[Footnote 725: Young, _The Sun_, p. 310.]

[Footnote 726: _Op._, t. vi., p. 198.]

[Footnote 727: _Rosa Ursina_, lib. iv., p. 618.]

[Footnote 728: _Mec. Cel._, liv. x., p. 323.]

[Footnote 729: _Le Soleil_ (1st ed.), p. 136.]

[Footnote 730: _Monatsber._, Berlin, 1877, p. 104.]

[Footnote 731: _Astr. Nach._, Nos. 3,105-6; _Astr. and Astrophysics_, vol. xi., p. 720.]

[Footnote 732: _Proc. Roy. Irish Acad._, vol. ii., No. 2, 1892.]

[Footnote 733: _Am. Jour. of Sc._, vol. xxi., p. 187.]

[Footnote 734: _Amer. Jour. of Science_, vol. v., p. 245, 1898.]

[Footnote 735: For J. W. Draper's partial antic.i.p.ation of this result, see _Ibid_. vol. iv., 1872, p. 174.]

[Footnote 736: _Phil. Mag._, vol. xiv., p. 179, 1883.]

[Footnote 737: "The Solar and the Lunar Spectrum," _Memoirs National Acad. of Science_, vol. x.x.xii.; "On hitherto Unrecognised Wave-lengths,"

_Amer. Jour. of Science_, vol. x.x.xii., August, 1886.]

[Footnote 738: _Astroph. Jour._, vol. i., p. 162.]

[Footnote 739: _Annals of the Smithsonian Astroph. Observatory_, vol.

i.; _Comptes Rendus_, t. cx.x.xi., p. 734; _Astroph. Jour._, vol. iii., p.

63.]

[Footnote 740: _Phil. Mag._, July, 1901.]

[Footnote 741: _Comptes Rendus_, t. xcii., p. 701.]

[Footnote 742: _Nature_, vol. xxvi., p. 589.]

[Footnote 743: _Phil. Trans._, vol. cx.x.xii., p. 273.]

[Footnote 744: _Ann. de Chim._, t. x., p. 321.]

[Footnote 745: _Ibid._, t. xi., p. 505.]

[Footnote 746: _Comptes Rendus_, t. cxii., p. 1200.]

[Footnote 747: _Wied. Ann._, Bd. x.x.xix., p. 294; Scheiner, _Temperatur der Sonne_, pp. 36, 38.]

CHAPTER VI

_THE SUN'S DISTANCE_

The question of the sun's distance arises naturally from the consideration of his temperature, since the intensity of the radiations emitted as compared with those received and measured, depends upon it.

But the knowledge of that distance has a value quite apart from its connection with solar physics. The semi-diameter of the earth's...o...b..t is our standard measure for the universe. It is the great fundamental datum of astronomy--the unit of s.p.a.ce, any error in the estimation of which is multiplied and repeated in a thousand different ways, both in the planetary and sidereal systems. Hence its determination was called by Airy "the n.o.blest problem in astronomy." It is also one of the most difficult. The quant.i.ties dealt with are so minute that their sure grasp tasks all the resources of modern science. An observational inaccuracy which would set the moon nearer to, or farther from us than she really is by one hundred miles, would vitiate an estimate of the sun's distance to the extent of sixteen million![748] What is needed in order to attain knowledge of the desired exactness is no less than this: to measure an angle about equal to that subtended by a halfpenny 2,000 feet from the eye, within a little more than a thousandth part of its value.

The angle thus represented is what is called the "horizontal parallax"

of the sun. By this amount--the breadth of a halfpenny at 2,000 feet--he is, to a spectator on the rotating earth, removed at rising and setting from his meridian place in the heavens. Such, in other terms, would be the magnitude of the terrestrial radius as viewed from the sun. If we knew this magnitude with certainty and precision, we should also know with certainty and precision--the dimensions of the earth being, as they are, well ascertained--the distance of the sun. In fact, the one quant.i.ty commonly stands for the other in works treating professedly of astronomy. But this angle of parallax or apparent displacement cannot be directly measured--cannot even be perceived with the finest instruments.

Not from its smallness. The parallactic shift of the nearest of the stars as seen from opposite sides of the earth's...o...b..t, is many times smaller. But at the sun's limb, and close to the horizon, where the visual angle in question opens out to its full extent, atmospheric troubles become overwhelming, and altogether swamp the far more minute effects of parallax.

There remain indirect methods. Astronomers are well acquainted with the proportions which the various planetary orbits bear to each other. They are so connected, in the manner expressed by Kepler's Third Law, that the periods being known, it only needs to find the interval between any two of them in order to infer at once the distances separating them all from one another and from the sun. The plan is given; what we want to discover is the scale upon which it is drawn; so that, if we can get a reliable measure of the distance of a single planet from the earth, our problem is solved.

Now some of our fellow-travellers in our unending journey round the sun, come at times well within the scope of celestial trigonometry. The orbit of Mars lies at one point not more than thirty-five million miles outside that of the earth, and when the two bodies happen to arrive together in or near the favourable spot--a conjuncture which occurs every fifteen years--the desired opportunity is granted. Mars is then "in opposition," or on the _opposite_ side of us from the sun, crossing the meridian consequently at midnight.[749] It was from an opposition of Mars, observed in 1672 by Richer at Cayenne in concert with Ca.s.sini in Paris, that the first scientific estimate of the sun's distance was derived. It appeared to be nearly eighty-seven millions of miles (parallax 95"); while Flamsteed deduced 81,700,000 (parallax 10") from his independent observations of the same occurrence--a difference quite insignificant at that stage of the inquiry. But Picard's result was just half Flamsteed's (parallax 20"; distance forty-one million miles); and Lahire considered that we must be separated from the hearth of our system by an interval of _at least_ 136 million miles.[750] So that uncertainty continued to have an enormous range.

Venus, on the other hand, comes closest to the earth when she pa.s.ses between it and the sun. At such times of "inferior conjunction" she is, however, still twenty-six million miles, or (in round numbers) 109 times as distant as the moon. Moreover, she is so immersed in the sun's rays that it is only when her path lies across his disc that the requisite facilities for measurement are afforded. These "partial eclipses of the sun by Venus" (as Encke termed them) are coupled together in pairs,[751]

of which the components are separated by eight years, recurring at intervals alternately of 105-1/2 and 121-1/2 years. Thus, the first calculated transit took place in December, 1631, and its companion (observed by Horrocks) in the same month (N.S.), 1639. Then, after the lapse of 121-1/2 years, came the June couple of 1761 and 1769; and again after 105-1/2, the two last observed, December 8, 1874, and December 6, 1882. Throughout the twentieth century there will be no transit of Venus; but the astronomers of the twenty-first will only have to wait four years for the first of a June pair. The rarity of these events is due to the fact that the orbits of the earth and Venus do not lie in the same plane. If they did, there would be a transit each time that our twin-planet overtakes us in her more rapid circling--that is, on an average, every 584 days. As things are actually arranged, she pa.s.ses above or below the sun, except when she happens to be very near the line of intersection of the two tracks.

Such an occurrence as a transit of Venus seems, at first sight, full of promise for solving the problem of the sun's distance. For nothing would appear easier than to determine exactly either the duration of the pa.s.sage of a small, dark orb across a large brilliant disc, or the instant of its entry upon or exit from it. And the differences in these times (which, owing to the comparative nearness of Venus, are quite considerable), as observed from remote parts of the earth, can be translated into differences of s.p.a.ce--that is, into apparent or parallactic displacements, whereby the distance of Venus becomes known, and thence, by a simple sum in proportion, the distance of the sun. But in that word "exactly" what snares and pitfalls lie hid! It is so easy to think and to say; so indefinitely hard to realise. The astronomers of the eighteenth century were full of hope and zeal. They confidently expected to attain, through the double opportunity offered them, to something like a permanent settlement of the statistics of our system.

They were grievously disappointed. The uncertainty as to the sun's distance, which they had counted upon reducing to a few hundred thousand miles, remained at many millions.

In 1822, however, Encke, then director of the Seeberg Observatory near Gotha, undertook to bring order out of the confusion of discordant, and discordantly interpreted observations. His combined result for both transits (1761 and 1769) was published in 1824,[752] and met universal acquiescence. The parallax of the sun thereby established was 85776", corresponding to a mean distance[753] of 95-1/4 million miles. Yet this abolition of doubt was far from being so satisfactory as it seemed.

Serenity on the point lasted exactly thirty years. It was disturbed in 1854 by Hansen's announcement[754] that the observed motions of the moon could be drawn into accord with theory only on the terms of bringing the sun considerably nearer to us than he was supposed to be.

Dr. Matthew Stewart, professor of mathematics in the University of Edinburgh, had made a futile attempt in 1763 to deduce the sun's distance from his disturbing power over our satellite.[755] Tobias Mayer of Gottingen, however, whose short career was fruitful of suggestions, struck out the right way to the same end; and Laplace, in the seventh book of the _Mecanique Celeste_,[756] gave a solar parallax derived from the lunar "parallactic inequality" substantially identical with that issuing from Encke's subsequent discussion of the eighteenth-century transits. Thus, two wholly independent methods--the trigonometrical, or method by survey, and the gravitational, or method by perturbation--seemed to corroborate each the upshot of the use of the other until the nineteenth century was well past its meridian. It is singular how often errors conspire to lead conviction astray.

Hansen's note of alarm in 1854 was echoed by Leverrier in 1858.[757] He found that an apparent monthly oscillation of the sun which reflects a real monthly movement of the earth round its common centre of gravity with the moon, and which depends for its amount solely on the ma.s.s of the moon and the distance of the sun, required a diminution in the admitted value of that distance by fully four million miles. Three years later he pointed out that certain perplexing discrepancies between the observed and computed places both of Venus and Mars, would vanish on the adoption of a similar measure.[758] Moreover, a favourable opposition of Mars gave the opportunity in 1862 for fresh observations, which, separately worked out by Stone and Winnecke, agreed with all the newer investigations in fixing the great unit at slightly over 91 million miles. In Newcomb's hands they gave 92-1/2 million.[759] The acc.u.mulating evidence in favour of a large reduction in the sun's distance was just then reinforced by an auxiliary result of a totally different and unexpected kind.

The discovery that light does not travel instantaneously from point to point, but takes some short time in transmission, was made by Olaus Romer in 1675, through observing that the eclipses of Jupiter's satellites invariably occurred later, when the earth was on the far side, than when it was on the near side of its...o...b..t. Half the difference, or the time spent by a luminous vibration in crossing the "mean radius" of the earth's...o...b..t, is called the "light-equation"; and the determination of its precise value has claimed the minute care distinctive of modern astronomy. Delambre in 1792 made it 493 seconds.

Glasenapp, a Russian astronomer, raised the estimate in 1874 to 501, Professor Harkness adopts a safe medium value of 498 seconds. Hence, if we had any independent means of ascertaining how fast light travels, we could tell at once how far off the sun is.

There is yet another way by which knowledge of the swiftness of light would lead us straight to the goal. The heavenly bodies are perceived, when carefully watched and measured, to be pushed forward out of their true places, in the direction of the earth's motion, by a very minute quant.i.ty. This effect (already adverted to) has been known since Bradley's time as "aberration." It arises from a combination of the two movements of the earth round the sun and of the light-waves through the ether. If the earth stood still, or if light spent no time on the road from the stars, such an effect would not exist. Its amount represents the proportion between the velocities with which the earth and the light-rays pursue their respective journeys. This proportion is, roughly, one to ten thousand. So that here again, if we knew the rate per second of luminous transmission, we should also know the rate per second of the earth's movement, consequently the size of its...o...b..t and the distance of the sun.

But, until lately, instead of finding the distance of the sun from the velocity of light, there has been no means of ascertaining the velocity of light except through the imperfect knowledge possessed as to the distance of the sun. The first successful terrestrial experiments on the point date from 1849; and it is certainly no slight triumph of human ingenuity to have taken rigorous account of the delay of a sunbeam in flashing from one mirror to another. Fizeau led the way,[760] and he was succeeded, after a few months, by Leon Foucault,[761] who, in 1862, had so far perfected Wheatstone's method of revolving mirrors, as to be able to announce with authority that light travelled slower, and that the sun was in consequence nearer than had been supposed.[762] Thus a third line of separate research was found to converge to the same point with the two others.

Such a conspiracy of proof was not to be resisted, and at the anniversary meeting of the Royal Astronomical Society in February, 1864, the correction of the solar distance took the foremost place in the annals of the year. Lest, however, a sudden bound of four million miles nearer to the centre of our system should shake public faith in astronomical accuracy, it was explained that the change in the solar parallax corresponding to that huge leap, amounted to no more than the breadth of a human hair 125 feet from the eye![763] The Nautical Almanac gave from 1870 the altered value of 8.95", for which Newcomb's result of 8.85", adopted in 1869 in the Berlin Ephemeris, was subst.i.tuted some ten years later. In astronomical literature the change was initiated by Sir Edmund Beckett in the first edition (1865) of his _Astronomy without Mathematics_.

If any doubt remained as to the misleading character of Encke's deduction, so long implicitly trusted in, it was removed by Powalky's and Stone's rediscussions, in 1864 and 1868 respectively, of the transit observations of 1769. Using improved determinations of the longitude of the various stations, and a selective judgment in dealing with their materials, which, however indispensable, did not escape adverse criticism, they brought out results confirmatory of the no longer disputed necessity for largely increasing the solar parallax, and proportionately diminishing the solar distance. Once more in 1890, and this time with better success, the eighteenth-century transits were investigated by Professor Newcomb.[764] Turning to account the experience gained in the interim regarding the optical phenomena accompanying such events, he elicited from the ma.s.s of somewhat discordant observations at his command, a parallax (879") in close agreement with the value given by sundry modes of recent research.

Conclusions on the subject, however, were still regarded as purely provisional. A transit of Venus was fast approaching, and to its arbitrament, as to that of a court of final appeal, the pending question was to be referred. It is true that the verdict in the same case by the same tribunal a century earlier had proved of so indecisive a character as to form only a starting-point for fresh litigation; but that century had not pa.s.sed in vain, and it was confidently antic.i.p.ated that observational difficulties, then equally unexpected and insuperable, would yield to the elaborate care and skill of forewarned modern preparation.

The conditions of the transit of December 8, 1874, were sketched out by Sir George Airy, then Astronomer-Royal, in 1857,[765] and formed the subject of eager discussion in this and other countries down to the very eve of the occurrence. In these Mr. Proctor took a leading part; and it was due to his urgent representations that provision was made for the employment of the method identified with the name of Halley,[766] which had been too hastily a.s.sumed inapplicable to the first of each transit-pair. It depends upon the difference in the length of time taken by the planet to cross the sun's disc, as seen from various points of the terrestrial surface, and requires, accordingly, the visibility of both entrance and exit at the same station. Since these were, in 1874, separated by about three and a half hours, and the interval may be much longer, the choice of posts for the successful use of the "method of durations" is a matter of some difficulty.

The system described by Delisle in 1760, on the other hand, involves merely noting the instant of ingress or egress (according to situation) from opposite extremities of a terrestrial diameter; the disparity in time giving a measure of the planet's apparent displacement, hence of its actual rate of travel in miles per minute, from which its distances severally from earth and sun are immediately deducible. Its chief attendant difficulty is the necessity for accurately fixing the longitudes of the points of observation. But this was much more sensibly felt a century ago than it is now, the improved facility and certainty of modern determinations tending to give the Delislean plan a decided superiority over its rival.

These two traditional methods were supplemented in 1874 by the camera and the heliometer. From photography, above all, much was expected.