Part 5 (1/2)
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.
[Ill.u.s.tration: Fig. 25.--Measuring Distances.]
[Ill.u.s.tration: Fig. 26.--Measuring Elevations.]
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 ill.u.s.trate 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.
[Ill.u.s.tration: 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.
It is not necessary for two observers to actually station themselves at two distant parts of the earth in order to determine a parallax.
If an observer could go from one end of the base-line to the other, he could determine both angles. Every observer is actually carried along through s.p.a.ce by two motions: one is that of the earth's revolution of one thousand miles an hour around the axis; and the other is the movement of the earth around the sun of one thousand miles in a minute. Hence we can have the diameter not only of [Page 70] the earth (eight thousand miles) for a base-line, but the diameter of the earth's...o...b..t (184,000,000 miles), or any part of it, for such a base. Two observers at the ends of the earth's diameter, looking at a star at the same instant, would find that it made the same angle at both ends; it has no parallax on so short a base. We must seek a longer one. Observe a certain star on the 21st of March; then let us traverse the realms of s.p.a.ce for six months, at one thousand miles a minute. We come round in our orbit to a point opposite where we were six months ago, with 184,000,000 of miles between the points. Now, with this for a base-line, measure the angles of the same stars: it is the same angle. Sitting in my study here, I glance out of the window and discern separate bricks, in houses five hundred feet away, with my unaided eye; they subtend a discernible angle. But one thousand feet away I cannot distinguish individual bricks; their width, being only two inches, does not subtend an angle apprehensible to my vision. So at these distant stars the earth's enormous...o...b..t, if lying like a blazing ring in s.p.a.ce, with the world set on its edge like a pearl, and the sun blazing like a diamond in the centre, would all shrink to a mere point. Not quite to a point from the nearest stars, or we should never be able to measure the distance of any of them. Professor Airy says that our orbit, seen from the nearest star, would be the same as a circle six-tenths of an inch in diameter seen at the distance of a mile: it would all be hidden by a thread one-twenty-fifth of an inch in diameter, held six hundred and fifty feet from the eye. If a straight line could be drawn from a star, Sirius in the east to the star Vega in the west, touching our [Page 71] earth's...o...b..t on one side, as T R A (Fig. 28), and a line were to be drawn six months later from the same stars, touching our earth's...o...b..t on the other side, as R B T, such a line would not diverge sufficiently from a straight line for us to detect its divergence. Numerous vain attempts had been made, up to the year 1835, to detect and measure the angle of parallax by which we could rescue some one or more of the stars from the inconceivable depths of s.p.a.ce, and ascertain their distance from us. We are ever impelled to triumph over what is declared to be unconquerable. There are peaks in the Alps no man has ever climbed. They are a.s.saulted every year by men zealous of more worlds to conquer. So these greater heights of the heavens have been a.s.saulted, till some ambitious spirits have outsoared even imagination by the certainties of mathematics.
[Ill.u.s.tration: Fig. 28.]
It is obvious that if one star were three times as far from us as another, the nearer one would seem to be displaced by our movement in our orbit three times as much as the other; so, by comparing one star with another, we reach a ground of judgment. The ascertainment of longitude at sea by means of the moon affords a good ill.u.s.tration.
Along the track where the moon sails, nine bright stars, four planets, and the sun have been selected. The nautical almanacs give the distance of the moon from these successive stars every hour in the night for three years in advance. The sailor can measure the distance at any time by his s.e.xtant. Looking from the world at D (Fig. 29), the distance of the moon and [Page 72] star is A E, which is given in the almanac. Looking from C, the distance is only B E, which enables even the uneducated sailor to find the distance, C D, on the earth, or his distance from Greenwich.
[Ill.u.s.tration: Fig. 29.--Mode of Ascertaining Longitude.]
So, by comparisons of the near and far stars, the approximate distance of a few of them has been determined. The nearest one is the brightest star in the Centaur, never visible in our northern lat.i.tudes, which has a parallax of about one second. The next nearest is No. 61 in the Swan, or 61 Cygni, having a parallax of 0”.34. Approximate measurements have been made on Sirius, Capella, the Pole Star, etc., about eighteen in all. The distances are immense: only the swiftest agents can traverse them. If our earth were suddenly to dissolve its allegiance to the king of day, and attempt a flight to the North Star, and should maintain its flight of one thousand miles a minute, it would flyaway toward Polaris for thousands upon thousands of years, till a million years had pa.s.sed away, before it reached that northern dome of the distant sky, and gave its new allegiance to another sun. The sun it had left behind it would gradually diminish till it was small as Arcturus, then small as could be discerned by the naked eye, until at last it would finally fade out in utter darkness long before the new sun was reached.
Light can traverse the distance around our earth eight times in one second. It comes in eight minutes from the sun, but it takes three and a quarter years to come from Alpha [Page 73] Centauri, seven and a quarter years from 61 Cygni, and forty-five years from the Polar Star.
Sometimes it happens that men steer along a lee sh.o.r.e, dependent for direction on Polaris, that light-house in the sky. Sometimes it has happened that men have traversed great swamps by night when that star was the light-housse of freedom. In either case the exigency of life and liberty was provided for forty-five years before by a Providence that is divine.
We do not attempt to name in miles these enormous distances; we must seek another yard-stick. Our astronomical unit and standard of measurement is the distance of the earth from the sun--92,500,000 miles. This is the golden reed with which we measure the celestial city. Thus, by laying down our astronomical unit 226,000 times, we measure to Alpha Centauri, more than twenty millions of millions of miles. Doubtless other suns are as far from Alpha Centauri and each other as that is from ours.
Stars are not near or far according to their brightness. 61 Cygni is a telescopic star, while Sirius, the brightest star in the heavens, is twice as far away from us. One star differs from another star in intrinsic glory.
The highest testimonies to the accuracy of these celestial observations are found in the perfect predictions of eclipses, transits of planets over the sun, occultation of stars by the moon, and those statements of the Nautical Almanac that enable the sailor to know exactly where he is on the pathless ocean by the telling of the stars: ”On the trackless ocean this book is the mariner's trusted friend and counsellor; daily and nightly its revelations bring safety to s.h.i.+ps in all parts of the [Page 74] world. It is something more than a mere book; it is an ever-present manifestation of the order and harmony of the universe.”
Another example of this wonderful accuracy is found in tracing the asteroids. Within 200,000,000 or 300,000,000 miles from the sun, the one hundred and ninety-two minute bodies that have been already discovered move in paths very nearly the same--indeed two of them traverse the same orbit, being one hundred and eighty degrees apart;--they look alike, yet the eye of man in a few observations so determines the curve of each orbit, that one is never mistaken for another. But astronomy has higher uses than fixing time, establis.h.i.+ng landmarks, and guiding the sailor. It greatly quickens and enlarges thought, excites a desire to know, leads to the utmost exactness, and ministers to adoration and love of the Maker of the innumerable suns.
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V.
THE SUN.
”And G.o.d made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.”--_Gen._ i. 16.
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”It is perceived that the sun of the world, with all its essence, which is heat and light, flows into every tree, and into every shrub and flower, and into every stone, mean as well as precious; and that every object takes its portion from this common influx, and that the sun does not divide its light and heat, and dispense a part to this and a part to that. It is similar with the sun of heaven, from which the Divine love proceeds as heat, and the Divine wisdom as light; these two flow into human minds, as the heat and light of the sun of the world into bodies, and vivify them according to the quality of the minds, each of which takes from the common influx as much as is necessary.”--SWEDENBORG.
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V.