Chapter II: Part 2

A very strong current of heat may be sent right through the heart of a block of ice without melting the ice at all or cooling off the heat in the least. It is done in this way: Send the beam of heat through water in a glass trough, and this absorbs all the heat that can affect water or ice, getting itself hot, and leaving all other kinds of heat to go through the ice beyond; and appropriate tests show that as much heat comes out on the other side as goes in on this side, and it does not melt the ice at all. Gunpowder may be exploded by heat sent through ice. Dr. Kane, years ago, made this experiment. He was coming down from the north, and fell in with some Esquimaux, whom he was anxious to conciliate. He said to the old wizard of the tribe, "I am a wizard; I can bring the sun down out of the heavens with a piece of ice." That was a good, deal to say in a country where there was so little sun. "So," he writes, "I took my hatchet, chipped a small piece of ice into the form of a double-convex lens, [Page 33] smoothed it with my warm hands, held it up to the sun, and, as the old man was blind, I kindly burned a blister on the back of his hand to show him I could do it."

These are simple illustrations of the various kinds of heat. The best furnace or stove ever invented consumes fifteen times as much fuel to produce a given amount of heat as the furnace in our bodies consumes to produce a similar amount. We lay in our supplies of carbon at the breakfast, dinner, and supper table, and keep ourselves warm by economically burning it with the oxygen we breathe.

Heat associated with light has very different qualities from that which is not. Sunlight melts ice in the middle, bottom, and top at once. Ice in the spring-time is honey-combed throughout. A piece of ice set in the summer sunshine crumbles into separate crystals. Dark heat only melts the surface.

Nearly all the heat of the sun passes through glass without hinderance; but take heat from white-hot platinum and only seventy-six per cent. of it goes through glass, twenty-four per cent. being so constituted that it cannot pass with facility. Of heat from copper at 752° only six per cent. can go through glass, the other ninety-four per cent. being absorbed by it.

The heat of the sun beam goes through glass without [Page 34] any hinderance whatever. It streams into the room as freely as if there were no glass there. But what if the furnace or stove heat went through glass with equal facility? We might as well try to heat our rooms with the window-panes all out, and the blast of winter sweeping through them.

The heat of the sun, by its intense vibrations, comes to the earth dowered with a power which pierces the miles of our atmosphere, but if our air were as pervious to the heat of the earth, this heat would flyaway every night, and our temperature would go down to 200° below zero. This heat comes with the light, and then, dissociated from it, the number of its vibrations lessened, it is robbed of its power to get away, and remains to work its beneficent ends for our good.

Worlds that are so distant as to receive only 1/1000 of the heat we enjoy, may have atmospheres that retain it all. Indeed it is probable that Mars, that receives but one-quarter as much heat as the earth, has a temperature as high as ours. The poet drew on his imagination when he wrote:

"Who there inhabit must have other powers,
Juices, and veins, and sense and life than ours;
One moment's cold like theirs would pierce the bone,
Freeze the heart's-blood, and turn us all to stone."

The power that journeys along the celestial spaces in the flashing sunshine is beyond our comprehension. It accomplishes with ease what man strives in vain to do with all his strength. At West Point there are some links of a chain that was stretched across the river to prevent British ships from ascending; these links were made of two-and-a-quarter-inch iron. A powerful locomotive might tug in vain at one of them and not stretch it the thousandth part of an inch. But the heat of a single gas-burner, that glows with the preserved sunlight of other ages, when suitably applied to the link, stretches it with ease; such enormous power has a little heat. There is a certain iron bridge across the Thames at London, resting on arches. The warm sunshine, acting [Page 35] upon the iron, stations its particles farther and farther apart. Since the bottom cannot give way the arches must rise in the middle. As they become longer they lift the whole bridge, and all the thundering locomotives and miles of goods-trains cannot bring that bridge down again until the power of the sunshine has been withdrawn. There is Bunker Hill Monument, thirty-two feet square at the base, with an elevation of two hundred and twenty feet. The sunshine of every summer's day takes hold of that mighty pile of granite with its aërial fingers, lengthens the side affected, and bends the whole great mass as easily as one would bend a whipstock. A few years ago we hung a plummet from the top of this monument to the bottom. At 9 A.M. it began to move toward the west; at noon it swung round toward the north; in the afternoon it went east of where it first was, and in the night it settled back to its original place.

The sunshine says to the sea, held in the grasp of gravitation, "Rise from your bed! Let millions of tons of water fly on the wings of the viewless air, hundreds of miles to the distant mountains, and pour there those millions of tons that shall refresh a whole continent, and shall gather in rivers fitted to bear the commerce and the navies of nations." Gravitation says, "I will hold every particle of this ocean as near the centre of the earth as I can." Sunshine speaks with its word of power, and says, "Up and away!" And in the wreathing mists of morning these myriads of tons rise in the air, flyaway hundreds of miles, and supply all the Niagaras, Mississippis and Amazons of earth. The sun says to the earth, wrapped in the mantle of winter, [Page 36] "Bloom again;" and the snows melt, the ice retires, and vegetation breaks forth, birds sing, and spring is about us.

Thus it is evident that every force is constitutionally arranged to be overcome by a higher, and all by the highest. Gravitation of earth naturally and legitimately yields to the power of the sun's heat, and then the waters fly into the clouds. It as naturally and legitimately yields to the power of mind, and the waters of the Red Sea are divided and stand "upright as an heap." Water naturally bursts into flame when a bit of potassium is thrown into it, and as naturally when Elijah calls the right kind of fire from above. What seems a miracle, and in contravention of law, is only the constitutional exercise of higher force over forces organized to be swayed. If law were perfectly rigid, there could be but one force; but many grades exist from cohesion to mind and spirit. The highest forces are meant to have victory, and thus give the highest order and perfectness.

Across the astronomic spaces reach all these powers, making creation a perpetual process rather than a single act. It almost seems as if light, in its varied capacities, were the embodiment of God's creative power; as if, having said, "Let there be light," he need do nothing else, but allow it to carry forward the creative processes to the end of time. It was Newton, one of the earliest and most acute investigators in this study of light, who said, "I seem to have wandered on the shore of Truth's great ocean, and to have gathered a few pebbles more beautiful than common; but the vast ocean itself rolls before me undiscovered and unexplored."

[Page 37] EXPERIMENTS WITH LIGHT.

A light set in a room is seen from every place; hence light streams in every possible direction. If put in the centre of a hollow sphere, every point of the surface will be equally illumined. If put in a sphere of twice the diameter, the same light will fall on all the larger surface. The surfaces of spheres are as the squares of their diameters; hence, in the larger sphere the surface is illumined only one-quarter as much as the smaller. The same is true of large and small rooms. In Fig. 7 it is apparent that the light that falls on the first square is spread, at twice the distance, over the second square, which is four times as large, and at three times the distance over nine times the surface. The varying amount of light received by each planet is also shown in fractions above each world, the amount received by the earth being 1.

The intensity of light is easily measured. Let two lights of different brightness, as in Fig. 8, cast shadows on the same screen. Arrange them as to distance so that both shadows shall be equally dark. Let them fall side by side, and study them carefully. Measure the respective distances. Suppose one is twenty inches, the other forty. Light varies as the square [Page 38] of the distance: the square of 20 is 400, of 40 is 1600. Divide 1600 by 400, and the result is that one light is four times as bright as the other.

Light can be handled, directed, and bent, as well as iron bars. Darken a room and admit a beam of sunlight through a shutter, or a ray of lamp-light through the key-hole. If there is dust in the room it will be observed that light goes in straight lines. Because of this men are able to arrange houses and trees in rows, the hunter aims his rifle correctly, and the astronomer projects straight lines to infinity. Take a hand-mirror, or better, a piece of glass coated on one side with black varnish, and you can send your ray anywhere. By using two mirrors, or having an assistant and using several, you can cause a ray of light to turn as many corners as you please. I once saw Mr. Tyndall send a ray into a glass jar filled with smoke (Fig. 9). Admitting a slender ray through a small hole in a card over the mouth, one ray appeared; removing the cover, the whole jar was luminous; as the smoke disappeared in spots cavities of darkness appeared. Turn the same ray into a tumbler of water, [Page 39] it becomes faintly visible; stir into it a teaspoonful of milk, then turn in the ray of sunlight, and it glows like a lamp, illuminating the whole room. These experiments show how the straight rays of the sun are diffused in every direction over the earth.

Set a small light near one edge of a mirror; then, by putting the eye near the opposite edge, you see almost as many flames as you please from the multiplied reflections. How can this be accounted for?

Into your beam of sunlight, admitted through a half-inch hole, put the mirror at an oblique angle; you can arrange it so as to throw half a dozen bright spots on the opposite wall.

In Fig. 10 the sunbeam enters at A, and, striking the mirror _m_ at _a_, is partly reflected to 1 on the wall, and partly enters the glass, passes through to the silvered back at B, and is totally reflected to _b_, where it again divides, some of it going to the wall at 2, and the rest, continuing to make the same reflections and divisions, causes spots 3, 4, 5, etc. The brightest spot is at No.2, because the silvered glass at B is the best reflector and has the most light.

When the discovery of the moons of Mars was announced in 1877, it was also widely published that they could be seen by a mirror. Of course this is impossible. The point of light mistaken for the moon in this secondary reflection was caused by holding the mirror in an oblique position.

Take a small piece of mirror, say an inch in surface, and putting under it three little pellets of wax, putty, or clay, set it on the wrist, with one of the pellets on the pulse. Hold the mirror steadily in the beam of light, and the frequency and prominence of each pulse-beat will be indicated by the tossing spot of light on the wall. If the operator becomes excited the fact will be evident to all observers.

Place a coin in a basin (Fig. 11), and set it so that the rim will conceal the coin from the eye. Pour in water, and the coin will [Page 40] appear to rise into sight. When light passes from a medium of one density to a medium of another, its direction is changed. Thus a stick in water seems bent. Ships below the horizon are sometimes seen above, because of the different density of the layers of air.

Thus light coming from the interstellar spaces, and entering our atmosphere, is bent down more and more by its increasing density. The effect is greatest when the sun or star is near the horizon, none at all in the zenith. This brings the object into view before it is risen. Allowance for this displacement is made in all delicate astronomical observations.

Notice on the floor the shadow of the window-frames. The glass of almost every window is so bent as to turn the sunlight aside enough to obliterate some of the shadows or increase their thickness.

DECOMPOSITION OF LIGHT.

Admit the sunbeam through a slit one inch long and one-twentieth of an inch wide. Pass it through a prism. Either purchase one or make it of three plain pieces of glass one and a half inch wide by six inches long, fastened together in triangular shape--fasten the edges with hot wax and fill it with water; then on a screen or wall you will have the colors of the rainbow, not merely seven but seventy, if your eyes are sharp enough.

Take a bit of red paper that matches the red color of the spectrum. Move it along the line of colors toward the violet. In the orange it is dark, in the yellow darker, in the green and all beyond, black. That is because there are no more red rays to be reflected by it. So a green object is true to its color only in the green rays, and black elsewhere. All these colors may be recombined by a second prism into white light.

[Page 41] III.

ASTRONOMICAL INSTRUMENTS.

"The eyes of the Lord are in every place."--_Proverbs_ xv. 3.

[Page 42] "Man, having one kind of an eye given him by his Maker, proceeds to construct two other kinds. He makes one that magnifies invisible objects thousands of times, so that a dull razor-edge appears as thick as three fingers, until the amazing beauty of color and form in infinitesimal objects is entrancingly apparent, and he knows that God's care of least things is infinite. Then he makes the other kind four or six feet in diameter, and penetrates the immensities of space thousands of times beyond where his natural eye can pierce, until he sees that God's immensities of worlds are infinite also."--BISHOP FOSTER.

[Page 43] III.

_THE TELESCOPE._

Frequent allusion has been made in the previous chapter to discovered results. It is necessary to understand more clearly the process by which such results have been obtained. Some astronomical instruments are of the simplest character, some most delicate and complex. When a man smokes a piece of glass, in order to see an eclipse of the sun, he makes a simple instrument. Ferguson, lying on his back and slipping beads on a string at a certain distance above his eye, measured the relative distances of the stars. The use of more complex instruments commenced when Galileo applied the telescope to the heavens. He cannot be said to have invented the telescope, but he certainly constructed his own without a pattern, and used it to good purpose. It consists of a lens, O B (Fig. 13), which acts as a multiple prism to bend all the rays to one point at R. Place the eye there, and it receives as much light as if it were as large as the lens O B. The rays, however, are convergent, and the point difficult to [Page 44] find. Hence there is placed at R a concave lens, passing through which the rays emerge in parallel lines, and are received by the eye. Opera-glasses are made upon precisely this principle to-day, because they can be made conveniently short.

If, instead of a concave lens at R, converting the converging rays into parallel ones, we place a convex or magnifying lens, the minute image is enlarged as much as an object seems diminished when the telescope is reversed. This is the grand principle of the refracting telescope. Difficulties innumerable arise as we attempt to enlarge the instruments. These have been overcome, one after another, until it is now felt that the best modern telescope, with an object lens of twenty-six inches, has fully reached the limit of optical power.

_The Reflecting Telescope_.

This is the only kind of instrument differing radically from the refracting one already described. It receives the light in a concave mirror, M (Fig. 14), which reflects it to the focus F, producing the same result as the lens of the refracting telescope. Here a mirror may be placed obliquely, reflecting the image at right angles to the eye, outside the tube, in which case it is called the Newtonian telescope; or a mirror at R may be placed perpendicularly, and send the rays through [Page 45] an opening in the mirror at M. This form is called the Gregorian telescope. Or the mirror M may be slightly inclined to the coming rays, so as to bring the point F entirely outside the tube, in which case it is called the Herschelian telescope. In either case the image may be magnified, as in the refracting telescope.

Reflecting telescopes are made of all sizes, up to the Cyclopean eye of the one constructed by Lord Rosse, which is six feet in diameter. The form of instrument to be preferred depends on the use to which it is to be put. The loss of light in passing through glass lenses is about two-tenths. The loss by reflection is often one-half. In view of this peculiarity and many others, it is held that a twenty-six-inch refractor is fully equal to any six-foot reflector.

The mounting of large telescopes demands the highest engineering ability. The whole instrument, with its vast weight of a twenty-six-inch glass lens, with its accompanying tube and appurtenances, must be pointed as nicely as a rifle, and held as steadily as the axis of the globe. To give it the required steadiness, the foundation on which it is placed is sunk deep in the earth, far from rail or other roads, and no part of the observatory is allowed to touch this support. When a star is once found, the earth swiftly rotates the telescope away from it, and it passes out of the field. To avoid this, clock-work is so arranged that the great telescope follows the star by the hour, if required. It will take a star at its eastern rising, and hold it constantly in view while it climbs to the meridian and sinks in the west (Fig. 15). The reflector demands still more difficult engineering. That of Lord Rosse has a metallic mirror [Page 46] weighing six tons, a tube forty feet long, which, with its appurtenances, weighs seven tons more. It moves between two walls only 10° east and west. The new Paris reflector (Fig. 16) has a much wider range of movement.

_The Spectroscope._

A spectrum is a collection of the colors which are dispersed by a prism from any given light. If it is sunlight, it is a solar spectrum; if the source of light is a [Page 49] star, candle, glowing metal, or gas, it is the spectrum of a star, candle, glowing metal, or gas. An instrument to see these spectra is called a spectroscope. Considering the infinite variety of light, and its easy modification and absorption, we should expect an immense number of spectra. A mere prism disperses the light so imperfectly that different orders of vibrations, perceived as colors, are mingled. No eye can tell where one commences or ends. Such a spectrum is said to be impure. What we want is that each point in the spectrum should be made of rays of the same number of vibrations. As we can let only a small beam of light pass through the prism, in studying celestial objects with a telescope and spectroscope we must, in every instance, contract the aperture of the instrument until we get only a small beam of light. In order to have the colors thoroughly dispersed, the best instruments pass the beam of light through a series of prisms called a battery, each one spreading farther the colors which the previous ones had spread. In Fig. 17 the ray is seen entering through the telescope A, which renders the rays parallel, and passing [Page 50] through the prisms out to telescope B, where the spectrum can be examined on the retina of the eye for a screen. In order to still farther disperse the rays, some batteries receive the ray from the last prism at O upon an oblique mirror, send it up a little to another, which delivers it again to the prism to make its journey back again through them all, and come out to be examined just above where it entered the first prism.

Attached to the examining telescope is a diamond-ruled scale of glass, enabling us to fix the position of any line with great exactness.

In Fig. 18 is seen, in the lower part, a spectrum of the sun, with about a score of its thousands of lines made evident. In the upper part is seen the spectrum of bright lines given by glowing hydrogen gas. These lines are given by no other known gas; they are its autograph. It is readily observed that they precisely correspond with certain dark lines in the solar spectrum. Hence we easily know that a glowing gas gives the same bright lines that it absorbs from the light of another source passing through it--that is, glowing gas gives out the same rays of light that it absorbs when it is not glowing.

The subject becomes clearer by a study of the chromolithic plate. No. 1 represents the solar spectrum, with a few of its lines on an accurately graduated scale. [Page 51] No.3 shows the bright line of glowing sodium, and, corresponding to a dark line in the solar spectrum, shows the presence of salt in that body. No. 2 shows that potassium has some violet rays, but not all; and there being no dark line to correspond in the solar spectrum, we infer its absence from the sun. No.6 shows the numerous lines and bands of barium--several red, orange, yellow, and four are very bright green ones. The lines given by any volatilized substances are always in the same place on the scale.

A patient study of these signs of substances reveals, richer results than a study of the cuniform characters engraved on Assyrian slabs; for one is the handwriting of men, the other the handwriting of God.

One of the most difficult and delicate problems solved by the spectroscope is the approach or departure of a light-giving body in the line of sight. Stand before a locomotive a mile away, you cannot tell whether it approaches or recedes, yet it will dash by in a minute. How can the movements of the stars be comprehended when they are at such an immeasurable distance?

It can best be illustrated by music. The note C of the G clef is made by two hundred and fifty-seven vibrations of air per second. Twice as many vibrations per second would give us the note C an octave above. Sound travels at the rate of three hundred and sixty-four yards per second. If the source of these two hundred and fifty-seven vibrations could approach us at three hundred and sixty-four yards per second, it is obvious that twice as many waves would be put into a given space, and we should hear the upper C when only waves enough were made for the lower C. The same [Page 52] result would appear if we carried our ear toward the sound fast enough to take up twice as many valves as though we stood still. This is apparent to every observer in a railway train. The whistle of an approaching locomotive gives one tone; it passes, and we instantly detect another. Let two trains, running at a speed of thirty-six yards a second, approach each other. Let the whistle of one sound the note E, three hundred and twenty-three vibrations per second. It will be heard on the other as the note G, three hundred and eighty-eight vibrations per second; for the speed of each train crowds the vibrations into one-tenth less room, adding 32+ vibrations per second, making three hundred and eighty-eight in all. The trains pass. The vibrations are put into one-tenth more space by the whistle making them, and the other train allows only nine-tenths of what there are to overtake the ear. Each subtracts 32+ vibrations from three hundred and twenty-three, leaving only two hundred and fifty-eight, which is the note C. Yet the note E was constantly uttered.

If a source of light approach or depart, it will have a similar effect on the light waves. How shall we detect it? If a star approach us, it puts a greater number of waves into an inch, and shortens their length. If it recedes, it increases the length of the wave--puts a less number into an inch. If a body giving only the number of vibrations we call green were to approach sufficiently fast, it would crowd in vibrations enough to appear what we call blue, indigo, or even violet, according to its speed. If it receded sufficiently fast, it would leave behind it only vibrations enough to fill up [Page 53] the space with what we call yellow, orange, or red, according to its speed; yet it would be green, and green only, all the time. But how detect the change? If red waves are shortened they become orange in color; and from below the red other rays, too far apart to be seen by the eye, being shortened, become visible as red, and we cannot know that anything has taken place. So, if a star recedes fast enough, violet vibrations being lengthened become indigo; and from above the violet other rays, too short to be seen, become lengthened into visible violet, and we can detect no movement of the colors. The dark lines of the spectrum are the cutting out of rays of definite wave-lengths. If the color spectrum moves away, they move with it, and away from their proper place in the ordinary spectrum. If, then, we find them toward the red end, the star is receding; if toward the violet end, it is approaching. Turn the instrument on the centre of the sun. The dark lines take their appropriate place, and are recognized on the ruled scale. Turn it on one edge, that is approaching us one and a quarter miles a second by the revolution of the sun on its axis, the spectral lines move toward the violet end; turn the spectroscope toward the other edge of the sun, it is receding from us one and a quarter miles a second by reason of the axial revolution, and the spectral lines move toward the red end. Turn it near the spots, and it reveals the mighty up-rush in one place and the down-rush in another of one hundred miles a second. We speak of it as an easy matter, but it is a problem of the greatest delicacy, almost defying the mind of man to read the movements of matter.

It should be recognized that Professor Young, of [Page 54] Princeton, is the most successful operator in this recent realm of science. He already proposes to correct the former estimate of the sun's axial revolutions, derived from observing its spots, by the surer process of observing accelerated and retarded light.

Within a very few years this wonderful instrument, the spectroscope, has made amazing discoveries. In chemistry it reveals substances never known before; in analysis it is delicate to the detection of the millionth of a grain. It is the most deft handmaid of chemistry, the arts, of medical science, and astronomy. It tells the chemical constitution of the sun, the movements taking place, the nature of comets, and nebulæ. By the spectroscope we know that the atmospheres of Venus and Mars are like our own; that those of Jupiter and Saturn are very unlike; it tells us which stars approach and which recede, and just how one star differeth from another in glory and substance.

In the near future we shall have the brilliant and diversely colored flowers of the sky as well classified into orders and species as are the flowers of the earth.

[Page 55] IV.

CELESTIAL MEASUREMENTS.

"Who hath measured the waters in the hollow of his hand, and meted out heaven with the span? Mine hand also hath laid the foundation of the earth, and my right hand hath spanned the heavens."--_Isa._ xl. 12; xlviii. 13.

[Page 56]
"Go to yon tower, where busy science plies
Her vast antennæ, feeling thro' the skies;
That little vernier, on whose slender lines
The midnight taper trembles as it shines,
A silent index, tracks the planets' march
In all their wanderings thro' the ethereal arch,
Tells through the mist where dazzled Mercury burns,
And marks the spot where Uranus returns.

"So, till by wrong or negligence effaced,
The living index which thy Maker traced
Repeats the line each starry virtue draws
Through the wide circuit of creation's laws;
Still tracks unchanged the everlasting ray
Where the dark shadows of temptation stray;
But, once defaced, forgets the orbs of light,
And leaves thee wandering o'er the expanse of night."
OLIVER WENDELL HOLMES.

[Page 57] IV.

_CELESTIAL MEASUREMENTS._

We know that astronomy has what are called practical uses. If a ship had been driven by Euroclydon ten times fourteen days and nights without sun or star appearing, a moment's glance into the heavens from the heaving deck, by a very slightly educated sailor, would tell within one hundred yards where he was, and determine the distance and way to the nearest port. We know that, in all final and exact surveying, positions must be fixed by the stars. Earth's landmarks are uncertain and easily removed; those which we get from the heavens are stable and exact.

In 1878 the United States steam-ship _Enterprise_ was sent to survey the Amazon. Every night a "star party" went ashore to fix the exact latitude and longitude by observations of the stars. Our real landmarks are not the pillars we rear, but the stars millions of miles away. All our standards of time are taken from the stars; every railway train runs by their time to avoid collision; by them all factories start and stop. Indeed, we are ruled by the stars even more than the old astrologers imagined.

Man's finest mechanism, highest thought, and broadest exercise of the creative faculty have been inspired by astronomy. No other instruments approximate in delicacy those which explore the heavens; no other [Page 58] system of thought can draw such vast and certain conclusions from its premises. "Too low they build who build beneath the stars;" we should lay our foundations in the skies, and then build upward.

We have been placed on the outside of this earth, instead of the inside, in order that we may look abroad. We are carried about, through unappreciable distance, at the inconceivable velocity of one thousand miles a minute, to give us different points of vision. The earth, on its softly-spinning axle, never jars enough to unnest a bird or wake a child; hence the foundations of our observatories are firm, and our measurements exact. Whoever studies astronomy, under proper guidance and in the right spirit, grows in thought and feeling, and becomes more appreciative of the Creator.

_Celestial Movements._

Let it not be supposed that a mastery of mathematics and a finished education are necessary to understand the results of astronomical research. It took at first the highest power of mind to make the discoveries that are now laid at the feet of the lowliest. It took sublime faith, courage, and the results of ages of experience in navigation, to enable Columbus to discover that path to the New World which now any little boat can follow. Ages of experience and genius are stored up in a locomotive, but quite an unlettered man can drive it. It is the work of genius to render difficult matters plain, abstruse thoughts clear.

A brief explanation of a few terms will make the principles of world inspection easily understood. Imagine a perfect circle thirty feet in diameter--that is, create [Page 59] one (Fig. 19). Draw through it a diameter horizontally, another perpendicularly. The angles made by the intersecting lines are each said to be ninety degrees, marked thus °. The arc of a circle included between any two of the lines is also 90°. Every circle, great or small, is divided into these 360°. If the sun rose in the east and came to the zenith at noon, it would have passed 90°. When it set in the west it would have traversed half the circle, or 180°. In Fig. 20 the angle of the lines measured on the graduated arc is 10°. The mountain is 10° high, the world 10° in diameter, the comet moves 10° a day, the stars are 10° apart. The height of the mountain, the diameter of the world, the velocity of the comet, and the distance between the stars, depend on the distance of each from the point of sight. Every degree is divided into 60 minutes (marked '), and every minute into 60 seconds (marked ").

Imagine yourself inside a perfect sphere one hundred feet in diameter, with the interior surface above, around, and below studded with fixed bright points like stars. The familiar constellations of night might be blazoned there in due proportion.

If this star-sprent sphere were made to revolve once in twenty-four hours, all the stars would successively [Page 60] pass in review. How easily we could measure distances between stars, from a certain fixed meridian, or the equator! How easily we could tell when any particular star would culminate! It is as easy to take all these measurements when our earthly observatory is steadily revolved within the sphere of circumambient stars. Stars can be mapped as readily as the streets of a great city. Looking down on it in the night, one could trace the lines of lighted streets, and judge something of its extent and regularity. But the few lamps of evening would suggest little of the greatness of the public buildings, the magnificent enterprise and commerce of its citizens, or the intelligence of its scholars. Looking up to the lamps of the celestial city, one can judge something of its extent and regularity; but they suggest little of the magnificence of the many mansions.

Stars are reckoned as so many degrees, minutes, and seconds from each other, from the zenith, or from a given meridian, or from the equator. Thus the stars called the Pointers, in the Great Bear, are 5° apart; the nearest one is 29° from the Pole Star, which is 39° 56' 29" above the horizon at Philadelphia. In going to England you creep up toward the north end of the earth, till the Pole Star is 54° high. It stays near its place among the stars continually,

"Of whose true-fixed and resting quality
There is no fellow in the firmament."

_How to Measure._

Suppose a telescope, fixed to a mural circle, to revolve on an axis, as in Fig. 21; point it horizontally at a star; [Page 61] turn it up perpendicular to another star. Of course the two stars are 90° apart, and the graduated scale, which is attached to the outer edge of the circle, shows a revolution of a quarter circle, or 90°, But a perfect accuracy of measurement must be sought; for to mistake the breadth of a hair, seen at the distance of one hundred and twenty-five feet, would cause an error of 3,000,000 miles at the distance of the sun, and immensely more at the distance of the stars. The correction of an inaccuracy of no greater magnitude than that has reduced our estimate of the distance of our sun 3,000,000 miles.

Consider the nicety of the work. Suppose the graduated scale to be thirty feet in circumference. Divided into 360°, each would be one inch long. Divide each degree into 60', each one is 1/60 of an inch long. It takes good eyesight to discern it. But each minute must be [Page 62] divided into 60", and these must not only be noted, but even tenths and hundredths of seconds must be discerned. Of course they are not seen by the naked eye; some mechanical contrivance must be called in to assist. A watch loses two minutes a week, and hence is unreliable. It is taken to a watch-maker that every single second may be quickened 1/20160 part of itself. Now 1/20000 part of a second would be a small interval of time to measure, but it must be under control. If the temperature of a summer morning rises ten or twenty degrees we scarcely notice it; but the magnetic tastimeter measures 1/5000 of a degree.

Come to earthly matters. In 1874, after nearly twenty-eight years' work, the State of Massachusetts opened a tunnel nearly five miles long through the Hoosac Mountains. In the early part of the work the engineers sunk a shaft near the middle 1028 feet deep. Then the question to be settled was where to go so as to meet the approaching excavations from the east and west. A compass could not be relied on under a mountain. The line must be mechanically fixed. A little divergence at the starting-point would become so great, miles away, that the excavations might pass each other without meeting; the grade must also rise toward the central shaft, and fall in working away from it; but the lines were fixed with such infinitesimal accuracy that, when the one going west from the eastern portal and the one going east from the shaft met in the heart of the mountain, the western line was only one-eighth of an inch too high, and three-sixteenths of an inch too far north. To reach this perfect result they had to triangulate from the eastern portal to distant [Page 63] mountain peaks, and thence down the valley to the central shaft, and thus fix the direction of the proposed line across the mouth of the shaft. Plumb-lines were then dropped one thousand and twenty-eight feet, and thus the line at the bottom was fixed.

Three attempts were made--in 1867, 1870, and 1872--to fix the exact time-distance between Greenwich and Washington. These three separate efforts do not differ one-tenth of a second. Such demonstrable results on earth greatly increase our confidence in similar measurements in the skies.

A scale is frequently affixed to a pocket-rule, by which we can easily measure one-hundredth of an inch (Fig. 22). The upper and lower line is divided into tenths of an inch. Observe the slanting line at the right hand. It leans from the perpendicular one-tenth of an inch, as shown by noticing where it reaches the top line. When it reaches the second horizontal line it has left the perpendicular one-tenth of that tenth--that is, one-hundredth. The intersection marks 99/100 of an inch from one end, and one-hundredth from the other.

When division-lines, on measures of great nicety, get too fine to be read by the eye, we use the microscope. By its means we are able to count 112,000 lines ruled on a glass plate within an inch. The smallest object that can be seen by a keen eye makes an angle of 40", but by putting six microscopes on the scale of the telescope on the mural circle, we are able to reach an exactness of 0".1, or 1/3600 of an inch. This instrument is used to measure the declination of stars, or angular [Page 64] distance north or south of the equator. Thus a star's place in two directions is exactly fixed. When the telescope is mounted on two pillars instead of the face of a wall, it is called a transit instrument. This is used to determine the time of transit of a star over the meridian, and if the transit instrument is provided with a graduated circle it can also be used for the same purposes as the mural circle. Man's capacity to measure exactly is indicated in his ascertainment of the length of waves of light. It is easy to measure the three hundred feet distance between the crests of storm-waves in the wide Atlantic; easy to measure the different wave-lengths of the different tones of musical sounds. So men measure the lengths of the undulations of light. The shortest is of the violet light, 154.84 ten-millionths of an inch. By the horizontal pendulum Professor Root has made 1/36000000 of an inch apparent.

The next elements of accuracy must be perfect time and perfect notation of time. As has been said, we get our time from the stars. Thus the infinite and heavenly dominates the finite and earthly. Clocks are set to the invariable sidereal time. Sidereal noon is when we have turned ourselves under the point where the sun crosses the equator in March, called the vernal equinox. Sidereal clocks are figured to indicate twenty-four hours in a day: they tick exact seconds. To map stars we wish to know the exact second when they cross the meridian, or the north and south line in the celestial dome above us. The telescope (Fig. 21, p. 61) swings exactly north and south. In its focus a set of fine threads of spider-lines is placed (Fig. 23). The telescope is set just high enough, so that by the rolling over of the earth [Page 65] the star will come into the field just above the horizontal thread. The observer notes the exact second and tenth of a second when the star reaches each vertical thread in the instrument, adds together the times and divides by five to get the average, and the exact time is reached.

But man is not reliable enough to observe and record with sufficient accuracy. Some, in their excitement, anticipate its positive passage, and some cannot get their slow mental machinery in motion till after it has made the transit. Moreover, men fall into a habit of estimating some numbers of tenths of a second oftener than others. It will be found that a given observer will say three tenths or seven tenths oftener than four or eight. He is falling into ruts, and not trustworthy. General O. M. Mitchel, who had been director of the Cincinnati Observatory, once told one of his staff-officers that he was late at an appointment. "Only a few minutes," said the officer, apologetically. "Sir," said the general, "where I have been accustomed to work, hundredths of a second are too important to be neglected." And it is to the rare genius of this astronomer, and to others, that we owe the mechanical accuracy that we now attain. The clock is made to mark its seconds on paper wrapped around a revolving cylinder. Under the observer's fingers is an electric key. This he can touch at the instant of the transit of the star [Page 66] over each wire, and thus put his observation on the same line between the seconds dotted by the clock. Of course these distances can be measured to minute fractional parts of a second.

But it has been found that it takes an appreciable time for every observer to get a thing into his head and out of his finger-ends, and it takes some observers longer than others. A dozen men, seeing an electric spark, are liable to bring down their recording marks in a dozen different places on the revolving paper. Hence the time that it takes for each man to get a thing into his head and out of his fingers is ascertained. This time is called his personal equation, and is subtracted from all of his observations in order to get at the true time; so willing are men to be exact about material matters. Can it be thought that moral and spiritual matters have no precision? Thus distances east or west from any given star or meridian are secured; those north and south from the equator or the zenith are as easily fixed, and thus we make such accurate maps of the heavens that any movements in the far-off stars--so far that it may take centuries to render the swiftest movements appreciable--may at length be recognized and accounted for.

We now come to a little study of the modes of measuring distances. Create a perfect square (Fig. 24); draw a diagonal line. The square angles are 90°, the divided angles give two of 45° each. Now the base A B is equal to the perpendicular A C. Now any point--C, where a perpendicular, A C, and a diagonal, B C, meet--will be [Page 67] as far from A as B is. It makes no difference if a river flows between A and C, and we cannot go over it; we can measure its distance as easily as if we could. Set a table four feet by eight out-doors (Fig. 25); so arrange it that, looking along one end, the line of sight just strikes a tree the other side of the river. Go to the other end, and, looking toward the tree, you find the line of sight to the tree falls an inch from the end of the table on the farther side. The lines, therefore, approach each other one inch in every four feet, and will come together at a tree three hundred and eighty-four feet away.

The next process is to measure the height or magnitude of objects at an ascertained distance. Put two pins in a stick half an inch apart (Fig. 26). Hold it up two feet from the eye, and let the upper pin fall in line with your eye and the top of a distant church steeple, and the lower pin in line with the bottom of the church and your eye. If the church is three-fourths of a mile away, it must be eighty-two feet high; if a mile away, it must be one hundred and ten feet high. For if two lines spread [Page 68] one-half an inch going two feet, in going four feet they will spread an inch, and in going a mile, or five thousand two hundred and eighty feet, they will spread out one-fourth as many inches, viz., thirteen hundred and twenty--that is, one hundred and ten feet. Of course these are not exact methods of measurement, and would not be correct to a hair at one hundred and twenty-five feet, but they perfectly illustrate the true methods of measurement.

Imagine a base line ten inches long. At each end erect a perpendicular line. If they are carried to infinity they will never meet: will be forever ten inches apart. But at the distance of a foot from the base line incline one line toward the other 63/10000000 of an inch, and the lines will come together at a distance of three hundred miles. That new angle differs from the former right angle almost infinitesimally, but it may be measured. Its value is about three-tenths of a second. If we lengthen the base line from ten inches to all the miles we can command, of course the point of meeting will be proportionally more distant. The angle made by the lines where they come together will be obviously the same as the angle of divergence from a right angle at this end. That angle is called the parallax of any body, and is the angle that would be made by two lines coming from that body to the two ends of any conventional base, as the semi-diameter of the earth. That that angle would vary according to the various distances is easily seen by Fig. 27.

Let O P be the base. This would subtend a greater angle seen from star A than from star B. Let B be far enough away, and O P would become invisible, and B [Page 69] would have no parallax for that base. Thus the moon has a parallax of 57" with the semi-equatorial diameter of the earth for a base. And the sun has a parallax 8".85 on the same base. It is not necessary to confine ourselves to right angles in these measurements, for the same principles hold true in any angles. Now, suppose two observers on the equator should look at the moon at the same instant. One is on the top of Cotopaxi, on the west coast of South America, and one on the west coast of Africa. They are 90° apart--half the earth's diameter between them. The one on Cotopaxi sees it exactly overhead, at an angle of 90° with the earth's diameter. The one on the coast of Africa sees its angle with the same line to be 89° 59' 3"--that is, its parallax is 57". Try the same experiment on the sun farther away, as is seen in Fig. 27, and its smaller parallax is found to be only 8".85.