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 s.p.a.ce 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 r.e.t.a.r.ded light.

Within a very few years this wonderful instrument, the spectroscope, has made amazing discoveries. In chemistry it reveals substances never known before; in a.n.a.lysis 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 const.i.tution of the sun, the movements taking place, the nature of comets, and nebulae. 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 cla.s.sified 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 antennae, 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 Ura.n.u.s 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 ash.o.r.e to fix the exact lat.i.tude 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.

[Ill.u.s.tration: Fig. 19.]

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 pa.s.sed 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 ").

[Ill.u.s.tration: Fig. 20.--Ill.u.s.tration of Angles.]

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] pa.s.s 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 circ.u.mambient 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.

[Ill.u.s.tration: Fig. 21.--Mural Circle.]

Consider the nicety of the work. Suppose the graduated scale to be thirty feet in circ.u.mference. 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 a.s.sist. 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 Ma.s.sachusetts 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 compa.s.s 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 pa.s.s 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.

[Ill.u.s.tration: Fig. 22.]

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 gla.s.s 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.

[Ill.u.s.tration: Fig. 23.--Transit of a Star noted.]

But man is not reliable enough to observe and record with sufficient accuracy. Some, in their excitement, antic.i.p.ate its positive pa.s.sage, 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.

[Ill.u.s.tration: Fig. 24.]

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]