which appear to

be completely extinguished suns. It only remains to add on this subject

that, according to prevailing theories, the earth itself was once an

incandescent body, shining with its own light, and at that time it, too,

would have yielded a spectrum showing of what substances it consisted.

=4. The Moon.= The earth is a satellite of the sun, and the moon is a

satellite of the earth. The mean, or average, distance of the sun from

the earth is about 93,000,000 miles; the mean distance of the moon is a

little less than 239,000 miles. This distance is variable to the extent

of about 31,000 miles, owing to the eccentricity of the moon's orbit

about the earth. That is, the moon is sometimes nearly 253,000 miles

away, and sometimes only about 221,600. The diameter of the moon is 2163

miles. Its bulk is one-forty-ninth that of the earth, but its mass is

only one-eightieth, because its mean density is only about six-tenths as

great as the earth's.

The moon appears to travel in an orbit round the earth, but in fact the

orbit is always concave toward the sun, and the disturbing attraction of

the earth, as the two move together round the sun, causes it to appear

now on one side and now on the other. But we may treat the moon's orbit

as if the earth were the true centre of force, the attraction of the sun

being regarded as the disturbing element.

According to a mathematical theory, which has been largely accepted as

probably true, but into which we cannot enter here (see Prof. George

Darwin's _The Tides_, or Prof. R. Ball's _Time and Tide_), the moon was

thrown off from the earth many ages ago, as a consequence of tidal

“friction.” As it moves round in its orbit the moon keeps the same face

toward the earth. This fact is also ascribed to tidal influence.

[Illustration:

=Spiral Nebula in Cepheus (H IV 76)=

Photographed at the Lick Observatory by J. E. Keeler, with the

Crossley reflector. Exposure four hours.

Observe that the central portion is only of stellar magnitude.

]

[Illustration:

=Nebulous Groundwork in Taurus=

Photographed at the Yerkes Observatory by E. E. Barnard with 10-inch

Bruce telescope. Exposure six hours twenty-eight minutes.

Prof. Barnard has suggested that some of these dark lanes in rich

regions of stars are non-luminous nebulæ.

]

Apparently the moon has no atmosphere, or if it has any it is too rare

to be certainly detected. On its surface, there is no appearance of

water. Consequently we cannot suppose it to be inhabited, at least by

any forms of life familiar to us on the earth. But when the moon is

viewed with a telescope large relatively flat areas are seen, which some

think may have been the beds of seas in ancient times. They are still

called _maria_, or “seas,” and are visible to the naked eye in the form

of great irregular dusky regions. Nearly two-thirds of the surface of

the moon, as we see it, consists of bright regions, which are very

broken and mountainous. Most of the mountains of the moon are roughly

circular, surrounding enormous depressions, which look like gigantic

pits. For this reason they are called lunar volcanoes, but, to say

nothing of their immense size—for many are fifty or sixty miles

across—they differ in many ways from the volcanoes of the earth. It

suffices to point out that what resemble volcanic craters are not

situated, as is the case on the earth, at the summits of mountains, but

are vast sink-holes, descending thousands of feet below the general

surface of the moon. Their real origin is unknown, but it is possible

that volcanic forces may have produced them. (For a description, with

photographs, of these gigantic formations in the lunar world, see the

present author's _The Moon_.) In addition to the circular mountains, or

craters, there are several long and lofty chains of lunar mountains much

resembling terrestrial mountain ranges.

As to the absence of air and water from the moon, some have supposed

that they once existed, but, in the course of ages, have disappeared,

either by absorption, partly mechanical and partly chemical, into the

interior rocks, or by escaping into space on account of the slight force

of gravity on the moon, which appears to be insufficient to enable it to

retain, permanently, such volatile gases as oxygen, hydrogen, and

nitrogen. This leads us to consider the force of the moon's attraction

at its surface. We have seen that spherical bodies attract as if their

whole mass were collected at their centres. We also know that the force

of attraction varies directly as the mass of the attracting body and

inversely as the square of the distance from its centre. Now the mass of

the moon is one-eightieth that of the earth, so that, upon bodies

situated at an equal distance from the centres of both, the moon's

attraction would be only one-eightieth of the earth's. But the diameter

of the moon is not very much more than one quarter that of the earth,

and for the sake of round numbers let us call it one quarter. It follows

that an object on the surface of the moon is four times nearer the

centre of attraction than is an object on the surface of the earth, and

since the force varies inversely as the square of the distance the

moon's attraction upon bodies on its surface is relatively sixteen times

as great as the earth's. But the total force of the earth's attraction

is eighty times greater than the moon's. In order, then, to find the

real relative attraction of the moon at its surface we must divide 80 by

16, the quotient, 5, showing the ratio of the earth's force of

attraction at its surface to that of the moon at _its_ surface. In other

words, this calculation shows that the moon draws bodies on its surface

with only one-fifth the force with which the same bodies would be drawn

on the earth's surface. The weight of bodies of equal mass would,

therefore, be only one-fifth as great on the moon as on the earth.

But the real difference is greater than this, for we have used round

numbers, which exaggerated the size of the earth as compared with that

of the moon. If we employ the fractional numbers which show the actual

ratio of the moon's radius (half-diameter) to that of the earth, we

shall find that the weight of the same body would be only about

one-sixth as great on the moon as on the earth. It has been thought that

this relative lack of weight on the moon may account for the gigantic

proportions assumed by its craters, since the same elective force would

throw volcanic matter to a much greater height and distance there than

on our planet.

The connection of the slight force of gravity on the moon with its

ability to retain an atmosphere is shown by the following

considerations. It is possible to calculate for any planet of known mass

the velocity with which a particle would have to move in order to escape

from the control of that planet. In the case of the earth this critical

velocity, as it is called, amounts to about 7 miles per second, and in

the case of the moon to only 1½ miles per second. Now the kinetic theory

of gases informs us that their molecules are continually flying in all

directions with velocities varying with the nature and the temperature

of the gas. The maximum velocity of the molecules of oxygen is 1.8 miles

per second, of hydrogen 7.4 miles, of nitrogen 2 miles, of water vapour

2.5 miles. It is evident, then, that the force of the earth's attraction

is sufficient permanently to retain all these gases except hydrogen, and

in fact there is no gaseous hydrogen in the atmosphere, that element

being found on the earth only in combination with other substances. But

oxygen and nitrogen, which constitute the bulk of the atmosphere, have

maximum molecular velocities much less than the critical velocity above

described. In the case of the moon, however, the critical velocity is

less than those of the molecules of oxygen, nitrogen, and water vapour,

to say nothing of hydrogen; therefore the moon cannot permanently retain

them. We say “permanently,” because they might be retained for a time

for the reason that the molecules of a gas fly in all directions, and

continual collisions occur among them in the interior of the gaseous

mass, so that it would be only those at the exterior of the atmosphere

which would escape; but gradually all that remained free from

combination would get away.

[Illustration:

_Fig. 15. The Phases of the Moon._

As the moon goes round the earth in the direction indicated by the

arrows, the sun remaining always on the left-hand side, it is

evident that the illuminated half of the moon will be turned away

from the earth at new moon, and toward it at full moon, while

between these positions more or less will be seen according to the

direction of the moon with regard to the sun.

]

As the moon travels round the earth it shows itself in different forms,

gradually changing from one into another, which are known as phases. If

the moon shone with light of its own its outline would always be

circular, like the sun's. The apparent change of form is due, first, to

its being an opaque globe, reflecting the sunlight that falls upon it,

and necessarily illuminated on only one side at a time; and second, to

the fact that as it travels round the earth the half illuminated by the

sun is sometimes turned directly toward us, at other times only partly

toward us, and at still other times directly away from us. When it is in

that part of its orbit which passes between the sun and the earth, the

moon, so to speak, has its back turned to us, the illuminated side

being, of course, toward the sun. It is then invisible, and this unseen

phase is the true “new moon.” It is customary, however, to give the name

new moon to the narrow, sickle-shaped figure, which it shows in the

west, after sunset, a few days after the date of the real new moon. The

sickle gradually enlarges into a half circle as the moon passes away

from the sun, and the half circle phase, which occurs when the moon

arrives at a position in the sky at right angles to the direction of the

sun, is called first quarter. After first quarter the moon begins to

move round behind the earth, with respect to the sun, and when it has

arrived just behind the earth, its whole illuminated face is turned

toward the earth, because the sun, which causes the illumination, is on

that same side. This phase is called full moon. Afterward the moon

returns round the other part of its orbit toward its original position

between the earth and the sun, and as it does so, it again assumes,

first, the form of a half circle, which in this case is called third, or

last, quarter, then that of a sickle, known as “old moon,” and finally

disappears once more to become new moon again.

A perfectly evident explanation of these changes of form, clearer than

any description, can be graphically obtained in this way. Take a

billiard ball, a croquet ball, or a perfectly round, smooth, and tightly

rolled ball of white yarn, and, placing yourself not too near a brightly

burning lamp and sitting on a piano stool (in order to turn more

easily), hold the ball up in the light, and cause it to revolve round

you by turning upon the stool. As it passes from a position between you

and the lamp to one on the opposite side from the lamp, and so on round

to its original position, you will see its illuminated half go through

all the changes of form exhibited by the moon, and you will need no

further explanation of the lunar phases.

[Illustration:

=Nebula in Sagittarius (M 8)=

Photographed at the Lick Observatory by J. E. Keeler, with the

Crossley reflector. Exposure three hours.

Note the clustering of stars over the whole field, the intricate forms

of the nebula, and particularly the curious black spots, or “holes,”

resembling drops of ink.

]

The Harvest Moon and the Hunter's Moon, which are popularly celebrated

not only on account of their romantic associations, but also because in

some parts of the world they afford a useful prolongation of light after

sunset, occur only near the time of the autumnal equinox, and they are

always full moons. The full moon nearest the date of the equinox,

September 23d, is the Harvest Moon, and the full moon next following is

the Hunter's Moon. Their peculiarity is that they rise, for several

successive evenings, almost at the same hour, immediately after sunset.

This is due to the fact that at that time of the year the ecliptic, from

which the moon's path does not very widely depart, is, in high

latitudes, nearly parallel with the horizon.

The full moon in winter runs higher in the sky, and consequently gives a

brighter light, than in summer. The reason is because, since the full

moon must always be opposite to the sun, and since toe sun in winter

runs low, being south of the equator, the full moon rides proportionally

high.

=5. Eclipses.= We have mentioned the connection of the moon with the

tides, but there is another phenomenon in which the moon plays the most

conspicuous part—that of eclipses. There are two kinds of eclipses—solar

and lunar. In the former it is the moon that causes the eclipse, by

hiding the sun from view; and in the latter it is the moon that suffers

the eclipse, by passing through the shadow which the earth casts into

space on the side away from the sun. In both cases, in order that there

may be an eclipse it is necessary that the three bodies, the moon, the

sun, and the earth, shall be nearly on a straight line, drawn through

their centres. Since the moon occupies about a month in going round the

earth there would be two eclipses in every such period (one of the sun

and the other of the moon), if the moon's orbit lay exactly in the plane

of the ecliptic, or of the earth's orbit. But, in fact, the orbit of the

moon is inclined to that plane at an angle of something over 5°. Even

so, there would be eclipses every month if the two opposite points,

called nodes, where the moon crosses the plane of the ecliptic, always

lay in a direct line with the earth and the sun; but they do not lie

thus. If, then, the moon comes between the earth and the sun when she is

in a part of her orbit several degrees above or below the plane of the

ecliptic, it is evident that she will pass either above or below the

straight line joining the centres of the earth and the sun, and

consequently cannot hide the latter. But, since eclipses do occur in

some months and do not occur in others, we must conclude that the

situation of the nodes changes, and such is the fact. In consequence of

the conflicting attractions of the sun and the earth, the orbit of the

moon, although, like that of the earth, it always retains nearly the

same shape and the same inclination, swings round in space, so that the

nodes, or crossing points on the ecliptic, continually change their

position, revolving round the earth. This motion may be compared to that

of the precession of the equinoxes, but it is much more rapid, a

complete revolution occurring in a period of about nineteen years.

From this it follows that sometimes the moon in passing its nodes will

be in a line with the sun, and sometimes will not. But, owing to the

fact that the sun and moon are not mere points, but on the contrary

present to our view circular disks, each about half a degree in

diameter, an eclipse may occur even if the moon is not in an exact line

with the centres of the sun and the earth. The edge of the moon will

overlap the sun, and there will be a partial eclipse, if the centres of

the two bodies are within one degree apart. Now, the inclination of the

moon's orbit to the ecliptic being only a little over 5°, it is apparent

that in approaching one of its nodes, along so gentle a slope, it will

come within less than a degree of the ecliptic while still quite far

from the node. Thus, eclipses occur for a considerable time before and

after the moon passes a node. The distances on each side of the node,

within which an eclipse of the sun may occur, are called the solar

ecliptic limits, and they amount to 18° in either direction, or 36° in

sum. Within these limits the sun may be wholly or partially eclipsed

according as the moon is nearer to, or farther from, the node. If she is

exactly at, or very close to, the node the eclipse will be total.

Solar eclipses vary in another way. What would be a total eclipse, under

other circumstances, may be only an annular eclipse if the moon happens

to be near her greatest distance from the earth. We have described the

variations in her distance due to the eccentricity of her orbit, and we

have said that the orbit itself swings round the earth in such a way as

to cause the nodes continually to change their places on the ecliptic.

The motion of the orbit also causes the lunar apsides, or the points

where she is at her greatest and least distances from the earth, to

change their places, but their revolution is opposite in direction to

that of the nodes, as the revolution of the apsides of the earth's orbit

is opposite to that of the equinoxes. The moon's apsides sometimes move

eastward and sometimes westward, but upon the whole the eastward motion

prevails and the apsides complete one revolution in that direction once

in about nine and one-half years. In consequence of the combined effects

of the revolution of the nodes and that of the apsides, the moon is

sometimes at her greatest distance from the earth at the moment when she

passes centrally over the sun, and sometimes at her least distance, or

she may be at any intervening distance. If she is in the nearer part of

her orbit, her disk just covers that of the sun, and the eclipse is

total; if she is in the farther part (since the apparent size of bodies

diminishes with increase of distance), her disk does not entirely cover

the sun, and a rim of the latter is visible all around the moon. This is

called an annular eclipse, because of the ring shape of the part of the

sun remaining visible.

The length of the shadow which the moon casts toward the earth during a

solar eclipse also plays an important part in these phenomena. This

length varies with the distance from the sun. Since the moon accompanies

the earth, it follows that when the latter is in aphelion, or at its

greatest distance from the sun, the moon is also at its greatest mean

distance from the sun, and the length of the lunar shadow may, in such

circumstances, be as much as 236,000 miles. When the earth, attended by

the moon, is in perihelion, the length of the moon's shadow may be only

about 228,000 miles. The average length of the shadow is about 232,000

miles. This is nearly 7000 miles less than the average distance of the

moon from the earth, so it is evident that generally the shadow is too

short to reach the earth, and it would never reach it, and there would

never be a total eclipse of the sun, but for the varying distance of the

moon from the earth. When the moon is nearest the earth, or in perigee,

its distance may be as small as 221,600 miles, and in all cases when

near perigee it is near enough for the shadow to reach the earth.

Inasmuch, as the moon's shadow, even under the most favourable

circumstances, is diminished almost to a point before touching the

earth, it hardly need be said that it can cover but a very small area on

the earth's surface. Its greatest possible diameter cannot exceed about

167 miles, but ordinarily it is much smaller. If both the earth and the

moon were motionless, this shadow would be a round or oblong dot on the

earth, its shape varying according as it fell square or sloping to the

surface; but since the moon is continually advancing in its orbit, and

the earth is continually rotating on its axis, the shadow moves across

the earth, in a general west to east direction. But the precise

direction varies with circumstances, as does also the speed. The latter

can never be less than about a thousand miles per hour, and that, only

in the neighbourhood of the equator. The moon advances eastward about

2100 miles per hour, and the earth's surface turns in the same direction

with a velocity diminishing from about a thousand miles an hour at the

equator to 0 at the poles. It is the difference between the velocity of

the earth's rotation and that of the moon's orbital revolution which

determines the speed of the shadow. The greatest time, which the shadow

can occupy in passing a particular point on the earth is only eight

minutes, but ordinarily this is reduced to one, two, or three minutes.

The true shadow only lasts during the time that the moon covers the

whole face of the sun, but before and after this total obscuration of

the solar disk the sun is seen partially covered by the moon, and these

partial phases of the eclipse may be seen from places far aside from the

track which the central shadow pursues. It is only during a total

eclipse, and only from points situated within the shadow track, that the

solar corona is visible.

In a lunar eclipse it is the earth that is the intervening body, and its

shadow falls upon the moon. A solar eclipse can only occur at the time

of new moon, and a lunar eclipse only at the time of full moon. The

shadow of the earth is much longer and broader than that of the moon,

and it never fails to reach the moon, so that it is not necessary here

to consider its varying length. The width, or diameter, of the shadow at

the average distance of the moon from the earth is about 5700 miles. The

moon may pass through the centre of the shadow, or to one side of the

centre, or merely dip into the edge of it. When it goes deep enough into

the shadow to be entirely covered, the eclipse is total; otherwise it is

partial. Since in a total lunar eclipse the entire moon is covered by

the shadow, it is evident that such an eclipse, unlike a solar one, may

be visible simultaneously from all parts of the earth which, at the

time, lie on the side facing the moon. In other words, the earth's

shadow does not make merely a narrow track across the face of the moon,

but completely buries it. When the moon passes centrally through the

shadow, she may remain totally obscured for about two hours. But the

moon does not completely disappear at such times, because the refraction

of the earth's atmosphere bends a little sunlight round its edges and

casts it into the shadow. If the atmosphere round the edges of the earth

happens to be thickly charged with clouds, but little light is thus

refracted into the shadow, and the moon appears very faint, or almost

entirely disappears. But this is rare, and ordinarily the eclipsed moon

shines with a pale copperish light.

The occurrence of a lunar eclipse is governed by similar circumstances

to those affecting solar eclipses. The lunar ecliptic limits, or the

distance on each side of the node within which an eclipse may occur,

vary from 9½° to 12¼° in either direction.

Taking all the various circumstances into account, it is found that

there may be, though rarely, seven eclipses in a year, two being of the

moon and five of the sun, and that the least possible number of eclipses

in a year is two, in which case both will be of the sun. Taking into

account also all the various positions which the sun and moon occupy

with regard to the earth, it is found that there exists a period of 18

years, 11 days, 8 hours, at the return of which eclipses of both kinds

begin to recur again in the same order that they occur in the next

preceding period. This is called the saros, and it was known to the

Chaldeans 2600 years ago.

=6. The Planets.= We have several times mentioned the fact that, beside

the earth, there are seven other principal planets revolving round the

sun, in the same direction as the earth, but at various distances. We

shall consider each of these in the order of its distance from the sun.

But first it is desirable to explain briefly certain so-called “laws”

which govern the motions of all the planets. These are known as Kepler's

laws of planetary motion, and are three in number. The demonstration of

their truth would carry us beyond the scope of this book, and

consequently we shall merely state them as they are recognised by

astronomers.

1st Law: The orbit of every planet is an ellipse, having the sun

situated in one of the foci.

2d Law: The radius vector of a planet describes equal areas in equal

times. By the radius vector is meant the straight line joining the

planet to the sun, and the law declares that as the planet moves round

the sun, the area of space swept over by this line in any given time,

say one day, is equal to the area which it will sweep over in any other

equal length of time. If the orbit were a circle it is evident at a

glance that the law must be true, because then the sun would be situated

in the centre of the circle, the length of the radius vector, no matter

where the planet might be in the orbit, would never vary, and the area

swept over by it in one day would be equal to the area swept over in any

other day, because all these areas would be precisely similar and equal

triangles. But Kepler discovered that the same thing is true when the

orbit is an ellipse, and when, in consequence of the eccentricity of the

orbit, the planet is sometimes farther from the sun than at other times.

As the triangular area swept over in a given time increases in length

with the planet's recession from the sun, it diminishes in breadth just

enough to make up the difference which would otherwise exist between the

different areas. This law grows out of the fact that the force of

gravitation varies inversely with the square of the distance.

3d Law: The squares of the periods (_i. e._ times of revolution in their

orbits) of the different planets are proportional to the cubes of their

mean (average) distances from the sun. The meaning of this will be best

explained by an example. Suppose one planet, whose distance we know, has

a period only one-eighth as long as that of another planet, whose

distance we do not know. Then Kepler's third law enables us to calculate

the distance of the second planet. Call the period of the first planet

1, and that of the second 8, and also call the distance of the first 1,

since all we really need to know is the _relative_ distance of the

second, from which its distance in miles is readily deduced by

comparison with the distance of the first. Then, by the law, 1^2 : 8^2 :

1^3 : x^3 (“x” representing the unknown quantity). Now, this is simply a

problem in proportion where the product of the means is equal to the

product of the extremes. But 1^2 = 1, and also 1^3= 1; therefore x^3 =

8^2, and x = ∛(8^2) (the cube root of the square of 8), which is 4. Thus

we see that the distance of the second planet must be four times that of

the first.

This third law of Kepler is applied to ascertain the distances of newly

discovered planets, whose periods are easily ascertained by simple

observation. If we know the distance of any one planet by measurement,

we can calculate the distances of all the others after observing their

periods. The law also works conversely, _i. e._ from the distances the

periods can be calculated.

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