Chapter 5

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.

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 space 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 orbit (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 space 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 orbit, if lying like a blazing ring in space, 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 orbit 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 orbit 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 space, 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 assaulted every year by men zealous of more worlds to conquer. So these greater heights of the heavens have been assaulted, till some ambitious spirits have outsoared even imagination by the certainties of mathematics.

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 illustration. 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 sextant. 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.

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 latitudes, 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 passed 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 shore, 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 ships 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, establishing 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.

[Page 75] V.

THE SUN.

"And God 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.

[Page 76] "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.

[Page 77] V.

_THE SUN._

Suppose we had stood on the dome of Boston Statehouse November 9th, 1872, on the night of the great conflagration, and seen the fire break out; seen the engines dash through the streets, tracking their path by their sparks; seen the fire encompass a whole block, leap the streets on every side, surge like the billows of a storm-swept sea; seen great masses of inflammable gas rise like dark clouds from an explosion, then take fire in the air, and, cut off from the fire below, float like argosies of flame in space. Suppose we had felt the wind that came surging from all points of the compass to fan that conflagration till it was light enough a mile away to see to read the finest print, hot enough to decompose the torrents of water that were dashed on it, making new fuel to feed the flame. Suppose we had seen this spreading fire seize on the whole city, extend to its environs, and, feeding itself on the very soil, lick up Worcester with its tongues of flame--Albany, New York, Chicago, St. Louis, Cincinnati--and crossing the plains swifter than a prairie fire, making each peak of the Rocky Mountains hold up aloft a separate torch of flame, and the Sierras whiter with heat than they ever were with snow, the waters of the Pacific resolve into their constituent elements of oxygen and hydrogen, and [Page 78] burn with unquenchable fire! We withdraw into the air, and see below a world on fire. All the prisoned powers have burst into intensest activity. Quiet breezes have become furious tempests. Look around this flaming globe--on fire above, below, around--there is nothing but fire. Let it roll beneath us till Boston comes round again. No ember has yet cooled, no spire of flame has shortened, no surging cloud has been quieted. Not only are the mountains still in flame, but other ranges burst up out of the seething sea. There is no place of rest, no place not tossing with raging flame! Yet all this is only a feeble figure of the great burning sun. It is but the merest hint, a million times too insignificant.

The sun appears small and quiet to us because we are so far away. Seen from the various planets, the relative size of the sun appears as in Fig. 30. Looked for from some of the stars about us, the sun could not be seen at all. Indeed, seen from the earth, it is not always the same size, because the distance is not always the same. If we represent the size of the sun by one thousand on the 23d of September or 21st of March, it would be represented by nine hundred and sixty-seven on the 1st of July, and by one thousand and thirty-four on the 1st of January.

We sometimes speak of the sun as having a diameter of 860,000 miles. We mean that that is the extent of the body as soon by the eye. But that is a small part of its real diameter. So we say the earth has an equatorial diameter of 7925-1/2 miles, and a polar one of 7899. But the air is as much a part of the earth as the rocks are. The electric currents are as much a part of the [Page 79] earth as the ores and mountains they traverse. What the diameter of the earth is, including these, no man can tell. We used to say the air extended forty-five miles, but we now know that it reaches vastly farther. So of the sun, we might almost say that its diameter is infinite, for its light and heat reach beyond our measurement. Its living, throbbing heart sends out pulsations, keeping all space full of its tides of living light.

[Page 80] [Illustration: Fig. 31.--Zodiacal Light.]

We might say with evident truth that the far-off planets are a part of the sun, since the space they traverse is filled with the power of that controlling king; not only with light, but also with gravitating power.

But come to more ponderable matters. If we look [Page 81] into our western sky soon after sunset, on a clear, moonless night in March or April, we shall see a dim, soft light, somewhat like the milky-way, often reaching, well defined, to the Pleiades. It is wedge-shaped, inclined to the south, and the smallest star can easily be seen through it. Mairan and Cassini affirm that they have seen sudden sparkles and movements of light in it. All our best tests show the spectrum of this light to be continuous, and therefore reflected; which indicates that it is a ring of small masses of meteoric matter surrounding the sun, revolving with it and reflecting its light. One bit of stone as large as the end of one's thumb, in a cubic mile, would be enough to reflect what light we see looking through millions of miles of it. Perhaps an eye sufficiently keen and far away would see the sun surrounded by a luminous disk, as Saturn is with his rings. As it extends beyond the earth's orbit, if this be measured as a part of the sun, its diameter would be about 200,000,000 miles.

Come closer. When the sun is covered by the disk of the moon at the instant of total eclipse, observers are startled by strange swaying luminous banners, ghostly and weird, shooting in changeful play about the central darkness (Fig. 32). These form the corona. Men have usually been too much moved to describe them, and have always been incapable of drawing them in the short minute or two of their continuance. But in 1878 men travelled eight thousand miles, coming and returning, in order that they might note the three minutes of total eclipse in Colorado. Each man had his work assigned to him, and he was drilled to attend to that and nothing else. Improved instruments were put into his [Page 82] hands, so that the sun was made to do his own drawing and give his own picture at consecutive instants. Fig. 33 is a copy of a photograph of the corona of 1878, by Mr. Henry Draper. It showed much less changeability that year than common, it being very near the time of least sun-spot. The previous picture was taken near the time of maximum sun-spot.

It was then settled that the corona consists of reflected light, sent to us from dust particles or meteoroids swirling in the vast seas, giving new densities and [Page 83] rarities, and hence this changeful light. Whether they are there by constant projection, and fall again to the sun, or are held by electric influence, or by force of orbital revolution, we do not know. That the corona cannot be in any sense an atmosphere of any continuous gas, is seen from the fact that the comet of 1843, passing within 93,000 miles of the body of the sun, was not burned out of existence as a comet, nor in any perceptible degree retarded in its motion. If the sun's diameter is to include the corona, it will be from 1,260,000 to 1,460,000 miles.