Observations made by its means would have the advantages of impartiality, mult.i.tude, 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 ma.s.s of acc.u.mulated 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 circ.u.mstances of contacts, the precise determination of which const.i.tuted the only tried, though by no means an a.s.suredly 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 subst.i.tuting 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 pa.s.sed 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 876" (corrected to 8754"), indicating a mean distance of 93,375,000 miles. Mr. Stone obtained a value of ninety-two millions (parallax 888"), and held any parallax less than 884" or more than 893" to be "absolutely negatived"

by the doc.u.ments available.[769] Yet, from the same, Colonel Tupman deduced 881",[770] implying a distance 700,000 miles greater than Stone had obtained. The best French observations of contacts gave a parallax of about 888"; French micrometric measures the obviously exaggerated one of 905".[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 8883" 0034"),[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...o...b..t which lies nearest to that of the earth, and Dr. Gill (now Sir David) took advantage of the circ.u.mstance 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 subst.i.tuting 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 878", 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 887".[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 pa.s.sing 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 8802", 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 pa.s.s 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 exact.i.tude. 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 cla.s.ses--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 acc.u.mulate 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 ent.i.tled to four times as much confidence as any previous one; and if the solar parallax of 8758" 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 sh.o.r.es 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 20445" to 20492". 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 = 8794"). 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 20447" varying from it only to an insignificant extent. Professor Hall had, moreover, deduced nearly the same value (20454") 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 881".[793] Inverting the process, Sir David Gill in 1897 derived the constant from the parallax. If the earth's...o...b..t 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 quant.i.ties 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 s.p.a.ce.

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. Ca.s.sini, _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...o...b..t, the earth is nearer to the sun in January than in June by 3,100,000 miles. The quant.i.ty 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 895"

derived by Leverrier from the above-described inequality in the earth's motion, was corrected by Stone to 891". _Month. Not._, vol. xxviii., p.

25.]

[Footnote 758: _Month. Not._, vol. x.x.xv., p. 156.]

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

[Footnote 760: _Comptes Rendus_, t. xxix., p. 90.]

[Footnote 761: _Ibid._, t. x.x.x., 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 repet.i.tion 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. x.x.xviii., p. 447.]

[Footnote 768: _Ibid._, p. 11.]

[Footnote 769: _Ibid._, p. 294.]