A new line of inquiry was struck out by Zoellner in 1870. Instead of tracking the solar radiations backward with the dubious guide of empirical formulae, he investigated their intensity at their source. He showed[722] that, taking prominences to be simple effects of the escape of powerfully compressed gases, it was possible, from the known mechanical laws of heat and gaseous constitution, to deduce minimum values for the temperatures prevailing in the area of their development. These came out 27,700 deg. C. for the strata lying immediately above, and 68,400 deg. C. for the strata lying immediately below the photosphere, the former being regarded as the region into which, and the latter as the region from which the eruptions took place. In this calculation, no prominences exceeding 40,000 miles (1.5') in height were included. But in 1884, G. A. Hirn of Colmar, having regard to the enormous velocities of projection observed in the interim, fixed two million degrees Centigrade as the lowest internal temperature by which they could be accounted for; although admitting the photospheric condensations to be incompatible with a higher external temperature than 50,000 deg. to 100,000 deg. C.[723]

This method of going straight to the sun itself, observing what goes on there, and inferring conditions, has much to recommend it; but its profitable use demands knowledge we are still very far from possessing. We are quite ignorant, for instance, of the actual circumstances attending the birth of the solar flames. The assumption that they are nothing but phenomena of elasticity is a purely gratuitous one. Spectroscopic indications, again, give hope of eventually affording a fixed point of comparison with terrestrial heat sources; but their interpretation is still beset with uncertainties; nor can, indeed, the expression of transcendental temperatures in degrees of impossible thermometers be, at the best, other than a futile attempt to convey notions respecting a state of things altogether outside the range of our experience.

A more tangible, as well as a less disputable proof of solar radiative intensity than any mere estimates of temperature, was provided in some experiments made by Professor Langley in 1878.[724] Using means of unquestioned validity, he found the sun's disc to radiate 87 times as much heat, and 5,300 times as much light as an equal area of metal in a Bessemer converter after the air-blast had continued about twenty minutes. The brilliancy of the incandescent steel, nevertheless, was so blinding, that melted iron, flowing in a dazzling white-hot stream into the crucible, showed "deep brown by comparison, presenting a contrast like that of dark coffee poured into a white cup." Its temperature was estimated (not quite securely)[725] at about 2,000 deg. C.; and no allowances were made, in computing relative intensities, for atmospheric ravages on sunlight, for the extra impediments to its passage presented by the smoke-laden air of Pittsburgh, or for the obliquity of its incidence. Thus, a very large balance of advantage lay on the side of the metal.

A further element of uncertainty in estimating the intrinsic strength of the sun's rays has still to be considered. From the time that his disc first began to be studied with the telescope, it was perceived to be less brilliant near the edges. Lucas Valerius, of the Lyncean Academy, seems to have been the first to note this fact, which, strangely enough, was denied by Galileo in a letter to Prince Cesi of January 25, 1613.[726] Father Scheiner, however, fully admitted it, and devoted some columns of his bulky tome to the attempt to find its appropriate explanation.[727] In 1729 Bouguer measured, with much accuracy, the amount of this darkening; and from his data, Laplace, adopting a principle of emission now known to be erroneous, concluded that the sun loses eleven-twelfths of his light through absorption in his own atmosphere.[728] The real existence of this atmosphere, which is totally distinct from the beds of ignited vapours producing the Fraunhofer lines, is not open to doubt, although its nature is still a matter of conjecture. The separate effects of its action on luminous, thermal, and chemical rays were carefully studied by Father Secchi, who in 1870[729] inferred the total absorption to be 88/100 of all radiations taken together, and added the important observation that the light from the limb is no longer white, but reddish-brown. Absorptive effects were thus seen to be unequally distributed; and they could evidently be studied to advantage only by taking the various rays of the spectrum separately, and finding out how much each had suffered in transmission.

This was done by H. C. Vogel in 1877.[730] Using a polarising photometer, he found that only 13 per cent. of the violet rays escape at the edge of the solar disc, 16 of the blue and green, 25 of the yellow, and 30 per cent. of the red. Midway between centre and limb, 88.7 of violet light and 96.7 of red penetrate the absorbing envelope, the abolition of which would increase the intensity of the sun's visible spectrum above two and a half times in the most, and once and a half times in the least refrangible parts. The nucleus of a small spot was ascertained to be of the same luminous intensity as a portion of the unbroken surface about two and a half minutes from the limb. These experiments having been made during a spot-minimum when there is reason to think that absorption is below its average strength, Vogel suggested their repetition at a time of greater activity. They were extended to the heat-rays by Edwin B. Frost. Detailed inquiries made at Potsdam in 1892[731] went to show that, were the sun's atmosphere removed, his thermal power, as regards ourselves, would be increased 1.7 times. They established, too, the practical uniformity in radiation of all parts of his disc. A confirmatory result was obtained about the same time by Wilson and Rambaut, who found that the unveiled sun would be once and a half times hotter than the actual sun.[732]

Professor Langley, now of Washington, gave to measures of the kind a refinement previously undreamt of. Reliable determinations of the "energy" of the individual spectral rays were, for the first time, rendered possible by his invention of the "bolometer" in 1880.[733] This exquisitely sensitive instrument affords the means of measuring heat, not directly, like the thermopile, but in its effects upon the conduction of electricity. It represents, in the phrase of the inventor, the finger laid upon the throttle-valve of a steam-engine. A minute force becomes the modulator of a much greater force, and thus from imperceptible becomes conspicuous. By locally raising the temperature of an inconceivably fine strip of platinum serving as the conducting-wire in a circuit, the flow of electricity is impeded at that point, and the included galvanometer records a disturbance of the electrical flow. Amounts of heat were thus detected in less than ten seconds, which, expended during a thousand years on the melting of a kilogramme of ice, would leave a part of the work still undone; and further improvements rendered this marvellous instrument capable of thrilling to changes of temperature falling short of one ten-millionth of a degree Centigrade.[734]

The heat contained in the diffraction spectrum is, with equal dispersions, barely one-tenth of that in the prismatic spectrum. It had, accordingly, never previously been found possible to measure it in detail—that is, ray by ray. But it is only from the diffraction, or normal spectrum that any true idea can be gained as to the real distribution of energy among the various constituents, visible and invisible, of a sunbeam. The effect of passage through a prism is to crowd together the red rays very much more than the blue. To this prismatic distortion was owing the establishment of a pseudo-maximum of heat in the infra-red, which disappeared when the natural arrangement by wave-length was allowed free play. Langley's bolometer has shown that the hottest part of the normal spectrum virtually coincides with its most luminous part, both lying in the orange, close to the D-line.[735] Thus the last shred of evidence in favour of the threefold division of solar radiations vanished, and it became obvious that the varying effects—thermal, luminous, or chemical—produced by them are due, not to any distinction of quality in themselves, but to the different properties of the substances they impinge upon. They are simply bearers of energy, conveyed in shorter or longer vibrations; the result in each separate case depending upon the capacity of the material particles meeting them for taking up those shorter or longer vibrations, and turning them variously to account in their inner economy.

A long series of experiments at Allegheny was completed in the summer of 1881 on the crest of Mount Whitney in the Sierra Nevada. Here, at an elevation of 14,887 feet, in the driest and purest air, perhaps, in the world, atmospheric absorptive inroads become less sensible, and the indications of the bolometer, consequently, surer and stronger. An enormous expansion was at once given to the invisible region in the solar spectrum below the red. Captain Abney had got chemical effects from undulations twelve ten-thousandths of a millimetre in length. These were the longest recognised as, or indeed believed, on theoretical grounds, to be capable of existing. Professor Langley now got heating effects from rays of above twice that wave-length, his delicate thread of platinum groping its way down nearly to thirty ten-thousandths of a millimetre, or three "microns." The known extent of the solar spectrum was thus at once more than doubled. Its visible portion covers a range of about one octave; bolometric indications already in 1884 comprised between three and four. The great importance of the newly explored region appears from the fact that three-fourths of the entire energy of sunlight reside in the infra-red, while scarcely more than one-hundredth part of that amount is found in the better known ultra-violet space.[736] These curious facts were reinforced, in 1886,[737] by further particulars learned with the help of rock-salt lenses and prisms, glass being impervious to very slow, as to very rapid vibrations. Traces were thus detected of solar heat distributed into bands of transmission alternating with bands of atmospheric absorption, far beyond the measurable limit of 5.3 microns.

In 1894, Langley described at the Oxford Meeting of the British Association[738] his new "bolographic" researches, in which the sensitive plate was substituted for the eye in recording deflections of the galvanometer responding to variations of invisible heat. Finally, in 1901,[739] he embodied in a splendid map of the infra-red spectrum 740 absorption-lines of determinate wave-lengths, ranging from 0.76 to 5.3 microns. Their chemical origin, indeed, remains almost entirely unknown, no extensive investigations having yet been undertaken of the slower vibrations distinctive of particular substances; but there is evidence that seven of the nine great bands crossing the "new spectrum" (as Langley calls it)[740] are telluric, and subject to seasonal change. Here, then, he thought, might eventually be found a sure standing-ground for vitally important previsions of famines, droughts, and bonanza-crops.

Atmospheric absorption had never before been studied with such precision as it was by Langley on Mount Whitney. Aided by simultaneous observations from Lone Pine, at the foot of the Sierra, he was able to calculate the intensity belonging to each ray before entering the earth's gaseous envelope—in other words, to construct an extra-atmospheric curve of energy in the spectrum. The result showed that the blue end suffered far more than the red, absorption varying inversely as wave-length. This property of stopping predominantly the quicker vibrations is shared, as both Vogel and Langley[741] have conclusively shown, by the solar atmosphere. The effect of this double absorption is as if two plates of reddish glass were interposed between us and the sun, the withdrawal of which would leave his orb, not only three or four times more brilliant, but in colour distinctly greenish-blue.[742]

The fact of the uncovered sun being blue has an important bearing upon the question of his temperature, to afford a somewhat more secure answer to which was the ultimate object of Professor Langley's persevering researches; for it is well known that as bodies grow hotter, the proportionate representation in their spectra of the more refrangible rays becomes greater. The lowest stage of incandescence is the familiar one of red heat. As it gains intensity, the quicker vibrations come in, and an optical balance of sensation is established at white heat. The final term of blue heat, as we now know, is attained by the photosphere. On this ground alone, then, of the large original preponderance of blue light, we must raise our estimate of solar heat; and actual measurements show the same upward tendency. Until quite lately, Pouillet's figure of 1.7 calories per minute per square centimetre of terrestrial surface, was the received value for the "solar constant." Forbes had, it is true, got 2.85 from observations on the Faulhorn in 1842;[743] but they failed to obtain the confidence they merited. Pouillet's result was not definitely superseded until Violle, from actinometrical measures at the summit and base of Mont Blanc in 1875, computed the intensity of solar radiation at 2.54,[744] and Crova, about the same time, at Montpellier, showed it to be above two calories.[745] Langley went higher still. Working out the results of the Mount Whitney expedition, he was led to conclude atmospheric absorption to be fully twice as effective as had hitherto been supposed. Scarcely 60 per cent., in fact, of those solar radiations which strike perpendicularly through a seemingly translucent sky, were estimated to attain the sea-level. The rest are reflected, dispersed, or absorbed. This discovery involved a large addition to the original supply so mercilessly cut down in transmission, and the solar constant rose at once to three calories. Nor did the rise stop there. M. Savelieff deduced for it a value of 3.47 from actinometrical observations made at Kieff in 1890;[746] and Knut Angstrom, taking account of the arrestive power of carbonic acid, inferred enormous atmospheric absorption, and a solar constant of four calories.[747] In other words, the sun's heat reaching the outskirts of our atmosphere is capable of doing without cessation the work of an engine of four-horse power for each square yard of the earth's surface. Thus, modern inquiries tend to render more and more evident the vastness of the thermal stores contained in the great central reservoir of our system, while bringing into fair agreement the estimates of its probable temperature. This is in great measure due to the acquisition of a workable formula by which to connect temperature with radiation. Stefan's rule of a fourth-power relation, if not actually a law of nature, is a colourable imitation of one; and its employment has afforded a practical certainty that the sun's temperature, so far as it is definable, neither exceeds 12,000 deg. C., nor falls short of 6,500 deg. C.

FOOTNOTES:

[Footnote 698: Principia, p. 498 (1st ed.).]

[Footnote 699: Comptes Rendus, t. vii., p. 24.]

[Footnote 700: Results of Astr. Observations, p. 446.]

[Footnote 701: "Est enim calor solis ut radiorum densitas, hoc est, reciproce ut quadratum distantiae locorum a sole."—Principia, p. 508 (3d ed., 1726).]

[Footnote 702: Jour. de Physique, t. lxxv., p. 215.]

[Footnote 703: Ann. de Chimie, t. vii., 1817, p. 365.]

[Footnote 704: Phil. Mag., vol. xxiii. (4th ser.), p. 505.]

[Footnote 705: Nuovo Cimento, t. xvi., p. 294.]

[Footnote 706: Comptes Rendus, t. lxv., p. 526.]

[Footnote 707: The direct result of 5-1/3 million degrees was doubled in allowance for absorption in the sun's own atmosphere. Comptes Rendus, t. lxxiv., p. 26.]

[Footnote 708: Ibid., p. 31.]

[Footnote 709: Nature, vols. iv., p. 204; v., p. 505.]

[Footnote 710: Ibid., vol. xxx., p. 467.]

[Footnote 711: Ann. de Chim., t. x. (5th ser.), p. 361.]

[Footnote 712: Comptes Rendus, t. xcvi., p. 254.]

[Footnote 713: Phil. Mag., vol. viii., p. 324, 1879.]

[Footnote 714: Ibid., p. 325.]

[Footnote 715: Sitzungsberichte, Wien, Bd. lxxix., ii., p. 391.]

[Footnote 716: Wiedemann's Annalen, Bd. xxii., p. 291; Scheiner, Strahlung und Temperatur der Sonne, p. 27.]

[Footnote 717: Comptes Rendus, March 28, 1892; Astr. and Astrophysics, vol. xi., p. 517.]

[Footnote 718: Phil. Trans., vol. clxxxv., p. 361.]

[Footnote 719: Proc. Roy. Society, December 12, 1901.]

[Footnote 720: Scheiner, Temp. der Sonne, p. 36.]

[Footnote 721: Astroph. Jour., vol. ii., p. 318.]

[Footnote 722: Astr. Nach., Nos. 1,815-16.]

[Footnote 723: L'Astronomie, September, 1884, p. 334.]

[Footnote 724: Amer. Jour. of Science, vol. i. (3rd ser.), p. 653.]

[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 anticipation 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. xxxii.; "On hitherto Unrecognised Wave-lengths," Amer. Jour. of Science, vol. xxxii., August, 1886.]

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

[Footnote 739: Annals of the Smithsonian Astroph. Observatory, vol. i.; Comptes Rendus, t. cxxxi., 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. cxxxii., 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. xxxix., 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 orbit is our standard measure for the universe. It is the great fundamental datum of astronomy—the unit of space, 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 noblest problem in astronomy." It is also one of the most difficult. The quantities 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 quantity 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 orbit, 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 Cassini 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 9.5"); 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 passes 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 passes 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 passage 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 space—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 8.5776", 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 mass 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 accumulating 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 Roemer 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 orbit. Half the difference, or the time spent by a luminous vibration in crossing the "mean radius" of the earth's orbit, 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 quantity. 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 orbit 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 substituted 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 mass of somewhat discordant observations at his command, a parallax (8.79") 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 passed in vain, and it was confidently anticipated 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 assumed 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. Observations made by its means would have the advantages of impartiality, multitude, and permanence. Peculiarities of vision and bias of judgment would be eliminated; the slow progress of the phenomenon would permit an indefinite number of pictures to be taken, their epochs fixed to a fraction of a second; while subsequent leisurely comparison and measurement could hardly fail, it was thought, to educe approximate truth from the mass of accumulated evidence. The use of the heliometer (much relied on by German observers) was so far similar to that of the camera that the object aimed at by both was the determination of the relative positions of the centres of the sun and Venus viewed, at the same absolute instant, from opposite sides of the globe. So that the principle of the two older methods was to ascertain the exact times of meeting between the solar and planetary limbs; that of the two modern to determine the position of the dark body already thrown into complete relief by its shining background. The former are "methods by contact," the latter "methods by projection."

Every country which had a reputation to keep or to gain for scientific zeal was forward to co-operate in the great cosmopolitan enterprise of the transit. France and Germany each sent out six expeditions; twenty-six stations were in Russian, twelve in English, eight in American, three in Italian, one in Dutch occupation. In all, at a cost of nearly a quarter of a million, some fourscore distinct posts of observation were provided; among them such inhospitable, and all but inaccessible rocks in the bleak Southern Ocean, as St. Paul's and Campbell Islands, swept by hurricanes, and fitted only for the habitation of seabirds, where the daring votaries of science, in the wise prevision of a long leaguer by the elements, were supplied with stores for many months, or even a whole year. Siberia and the Sandwich Islands were thickly beset with observers; parties of three nationalities encamped within the mists of Kerguelen Island, expressively termed the "Land of Desolation," in the sanguine, though not wholly frustrated hope of a glimpse of the sun at the right moment. M. Janssen narrowly escaped destruction from a typhoon in the China seas on his way to Nagasaki; Lord Lindsay (now Earl of Crawford and Balcarres) equipped, at his private expense, an expedition to Mauritius, which was in itself an epitome of modern resource and ingenuity.

During several years, the practical methods best suited to insure success for the impending enterprise formed a subject of European debate. Official commissions were appointed to receive and decide upon evidence; and experiments were in progress for the purpose of defining the actual circumstances of contacts, the precise determination of which constituted the only tried, though by no means an assuredly safe road to the end in view. In England, America, France, and Germany, artificial transits were mounted, and the members of the various expeditions were carefully trained to unanimity in estimating the phases of junction and separation between a moving dark circular body and a broad illuminated disc. In the previous century, a formidable and prevalent phenomenon, which acquired notoriety as the "Black Drop" or "Black Ligament," had swamped all pretensions to rigid accuracy. It may be described as substituting adhesion for contact, the limbs of the sun and planet, instead of meeting and parting with the desirable clean definiteness, clinging together as if made of some glutinous material, and prolonging their connection by means of a dark band or dark threads stretched between them. Some astronomers ascribed this baffling appearance entirely to instrumental imperfections; others to atmospheric agitation; others again to the optical encroachment of light upon darkness known as "irradiation." It is probable that all these causes conspired, in various measure, to produce it; and it is certain that its conspicuous appearance may, by suitable precautions, be obviated.

The organisation of the British forces reflected the utmost credit on the energy and ability of Lieutenant-Colonel Tupman, who was responsible for the whole. No useful measure was neglected. Each observer went out ticketed with his "personal equation," his senses drilled into a species of martial discipline, his powers absorbed, so far as possible, in the action of a cosmopolitan observing machine. Instrumental uniformity and uniformity of method were obtainable, and were attained; but diversity of judgment unhappily survived the best-directed efforts for its extirpation.

The eventful day had no sooner passed than telegrams began to pour in, announcing an outcome of considerable, though not unqualified success. The weather had proved generally favourable; the manifold arrangements had worked well; contacts had been plentifully observed; photographs in lavish abundance had been secured; a store of materials, in short, had been laid up, of which it would take years to work out the full results by calculation. Gradually, nevertheless, it came to be known that the hope of a definitive issue must be abandoned. Unanimity was found to be as remote as ever. The dreaded "black ligament" gave, indeed, less trouble than was expected; but another appearance supervened which took most observers by surprise. This was the illumination due to the atmosphere of Venus. Astronomers, it is true, were not ignorant that the planet had, on previous occasions, been seen girdled with a lucid ring; but its power to mar observations by the distorting effect of refraction had scarcely been reckoned with. It proved, however, to be very great. Such was the difficulty of determining the critical instant of internal contact, that (in Colonel Tupman's words) "observers side by side, with adequate optical means, differed as much as twenty or thirty seconds in the times they recorded for phenomena which they have described in almost identical language."[767]

Such uncertainties in the data admitted of a corresponding variety in the results. From the British observations of ingress and egress Sir George Airy[768] derived, in 1877, a solar parallax of 8.76" (corrected to 8.754"), indicating a mean distance of 93,375,000 miles. Mr. Stone obtained a value of ninety-two millions (parallax 8.88"), and held any parallax less than 8.84" or more than 8.93" to be "absolutely negatived" by the documents available.[769] Yet, from the same, Colonel Tupman deduced 8.81",[770] implying a distance 700,000 miles greater than Stone had obtained. The best French observations of contacts gave a parallax of about 8.88"; French micrometric measures the obviously exaggerated one of 9.05".[771]

Photography, as practised by most of the European parties, was a total failure. Utterly discrepant values of the microscopic displacements designed to serve as sounding lines for the solar system, issued from attempts to measure even the most promising pictures. "You might as well try to measure the zodiacal light," it was remarked to Sir George Airy. Those taken on the American plan of using telescopes of so great focal length as to afford, without further enlargement, an image of the requisite size, gave notably better results. From an elaborate comparison of those dating from Vladivostock, Nagasaki, and Pekin, with others from Kerguelen and Chatham Islands, Professor D. P. Todd, of Amherst College, deduced a solar distance of about ninety-two million miles (parallax 8.883" +-0.034"),[772] and the value was much favoured by concurrent evidence.

On the whole, estimates of the great spatial unit cannot be said to have gained any security from the combined effort of 1874. A few months before the transit, Mr. Proctor considered that the uncertainty then amounted to 1,448,000 miles;[773] five years after the transit, Professor Harkness judged it to be still 1,575,950 miles;[774] yet it had been hoped that it would have been brought down to 100,000. As regards the end for which it had been undertaken, the grand campaign had come to nothing. Nevertheless, no sign of discouragement was apparent. There was a change of view, but no relaxation of purpose. The problem, it was seen, could be solved by no single heroic effort, but by the patient approximation of gradual improvements. Astronomers, accordingly, looked round for fresh means or more refined expedients for applying those already known. A new phase of exertion was entered upon.

On September 5, 1877, Mars came into opposition near the part of his orbit which lies nearest to that of the earth, and Dr. Gill (now Sir David) took advantage of the circumstance to appeal once more to him for a decision on the quaestio vexata of the sun's distance. He chose, as the scene of his labours, the Island of Ascension, and for their plan a method recommended by Airy in 1857,[775] but never before fairly tried. This is known as the "diurnal method of parallaxes." Its principle consists in substituting successive morning and evening observations from the same spot, for simultaneous observations from remote spots, the rotation of the earth supplying the necessary difference in the points of view. Its great advantage is that of unity in performance. A single mind, looking through the same pair of eyes, reinforced with the same optical appliances, is employed throughout, and the errors inseparable from the combination of data collected under different conditions are avoided. There are many cases in which one man can do the work of two better than two men can do the work of one. The result of Gill's skilful determinations (made with Lord Lindsay's heliometer) was a solar parallax of 8.78", corresponding to a distance of 93,080,000 miles.[776] The bestowal of the Royal Astronomical Society's gold medal stamped the merit of this distinguished service.

But there are other subjects for this kind of inquiry besides Mars and Venus. Professor Galle of Breslau suggested in 1872[777] that some of the minor planets might be got to repay astronomers for much disinterested toil spent in unravelling their motions, by lending aid to their efforts towards a correct celestial survey. Ten or twelve come near enough, and are bright enough for the purpose; in fact, the absence of sensible magnitude is one of their chief recommendations, since a point of light offers far greater facilities for exact measurement than a disc. The first attempt to work this new vein was made at the opposition of Phocaea in 1872; and from observations of Flora in the following year at twelve observatories in the northern and southern hemispheres, Galle deduced a solar parallax of 8.87".[778] At Mauritius in 1874, Lord Lindsay and Sir David Gill applied the "diurnal method" to Juno, then conveniently situated for the purpose; and the continued use of similar occasions affords an unexceptionable means for improving knowledge of the sun's distance. They frequently recur; they need no elaborate preparation; a single astronomer armed with a heliometer can do all the requisite work. Dr. Gill, however, organized a more complex plan of operations upon Iris in 1888, and upon Victoria and Sappho in 1889. A novel method was adopted. Its object was to secure simultaneous observations made from opposite sides of the globe just when the planet lay in the plane passing through the centre of the earth and the two observers, the same pair of reference-stars being used on each occasion. The displacements caused by parallax were thus in a sense doubled, since the star to which the planet seemed approximated in the northern hemisphere, showed as if slightly removed from it in the southern, and vice versa. As the planet pursued its course, fresh star-couples came into play, during the weeks that the favourable period lasted. In these determinations, only heliometers were employed. Dr. Elkin, of Yale college, co-operated throughout, and the heliometers of Dresden, Gottingen, Bamberg, and Leipzig, shared in the work, while Dr. Auwers of Berlin was Sir David Gill's personal coadjutor at the Cape. Voluminous data were collected; meridian observations of the stars of reference for Victoria occupied twenty-one establishments during four months; the direct work of triangulation kept four heliometers in almost exclusive use for the best part of a year; and the ensuing toilsome computations, carried out during three years at the Cape Observatory, filled two bulky tomes[779] with their details. Gill's final result, published in 1897, was a parallax of 8.802", equivalent to a solar distance of 92,874,000; and it was qualified by a probable error so small that the value might well have been accepted as definitive but for an unlooked-for discovery. The minor planet Eros, detected August 14, 1898, was found to pursue a course rendering it an almost ideal intermediary in solar parallax-determinations. Once in thirty years, it comes within fifteen million miles of the earth; and although the next of these choice epochs must be awaited for some decades, an opposition too favourable to be neglected occurred in 1900. At an International Conference, accordingly, held at Paris in July of that year, a plan of photographic operations was concerted between the representatives of no less than 58 observatories.[780] Its primary object was to secure a large stock of negatives showing the planet with the comparison-stars along the route traversed by it from October, 1900, to March, 1901,[781] and this at least was successfully attained. Their measurement will in due time educe the apparent displacements of the moving object as viewed simultaneously from remote parts of the earth; and the upshot should be a solar parallax adequate in accuracy to the exigent demands of the twentieth century.

The second of the nineteenth-century pair of Venus-transits was looked forward to with much abated enthusiasm. Russia refused her active co-operation in observing it, on the ground that oppositions of the minor planets were trigonometrically more useful, and financially far less costly; and her example was followed by Austria; while Italian astronomers limited their sphere of action to their own peninsula. Nevertheless, it was generally held that a phenomenon which the world could not again witness until it was four generations older should, at the price of any effort, not be allowed to pass in neglect.

The persuasion of its importance justified the summoning of an International Conference at Paris in 1881, from which, however, America, preferring independent action, held aloof. It was decided to give Delisle's method another trial; and the ambiguities attending and marring its use were sought to be obviated by careful regulations for insuring agreement in the estimation of the critical moments of ingress and egress.[782] But in fact (as M. Puiseux had shown[783]), contacts between the limbs of the sun and planet, so far from possessing the geometrical simplicity attributed to them, are really made up of a prolonged succession of various and varying phases, impossible either to predict or identify with anything like rigid exactitude. Sir Robert Ball compared the task of determining the precise instant of their meeting or parting, to that of telling the hour with accuracy on a watch without a minute hand; and the comparison is admittedly inadequate. For not only is the apparent movement of Venus across the sun extremely slow, being but the excess of her real motion over that of the earth; but three distinct atmospheres—the solar, terrestrial, and Cytherean—combine to deform outlines and mask the geometrical relations which it is desired to connect with a strict count of time.

The result was very much what had been expected. The arrangements were excellent, and were only in a few cases disconcerted by bad weather. The British parties, under the experienced guidance of Mr. Stone, the late Radcliffe observer, took up positions scattered over the globe, from Queensland to Bermuda; the Americans collected a whole library of photographs; the Germans and Belgians trusted to the heliometer; the French used the camera as an adjunct to the method of contacts. Yet little or no approach was made to solving the problem. Thus, from 606 measures of Venus on the sun, taken with a new kind of heliometer at Santiago in Chili, M. Houzeau, of the Brussels Observatory, derived a solar parallax of 8.907", and a distance of 91,727,000 miles.[784] But the "probable errors" of this determination amounted to 0.084" either way: it was subject to a "more or less" of 900,000, or to a total uncertainty of 1,800,000 miles. The "probable error" of the English result, published in 1887, was less formidable,[785] yet the details of the discussion showed that no great confidence could be placed in it. The sun's distance came out 92,560,000 miles; while 92,360,000 was given by Professor Harkness's investigation of 1,475 American photographs.[786] Finally, Dr. Auwers deduced from the German heliometric measures the unsatisfactorily small value of 92,000,000 miles.[787] The transit of 1882 had not, then, brought about the desired unanimity.

The state and progress of knowledge on this important topic were summed up by Faye and Harkness in 1881.[788] The methods employed in its investigation fall (as we have seen) into three separate classes—the trigonometrical, the gravitational, and the "phototachymetrical"—an ungainly adjective used to describe the method by the velocity of light. Each has its special difficulties and sources of error; each has counter-balancing advantages. The only trustworthy result from celestial surveys, was at that time furnished by Gill's observations of Mars in 1877. But the method by lunar and planetary disturbances is unlike all the others in having time on its side. It is this which Leverrier declared with emphasis must inevitably prevail, because its accuracy is continually growing.[789] The scarcely perceptible errors which still impede its application are of such a nature as to accumulate year by year; eventually, then, they will challenge, and must receive, a more and more perfect correction. The light-velocity method, however, claimed, and for some years justified, M. Faye's preference.

By a beautiful series of experiments on Foucault's principle, Michelson fixed in 1879 the rate of luminous transmission at 299,930 (corrected later to 299,910) kilometres a second.[790] This determination was held by Professor Todd to be entitled to four times as much confidence as any previous one; and if the solar parallax of 8.758" deduced from it by Professor Harkness errs somewhat by defect, it is doubtless because Glasenapp's "light-equation," with which it was combined, errs slightly by excess. But all earlier efforts of the kind were thrown into the shade by Professor Newcomb's arduous operations at Washington in 1880-1882.[791] The scale upon which they were conducted was in itself impressive. Foucault's entire apparatus in 1862 had been enclosed in a single room; Newcomb's revolving and fixed mirrors, between which the rays of light were to run their timed course, were set up on opposite shores of the Potomac, at a distance of nearly four kilometres. This advantage was turned to the utmost account by ingenuity and skill in contrivance and execution; and the deduced velocity of 299,860 kilometres = 186,328 miles a second, had an estimated error (30 kilometres) only one-tenth that ascribed by Cornu to his own result in 1874.

Just as these experiments were concluded in 1882, M. Magnus Nyren, of St. Petersburg, published an elaborate investigation of the small annular displacements of the stars due to the successive transmission of light, involving an increase of Struve's "constant of aberration" from 20.445" to 20.492". And from the new value, combined with Newcomb's light-velocity, was derived a valuable approximation to the sun's distance, concluded at 92,905,021 miles (parallax = 8.794"). Yet it is not quite certain that Nyren's correction was an improvement. A differential method of determining the amount of aberration, struck out by M. Loewy of Paris,[792] avoids most of the objections to the absolute method previously in vogue; and the upshot of its application in 1891 was to show that Struve's constant might better be retained than altered, Loewy's of 20.447" varying from it only to an insignificant extent. Professor Hall had, moreover, deduced nearly the same value (20.454") from the Washington observations since 1862, of Alpha Lyrae (Vega); whence, in conjunction with Newcomb's rate of light transmission, he arrived at a solar parallax of 8.81".[793] Inverting the process, Sir David Gill in 1897 derived the constant from the parallax. If the earth's orbit have a mean radius, as found by him, of 92,874,000 miles, then, he calculated, the aberration of light—Newcomb's measures of its velocity being supposed exact—amounts to 20.467". This figure can need very slight correction.

Professor Harkness surveyed in 1891,[794] from an eclectic point of view, the general situation as regarded the sun's parallax. Convinced that no single method deserved an exclusive preference, he reached a plausible result through the combination, on the principle of least squares—that is, by the mathematical rules of probability—of all the various quantities upon which the great datum depends. It thus summed up and harmonised the whole of the multifarious evidence bearing upon the point, and, as modified in 1894,[795] falls very satisfactorily into line with the Cape determination. We may, then, at least provisionally, accept 92,870,000 miles as the length of our measuring-rod for space. Nor do we hazard much in fixing 100,000 miles as the outside limit of its future correction.

FOOTNOTES:

[Footnote 748: Airy, Month. Not., vol. xvii., p. 210.]

[Footnote 749: Mars comes into opposition once in about 780 days; but owing to the eccentricity of both orbits, his distance from the earth at those epochs varies from thirty-five to sixty-two million miles.]

[Footnote 750: J. D. Cassini, Hist. Abregee de la Parallaxe du Soleil, p. 122, 1772.]

[Footnote 751: The present period of coupled eccentric transits will, in the course of ages, be succeeded by a period of single, nearly central transits. The alignments by which transits are produced, of the earth, Venus, and the sun, close to the place of intersection of the two planetary orbits, now occur, the first a little in front of, the second, after eight years less two and a half days, a little behind the node. But when the first of these two meetings takes place very near the node, giving a nearly central transit, the second falls too far from it, and the planet escapes projection on the sun. The reason of the liability to an eight-yearly recurrence is that eight revolutions of the earth are accomplished in only a very little more time than thirteen revolutions of Venus.]

[Footnote 752: Die Entfernung der Sonne: Fortsetzung, p. 108. Encke slightly corrected his results of 1824 in Berlin Abh., 1835, p. 295.]

[Footnote 753: Owing to the ellipticity of its orbit, the earth is nearer to the sun in January than in June by 3,100,000 miles. The quantity to be determined, or "mean distance," is that lying midway between these extremes—is, in other words, half the major axis of the ellipse in which the earth travels.]

[Footnote 754: Month. Not., vol. xv., p. 9.]

[Footnote 755: The Distance of the Sun from the Earth determined by the Theory of Gravity, Edinburgh, 1763.]

[Footnote 756: Opera, t. iii., p. 326.]

[Footnote 757: Comptes Rendus, t. xlvi., p. 882. The parallax 8.95" derived by Leverrier from the above-described inequality in the earth's motion, was corrected by Stone to 8.91". Month. Not., vol. xxviii., p. 25.]

[Footnote 758: Month. Not., vol. xxxv., p. 156.]

[Footnote 759: Wash. Obs., 1865, App. ii., p. 28.]

[Footnote 760: Comptes Rendus, t. xxix., p. 90.]

[Footnote 761: Ibid., t. xxx., p. 551.]

[Footnote 762: Ibid., t. lv., p. 501. The previously admitted velocity was 308 million metres per second; Foucault reduced it to 298 million. Combined with Struve's "constant of aberration" this gave 8.86" for the solar parallax, which exactly agreed with Cornu's result from a repetition of Fizeau's experiments in 1872. Comptes Rendus, t. lxxvi., p. 338.]

[Footnote 763: Month. Not., vol. xxiv., p. 103.]

[Footnote 764: Astr. Papers of the American Ephemeris, vol. ii., p. 263.]

[Footnote 765: Month. Not., vol. xvii., p. 208.]

[Footnote 766: Because closely similar to that proposed by him in Phil. Trans. for 1716.]

[Footnote 767: Month. Not., vol. xxxviii., p. 447.]

[Footnote 768: Ibid., p. 11.]

[Footnote 769: Ibid., p. 294.]

[Footnote 770: Ibid., p. 334.]

[Footnote 771: Comptes Rendus, t. xcii., p. 812.]

[Footnote 772: Observatory, vol. v., p. 205.]

[Footnote 773: Transits of Venus, p. 89 (1st ed.).]

[Footnote 774: Am. Jour. of Sc., vol. xx., p. 393.]

[Footnote 775: Month. Not., vol. xvii., p. 219.]

[Footnote 776: Mem. Roy. Astr. Soc., vol. xlvi., p. 163.]

[Footnote 777: Astr. Nach., No. 1,897.]

[Footnote 778: Hilfiker, Bern Mittheilungen, 1878, p. 109.]

[Footnote 779: Annals of the Cape Observatory, vols. vi., vii.]

[Footnote 780: Rapport sur l'Etat de l'Observatoire de Paris pour l'Annee 1900, p. 7.]

[Footnote 781: Observatory, vol. xxiii., p. 311; Newcomb, Astr. Jour., No. 480.]

[Footnote 782: Comptes Rendus, t. xciii., p. 569.]

[Footnote 783: Ibid., t. xcii., p. 481.]

[Footnote 784: Bull. de l'Acad., t. vi., p. 842.]

[Footnote 785: Month. Not., vol. xlviii., p. 201.]

[Footnote 786: Astr. Jour., No. 182.]

[Footnote 787: Astr. Nach., No. 3,066.]

[Footnote 788: Comptes Rendus, t. xcii., p. 375; Am. Jour. of Sc., vol. xxii., p. 375.]

[Footnote 789: Month. Not., vol. xxxv., p. 401.]

[Footnote 790: Am. Jour. of Sc., vol. xviii., p. 393.]

[Footnote 791: Nature, vol. xxxiv., p. 170; Astron. Papers of the American Ephemeris, vol. ii., p. 113.]

[Footnote 792: Comptes Rendus, t. cxii., p. 549.]

[Footnote 793: Astr. Journ., Nos. 169, 170]

[Footnote 794: The Solar Parallax and its Related Constants, Washington, 1891.]

[Footnote 795: Astr. and Astrophysics, vol. xiii., p. 626.]



CHAPTER VII

PLANETS AND SATELLITES

Johann Hieronymus Schroeter was the Herschel of Germany. He did not, it is true, possess the more brilliant gifts of his rival. Herschel's piercing discernment, comprehensive intelligence, and inventive splendour were wanting to him. He was, nevertheless, the founder of descriptive astronomy in Germany, as Herschel was in England.

Born at Erfurt in 1745, he prosecuted legal studies at Gottingen, and there imbibed from Kaestner a life-long devotion to science. From the law, however, he got the means of living, and, what was to the full as precious to him, the means of observing. Entering the sphere of Hanoverian officialism in 1788, he settled a few years later at Lilienthal, near Bremen, as "Oberamtmann," or chief magistrate. Here he built a small observatory, enriched in 1785 with a seven-foot reflector by Herschel, then one of the most powerful instruments to be found anywhere out of England. It was soon surpassed, through his exertions, by the first-fruits of native industry in that branch. Schrader of Kiel transferred his workshops to Lilienthal in 1792, and constructed there, under the superintendence and at the cost of the astronomical Oberamtmann, a thirteen-foot reflector, declared by Lalande to be the finest telescope in existence, and one twenty-seven feet in focal length, probably as inferior to its predecessor in real efficiency as it was superior in size.

Thus, with instruments of gradually increasing power, Schroeter studied during thirty-four years the topography of the moon and planets. The field was then almost untrodden; he had but few and casual predecessors, and has since had no equal in the sustained and concentrated patience of his hourly watchings. Both their prolixity and their enthusiasm are faithfully reflected in his various treatises. Yet the one may be pardoned for the sake of the other, especially when it is remembered that he struck out a substantially new line, and that one of the main lines of future advance. Moreover, his infectious zeal communicated itself; he set the example of observing when there was scarcely an observer in Germany; and under his roof Harding and Bessel received their training as practical astronomers.

But he was reserved to see evil days. Early in 1813 the French under Vandamme occupied Bremen. On the night of April 20, the Vale of Lilies was, by their wanton destructiveness, laid waste with fire; the Government offices were destroyed, and with them the chief part of Schroeter's property, including the whole stock of his books and writings. There was worse behind. A few days later, his observatory, which had escaped the conflagration, was broken into, pillaged, and ruined. His life was wrecked with it. He survived the catastrophe three years without the means to repair, or the power to forget it, and gradually sank from disappointment into decay, terminated by death, August 29, 1816. He had, indeed, done all the work he was capable of; and though not of the first quality, it was far from contemptible. He laid the foundation of the comparative study of the moon's surface, and the descriptive particulars of the planets laboriously collected by him constituted a store of more or less reliable information hardly added to during the ensuing half century. They rested, it is true, under some shadow of doubt; but the most recent observations have tended on several points to rehabilitate the discredited authority of the Lilienthal astronomer. We may now briefly resume, and pursue in its further progress, the course of his studies, taking the planets in the order of their distances from the sun.

In April, 1792, Schroeter saw reason to conclude, from the gradual degradation of light on its partially illuminated disc, that Mercury possesses a tolerably dense atmosphere.[796] During the transit of May 7, 1799, he was, moreover, struck with the appearance of a ring of softened luminosity encircling the planet to an apparent height of three seconds, or about a quarter of its own diameter.[797] Although a "mere thought" in texture, it remained persistently visible both with the seven-foot and the thirteen-foot reflectors, armed with powers up to 288. It had a well-marked grayish boundary, and reminded him, though indefinitely fainter, of the penumbra of a sun-spot. A similar appendage had been noticed by De Plantade at Montpellier, November 11, 1736, and again in 1786 and 1789 by Prosperin and Flaugergues; but Herschel, on November 9, 1802, saw the preceding limb of the planet projected on the sun cut the luminous solar clouds with the most perfect sharpness.[798] The presence, however, of a "halo" was unmistakable in 1832, when Professor Moll, of Utrecht, described it as a "nebulous ring of a darker tinge approaching to the violet colour."[799] Again, to Huggins and Stone, November 5, 1868, it showed as lucid and most distinct. No change in the colour of the glasses used, or the powers applied, could get rid of it, and it lasted throughout the transit.[800] It was next seen by Christie and Dunkin at Greenwich, May 6, 1878,[801] and with much precision of detail by Trouvelot at Cambridge (U.S.).[802] Professor Holden, on the other hand, noted at Hastings-on-Hudson the total absence of all anomalous appearances.[803] Nor could any vestige of them be perceived by Barnard at Lick on November 10, 1894.[804] Various effects of irradiation and diffraction were, however, observed by Lowell and W. H. Pickering at Flagstaff;[805] and Davidson was favoured at San Francisco with glimpses of the historic aureola,[806] as well as of a central whitish spot, which often accompanies it. That both are somehow of optical production can scarcely be doubted.

Nothing can be learned from them regarding the planet's physical condition. Airy showed that refraction in a Mercurian atmosphere could not possibly originate the noted aureola, which must accordingly be set down as "strictly an ocular nervous phenomenon."[807] It is the less easy to escape from this conclusion that we find the virtually airless moon capable of exhibiting a like appendage. Professor Stephen Alexander, of the United States Survey, with two other observers, perceived, during the eclipse of the sun of July 18, 1860, the advancing lunar limb to be bordered with a bright band;[808] and photographic effects of the same kind appear in pictures of transits of Venus and partial solar eclipses.

The spectroscope affords little information as to the constitution of Mercury. Its light is of course that of the sun reflected, and its spectrum is consequently a faint echo of the Fraunhofer spectrum. Dr. H. C. Vogel, who first examined it in April, 1871, suspected traces of the action of an atmosphere like ours,[809] but, it would seem, on slight grounds. It is, however, certainly very poor in blue rays. More definite conclusions were, in 1874,[810] derived by Zoellner from photometric observations of Mercurian phases. A similar study of the waxing and waning moon had afforded him the curious discovery that light-changes dependent upon phase vary with the nature of the reflecting surface, following a totally different law on a smooth homogeneous globe and on a rugged and mountainous one. Now the phases of Mercury—so far as could be determined from only two sets of observations—correspond with the latter kind of structure. Strictly analogous to those of the moon, they seem to indicate an analogous mode of surface-formation. This conclusion was fully borne out by Mueller's more extended observations at Potsdam during the years 1885-1893.[811] Practical assurance was gained from them that the innermost planet has a rough rind of dusky rock, absorbing all but 17 per cent. of the light poured upon it by the fierce adjacent sun. Its "albedo," in other words, is 0.17,[812] which is precisely that ascribed to the moon. The absence of any appreciable Mercurian atmosphere followed almost necessarily from these results.

On March 26, 1800, Schroeter, observing with his 13-foot reflector in a peculiarly clear sky, perceived the southern horn of Mercury's crescent to be quite distinctly blunted.[813] Interception of sunlight by a Mercurian mountain rather more than eleven English miles high explained the effect to his satisfaction. By carefully timing its recurrence, he concluded rotation on an axis in a period of 24 hours 4 minutes. The first determination of the kind rewarded twenty years of unceasing vigilance. It received ostensible confirmation from the successive appearances of a dusky streak and blotch in May and June, 1801.[814] These, however, were inferred to be no permanent markings on the body of the planet, but atmospheric formations, the streak at times drifting forwards (it was thought) under the fluctuating influence of Mercurian breezes. From a rediscussion of these somewhat doubtful observations Bessel inferred that Mercury rotates on an axis inclined 70 deg. to the plane of its orbit in 24 hours 53 seconds.

The rounded appearance of the southern horn seen by Schroeter was more or less doubtfully caught by Noble (1864), Burton, and Franks (1877);[815] but was obvious to Mr. W. F. Denning at Bristol on the morning of November 5, 1882.[816] That the southern polar regions are usually less bright than the northern is well ascertained; but the cause of the deficiency remains dubious. If inequalities of surface are in question, they must be on a considerable scale; and a similar explanation might be given of the deformations of the "terminator"—or dividing-line between darkness and light in the planet's phases—first remarked by Schroeter, and again clearly seen by Trouvelot in 1878 and 1881.[817] The displacement, during four days, of certain brilliant and dusky spaces on the disc indicated to Mr. Denning in 1882 rotation in about twenty-five hours; while the general aspect of the planet reminded him of that of Mars.[818] But the difficulties in the way of its observation are enormously enhanced by its constant close attendance on the sun.

In his sustained study of the features of Mercury, Schroeter had no imitator until Schiaparelli took up the task at Milan in 1882. His observations were made in daylight. It was found that much more could be seen, and higher magnifying powers used, high up in the sky near the sun, than at low altitudes, through the agitated air of morning or evening twilight. A notable discovery ensued.[819] Following the planet hour by hour, instead of making necessarily brief inspections at intervals of about a day, as previous observers had done, it was found that the markings faintly visible remained sensibly fixed, hence, that there was no rotation in a period at all comparable with that of the earth. And after long and patient watching, the conclusion was at last reached that Mercury turns on his axis in the same time needed to complete a revolution in his orbit. One of his hemispheres, then, is always averted from the sun, as one of the moon's hemispheres from the earth, while the other never shifts from beneath his torrid rays. The "librations," however, of Mercury are on a larger scale than those of the moon, because he travels in a more eccentric path. The temporary inequalities arising between his "even pacing" on an axis and his alternately accelerated and retarded elliptical movement occasion, in fact, an oscillation to and fro of the boundaries of light and darkness on his globe over an arc of 47 deg. 22', in the course of his year of 88 days. Thus the regions of perpetual day and perpetual night are separated by two segments, amounting to one-fourth of the entire surface, where the sun rises and sets once in 88 days. Else there is no variation from the intense glare on one side of the globe, and the nocturnal blackness on the other.

To Schiaparelli's scrutiny, Mercury appeared as a "spotty globe," enveloped in a tolerably dense atmosphere. The brownish stripes and streaks, discerned on his rose-tinged disc, and judged to be permanent, were made the basis of a chart. They were not indeed always equally well seen. They disappeared regularly near the limb, and were at times veiled even when centrally situated. Some of them had been clearly perceived by De Ball at Bothkamp in 1882.[820]

Mr. Lowell followed Schiaparelli's example by observing Mercury in the full glare of noon. "The best time to study him," he remarked, "is when planetary almanacs state 'Mercury invisible.'" A remarkable series of drawings executed, some at Flagstaff in 1896, the remainder at Mexico in 1897, supplied grounds for the following, among other, conclusions.[821] Mercury rotates synchronously with its revolution—that is, once in 88 days—on an axis sensibly perpendicular to its orbital plane. No certain signs of a Mercurian atmosphere are visible. The globe is seamed and furrowed with long narrow markings, explicable as cracks in cooling. It is, and always was, a dead world. From micrometrical measures, moreover, the inferences were drawn that the planet's mass has a probable value about 1/20 that of the earth, while its mean density falls considerably short of the terrestrial standard.

The theory of Mercury's movements has always given trouble. In Lalande's,[822] as in Maestlin's time, the planet seemed to exist for no other purpose than to throw discredit on astronomers; and even to Leverrier's powerful analysis it long proved recalcitrant. On the 12th of September, 1869, however, he was able to announce before the Academy of Sciences[823] the terms of a compromise between observation and calculation. They involved the addition of a new member to the solar system. The hitherto unrecognised presence of a body about the size of Mercury itself revolving at somewhat less than half its mean distance from the sun (or, if farther, then of less mass, and vice versa), would, it was pointed out, produce exactly the effect required, of displacing the perihelion of the former planet 38" a century more than could otherwise be accounted for. The planes of the two orbits, however, should not lie far apart, as otherwise a nodal disturbance would arise not perceived to exist. It was added that a ring of asteroids similarly placed would answer the purpose equally well, and was more likely to have escaped notice.

Upon the heels of this forecast followed promptly a seeming verification. Dr. Lescarbault, a physician residing at Orgeres, whose slender opportunities had not blunted his hopes of achievement, had, ever since 1845, when he witnessed a transit of Mercury, cherished the idea that an unknown planet might be caught thus projected on the solar background. Unable to observe continuously until 1858, he, on March 26, 1859, saw what he had expected—a small perfectly round object slowly traversing the sun's disc. The fruitless expectation of reobserving the phenomenon, however, kept him silent, and it was not until December 22, after the news of Leverrier's prediction had reached him, that he wrote to acquaint him with his supposed discovery.[824] The Imperial Astronomer thereupon hurried down to Orgeres, and by personal inspection of the simple apparatus used, by searching cross-examination and local inquiry, convinced himself of the genuine character and substantial accuracy of the reported observation. He named the new planet "Vulcan," and computed elements giving it a period of revolution slightly under twenty days.[825] But it has never since been seen. M. Liais, director of the Brazilian Coast Survey, thought himself justified in asserting that it never had been seen. Observing the sun for twelve minutes after the supposed ingress recorded at Orgeres, he noted those particular regions of its surface as "tres uniformes d'intensite."[826] He subsequently, however, admitted Lescarbault's good faith, at first rashly questioned. The planet-seeking doctor was, in truth, only one among many victims of similar illusions.

Waning interest in the subject was revived by a fresh announcement of a transit witnessed, it was asserted, by Weber at Peckeloh, April 4, 1876.[827] The pseudo-planet, indeed, was detected shortly afterwards on the Greenwich photographs, and was found to have been seen by M. Ventosa at Madrid in its true character of a sun-spot without penumbra; but Leverrier had meantime undertaken the investigation of a list of twenty similar dubious appearances, collected by Haase, and republished by Wolf in 1872.[828] From these, five were picked out as referring in all likelihood to the same body, the reality of whose existence was now confidently asserted, and of which more or less probable transits were fixed for March 22, 1877, and October 15, 1882.[829] But, widespread watchfulness notwithstanding, no suspicious object came into view at either epoch.

The next announcement of the discovery of "Vulcan" was on the occasion of the total solar eclipse of July 29, 1878.[830] This time it was stated to have been seen at some distance south-west of the obscured sun, as a ruddy star with a minute planetary disc; and its simultaneous detection by two observers—the late Professor James C. Watson, stationed at Rawlins (Wyoming Territory), and Professor Lewis Swift at Denver (Colorado)—was at first readily admitted. But their separate observations could, on a closer examination, by no possibility be brought into harmony, and, if valid, certainly referred to two distinct objects, if not to four; each astronomer eventually claiming a pair of planets. Nor could any one of the four be identified with Lescarbault's and Leverrier's Vulcan, which, if a substantial body revolving round the sun, must then have been found on the east side of that luminary.[831] The most feasible explanation of the puzzle seems to be that Watson and Swift merely saw each the same two stars in Cancer: haste and excitement doing the rest.[832] Nevertheless, they strenuously maintained their opposite conviction.[833]

Intra-Mercurian planets have since been diligently searched for when the opportunity of a total eclipse offered, especially during the long obscuration at Caroline Island. Not only did Professor Holden "sweep" in the solar vicinity, but Palisa and Trouvelot agreed to divide the field of exploration, and thus make sure of whatever planetary prey there might be within reach; yet with only negative results. Photographic explorations during recent eclipses have been equally fruitless. Belief in the presence of any considerable body or bodies within the orbit of Mercury is, accordingly, at a low ebb. Yet the existence of the anomaly in the Mercurian movements indicated by Leverrier has been made only surer by further research.[834] Its elucidation constitutes one of the "pending problems" of astronomy.

* * * * *

From the observation at Bologna in 1666-67 of some very faint spots, Domenico Cassini concluded a rotation or libration of Venus—he was not sure which—in about twenty-three hours.[835] By Bianchini in 1726 the period was augmented to twenty-four days eight hours. J. J. Cassini, however, in 1740, showed that the data collected by both observers were consistent with rotation in twenty-three hours twenty minutes.[836] So the matter rested until Schroeter's time. After watching nine years in vain, he at last, February 28, 1788, perceived the ordinarily uniform brightness of the planet's disc to be marbled with a filmy streak, which returned periodically to the same position in about twenty-three hours twenty-eight minutes. This approximate estimate was corrected by the application of a more definite criterion. On December 28, 1789, the southern horn of the crescent Venus was seen truncated, an outlying lucid point interrupting the darkness beyond. Precisely the same appearance recurred two years later, giving for the planet's rotation a period of 23h. 21m.[837] To this only twenty-two seconds were added by De Vico, as the result of over 10,000 observations made with the Cauchoix refractor of the Collegio Romano, 1839-41.[838] The axis of rotation was found to be much more bowed towards the orbital plane than that of the earth, the equator making with it an angle of 53 deg. 11'.

These conclusions inspired, it is true, much distrust, consequently there were no received ideas on the subject to be subverted. Nevertheless, a shock of surprise was felt at Schiaparelli's announcement, early in 1890,[839] that Venus most probably rotates after the fashion just previously ascribed to Mercury. A continuous series of observations, from November, 1877, to February, 1878, with their records in above a hundred drawings, supplied the chief part of the data upon which he rested his conclusions. They certainly appeared exceptionally well-grounded; and the doubts at first qualifying them were removed by a fresh set of determinations in July, 1895.[840] Most observers had depended, in their attempts to ascertain the rotation-period of Venus, upon evanescent shadings, most likely of atmospheric origin, and scarcely recognisable from day to day. Schiaparelli fixed his attention upon round, defined, lustrously white spots, the presence of which near the cusps of the illuminated crescent has been attested for close upon two centuries. His steady watch over them showed the invariability of their position with regard to the terminator; and this is as much as to say that the regions of day and night do not shift on the surface of the planet. In other words, she keeps the same face always turned towards the sun. Moreover, since her orbit is nearly circular, libratory effects are very small. They amount in fact to only just one-thirtieth of those serving to modify the severe contrasts of climate in Mercury.

Confirmatory evidence of Schiaparelli's result for Venus is not wanting. Thus, observations irreconcilable with a swift rate of rotation were made at Bothkamp in 1871 by Vogel and Lohse;[841] and a drawing executed by Professor Holden with the great Washington reflector, December 15, 1877, showed the same markings in the positions recorded at Milan to have been occupied by them eight hours previously. Further, a series of observations, carried out by M. Perrotin at Nice, May 15 to October 4, 1890, and from Mount Mounier in 1895-6, with the special aim of testing the inference of synchronous rotation and revolution, proved strongly corroborative of it.[842] A remarkable collection of drawings made by Mr. Lowell in 1896 appeared decisive in its favour;[843] Tacchini at Rome,[844] Mascari at Catania and Etna,[845] Cerulli at Terano,[846] obtained in 1892-6 evidence similar in purport. On the other hand, Niesten of Brussels found reason to revert to Vico's discarded elements for the planet's rotation;[847] and Trouvelot,[848] Stanley Williams,[849] Villiger,[850] and Leo Brenner,[851] so far agreed with him as to adopt a period of approximately twenty-four hours. Finally, E. Von Oppolzer suggested an appeal to the spectroscope;[852] and Belopolsky secured in 1900[853] spectrograms apparently marked by the minute displacements corresponding to a rapid rate of axial movement. But they were avowedly taken only as an experiment, with unsuitable apparatus; and the desirable verification of their supposed import is not yet forthcoming. Until it is, Schiaparelli's period of 225 days must be allowed to hold the field.

Effects attributed to great differences of level in the surface of Venus have struck many observers. Francesco Fontana at Naples in 1643 noticed irregularities along the inner edge of the crescent.[854] Lahire in 1700 considered them—regard being had to difference of distance—to be much more strongly marked than those visible in the moon.[855] Schroeter's assertions to the same effect, though scouted with some unnecessary vehemence by Herschel,[856] have since been repeatedly confirmed; amongst others by Maedler, De Vico, Langdon, who in 1873 saw the broken line of the terminator with peculiar distinctness through a veil of auroral cloud;[857] by Denning,[858] March 30, 1881, despite preliminary impressions to the contrary, as well as by C. V. Zenger at Prague, January 8, 1883. The great mountain mass, presumed to occasion the periodical blunting of the southern horn, was precariously estimated by the Lilienthal observer to rise to the prodigious height of nearly twenty-seven miles, or just five times the elevation of Mount Everest! Yet the phenomenon persists, whatever may be thought of the explanation. Moreover, the speck of light beyond, interpreted as the visible sign of a detached peak rising high enough above the encircling shadow to catch the first and last rays of the sun, was frequently discerned by Baron Van Ertborn in 1876;[859] while an object near the northern horn of the crescent, strongly resembling a lunar ring-mountain, was delineated both by De Vico in 1841 and by Denning forty years later.

We are almost equally sure that Venus, as that the earth is encompassed with an atmosphere. Yet, notwithstanding luminous appearances plainly due to refraction during the transits both of 1761 and 1769, Schroeter, in 1792, took the initiative in coming to a definite conclusion on the subject.[860] It was founded, first, on the rapid diminution of brilliancy towards the terminator, attributed to atmospheric absorption; next, on the extension beyond a semicircle of the horns of the crescent; lastly, on the presence of a bluish gleam illuminating the early hours of the Cytherean night with what was taken to be genuine twilight. Even Herschel admitted that sunlight, by the same effect through which the heavenly bodies show visibly above our horizons while still geometrically below them, appeared to be bent round the shoulder of the globe of Venus. Ample confirmation of the fact has since been afforded. At Dorpat in May, 1849, the planet being within 3 deg. 26' of inferior conjunction, Maedler found the arms of waning light upon the disc to embrace no less than 240 deg. of its extent;[861] and in December, 1842, Mr. Guthrie, of Bervie, N.B., actually observed, under similar conditions, the whole circumference to be lit up with a faint nebulous glow.[862] The same curious phenomenon was intermittently seen by Mr. Leeson Prince at Uckfield in September, 1861;[863] but with more satisfactory distinctness by Mr. C. S. Lyman of Yale College,[864] before and after the conjunction of December 11, 1866, and during nearly five hours previous to the transit of 1874, when the yellowish ring of refracted light showed at one point an approach to interruption, possibly through the intervention of a bank of clouds. Again, on December 2, 1898, Venus being 1 deg. 45' from the sun's centre, Mr. H. N. Russell, of the Halsted Observatory, descried the coalescence of the cusps, and founded on the observation a valuable discussion of such effects.[865] Taking account of certain features in the case left unnoticed by Neison[866] and Proctor,[867] he inferred from them the presence of a Cytherean atmosphere considerably less refractive than our own, although possibly, in its lower strata, encumbered with dust or haze.