Meanwhile a result of the same kind, but of a more striking character than either Bessel's or Struve's, had been obtained, one might almost say casually, by a different method and in a distant region. Thomas Henderson, originally an attorney's clerk in his native town of Dundee, had become known for his astronomical attainments, and was appointed in 1831 to direct the recently completed observatory at the Cape of Good Hope. He began observing in April, 1832, and, the serious shortcomings of his instrument notwithstanding, executed during the thirteen months of his tenure of office a surprising amount of first-rate work. With a view to correcting the declination of the lustrous double star α Centauri (which ranks after Sirius and Canopus as the third brightest orb in the heavens), he effected a number of successive determinations of its position, and on being informed of its very considerable proper motion (3·6′ annually), he resolved to examine the observations already made for possible traces of parallactic displacement. This was done on his return to Scotland, where he filled the office of Astronomer Royal from 1834 until his premature death in 1844. The result justified his expectations. From the declination measurements made at the Cape and duly reduced, a parallax of about one second of arc clearly emerged (diminished by Gill's and Elkin's observations, 1882-1883, to O·75′); but, by perhaps an excess of caution, was withheld from publication until fuller certainty was afforded by the concurrent testimony of Lieutenant Meadows's determinations of the same star's right ascension.[76] When at last, January 9, 1839, Henderson communicated his discovery to the Astronomical Society, he could no longer claim the priority which was his due. Bessel had anticipated him with the parallax of 61 Cygni by just two months.
Thus from three different quarters, three successful and almost simultaneous assaults were delivered upon a long-beleaguered citadel of celestial secrets. The same work has since been steadily pursued, with the general result of showing that, as regards their overwhelming majority, the stars are far too remote to show even the slightest trace of optical shifting from the revolution of the earth in its orbit. In nearly a hundred cases, however, small parallaxes have been determined, some certainly (that is, within moderate limits of error), others more or less precariously. The list is an instructive one, in its omissions no less than in its contents. It includes stars of many degrees of brightness, from Sirius down to a nameless telescopic star in the Great Bear;[77] yet the vicinity to the earth of this minute object is so much greater than that of the brilliant Vega, that the latter transported to its place would increase in lustre thirty-eight times. Moreover, many of the brightest stars are found to have no sensible parallax, while the majority of those ascertained to be nearest to the earth are of fifth, sixth, even ninth magnitudes. The obvious conclusions follow that the range of variety in the sidereal system is enormously greater than had been supposed, and that estimates of distance based upon apparent magnitude must be wholly futile. Thus, the splendid Canopus, Betelgeux, and Rigel can be inferred, from their indefinite remoteness, to exceed our sun thousands of times in size and lustre; while many inconspicuous objects, which prove to be in our relative vicinity, must be notably his inferiors. The limits of real stellar magnitude are then set very widely apart. At the same time, the so-called "optical" and "geometrical" methods of relatively estimating star-distances are both seen to have a foundation of fact, although so disguised by complicated relations as to be of very doubtful individual application. On the whole, the chances are in favour of the superior vicinity of a bright star over a faint one; and, on the whole, the stars in swiftest apparent motion are amongst those whose actual remoteness is least. Indeed, there is no escape from either conclusion, unless on the supposition of special arrangements in themselves highly improbable, and, we may confidently say, non-existent.
The distances even of the few stars found to have measurable parallaxes are on a scale entirely beyond the powers of the human mind to conceive. In the attempt both to realize them distinctly, and to express them conveniently, a new unit of length, itself of bewildering magnitude, has originated. This is what we may call the light-journey of one year. The subtle vibrations of the ether, propagated on all sides from the surface of luminous bodies, travel at the rate of 186,300 miles a second, or (in round numbers) six billions of miles a year. Four and a third such measures are needed to span the abyss that separates us from the nearest fixed star. In other words, light takes four years and four months to reach the earth from α Centauri; yet α Centauri lies some ten billions of miles nearer to us (so far as is yet known) than any other member of the sidereal system!
The determination of parallax leads, in the case of stars revolving in known orbits, to the determination of mass; for the distance from the earth of the two bodies forming a binary system being ascertained, the seconds of arc apparently separating them from each other can be translated into millions of miles; and we only need to add a knowledge of their period to enable us, by an easy sum in proportion, to find their combined mass in terms of that of the sun. Thus, since—according to Dr. Doberck's elements—the components of α Centauri revolve round their common centre of gravity at a mean distance nearly 25 times the radius of the earth's orbit, in a period of 88 years, the attractive force of the two together must be just twice the solar. We may gather some idea of their relations by placing in imagination a second luminary like our sun in circulation between the orbits of Neptune and Uranus. But systems of still more majestic proportions are reduced by extreme remoteness to apparent insignificance. A double star of the fourth magnitude in Cassiopeia (Eta), to which a small parallax is ascribed on the authority of O. Struve, appears to be above eight times as massive as the central orb of our world; while a much less conspicuous pair—85 Pegasi—exerts, if the available data can be depended upon, no less than thirteen times the solar gravitating power.
Further, the actual rate of proper motions, so far as regards that part of them which is projected upon the sphere, can be ascertained for stars at known distance. The annual journey, for instance, of 61 Cygni across the line of sight amounts to 1,000, and that of α Centauri to 446 millions of miles. A small star, numbered 1,830 in Groombridge's Circumpolar Catalogue, "devours the way" at the rate of at least 150 miles a second—a speed, in Newcomb's opinion, beyond the gravitating power of the entire sidereal system to control; and μ Cassiopeiæ possesses above two-thirds of that surprising velocity; while for both objects, radial movements of just sixty miles a second were disclosed by Professor Campbell's spectroscopic measurements.
Herschel's conclusion as to the advance of the sun among the stars was not admitted as valid by the most eminent of his successors. Bessel maintained that there was absolutely no preponderating evidence in favour of its supposed direction towards a point in the constellation Hercules.[78] Biot, Burckhardt, even Herschel's own son, shared his incredulity. But the appearance of Argelander's prize-essay in 1837[79] changed the aspect of the question. Herschel's first memorable solution in 1783 was based upon the motions of thirteen stars, imperfectly known; his second, in 1805, upon those of no more than six. Argelander now obtained an entirely concordant result from the large number of 390, determined with the scrupulous accuracy characteristic of Bessel's work and his own. The reality of the fact thus persistently disclosed could no longer be doubted; it was confirmed five years later by the younger Struve, and still more strikingly in 1847[80] by Galloway's investigations, founded exclusively on the apparent displacements of southern stars. In 1859 and 1863, Sir George Airy and Mr. Dunkin (1821-1898),[81] employing all the resources of modern science, and commanding the wealth of material furnished by 1,167 proper motions carefully determined by Mr. Main, reached conclusions closely similar to that indicated nearly eighty years previously by the first great sidereal astronomer; which Mr. Plummer's reinvestigation of the subject in 1883[82] served but slightly to modify. Yet astronomers were not satisfied. Dr. Auwers of Berlin completed in 1866 a splendid piece of work, for which he received in 1888 the Gold Medal of the Royal Astronomical Society. It consisted in reducing afresh, with the aid of the most refined modern data, Bradley's original stars, and comparing their places thus obtained for the year 1755 with those assigned to them from observations made at Greenwich after the lapse of ninety years. In the interval, as was to be anticipated, most of them were found to have travelled over some small span of the heavens, and there resulted a stock of nearly three thousand highly authentic proper motions. These ample materials were turned to account by M. Ludwig Struve[83] for a discussion of the sun's motion, of which the upshot was to shift its point of aim to the bordering region of the constellations Hercules and Lyra. And the more easterly position of the solar apex was fully confirmed by the experiments, with variously assorted lists of stars, of Lewis Boss of Albany,[84] and Oscar Stumpe of Bonn.[85] Fresh precautions of refinement were introduced into the treatment of the subject by Ristenpart of Karlsruhe,[86] by Kapteyn of Groningen,[87] by Newcomb[88] and Porter[89] in America, who ably availed themselves of the copious materials accumulated before the close of the century. Their results, although not more closely accordant than those of their predecessors, combined to show that the journey of our system is directed towards a point within a circle about ten degrees in radius, having the brilliant Vega for its centre. To determine its rate was a still more arduous problem. It involved the assumption, very much at discretion, of an average parallax for the stars investigated; and Otto Struve's estimate of 154 million miles as the span yearly traversed was hence wholly unreliable. Fortunately, however, as will be seen further on, a method of determining the sun's velocity independently of any knowledge of star-distances, has now become available.
As might have been expected, speculation has not been idle regarding the purpose and goal of the strange voyage of discovery through space upon which our system is embarked; but altogether fruitlessly. The variety of the conjectures hazarded in the matter is in itself a measure of their futility. Long ago, before the construction of the heavens had as yet been made the subject of methodical inquiry, Kant was disposed to regard Sirius as the "central sun" of the Milky Way; while Lambert surmised that the vast Orion nebula might serve as the regulating power of a subordinate group including our sun. Herschel threw out the hint that the great cluster in Hercules might prove to be the supreme seat of attractive force;[90] Argelander placed his central body in the constellation Perseus;[91] Fomalhaut, the brilliant of the Southern Fish, was set in the post of honour by Boguslawski of Breslau. Mädler (who succeeded Struve at Dorpat in 1839) concluded from a more formal inquiry that the ruling power in the sidereal system resided, not in any single prepondering mass, but in the centre of gravity of the self-controlled revolving multitude.[92] In the former case (as we know from the example of the planetary scheme), the stellar motions would be most rapid near the centre; in the latter, they would become accelerated with remoteness from it.[93] Mädler showed that no part of the heavens could be indicated as a region of exceptionally swift movements, such as would result from the presence of a gigantic (though possibly obscure) ruling body; but that a community of extremely sluggish movements undoubtedly existed in and near the group of the Pleiades, where, accordingly, he placed the centre of gravity of the Milky Way.[94] The bright star Alcyone thus became the "central sun," but in a purely passive sense, its headship being determined by its situation at the point of neutralisation of opposing tendencies, and of consequent rest. By an avowedly conjectural method, the solar period of revolution round this point was fixed at 18,200,000 years.
The scheme of sidereal government framed by the Dorpat astronomer was, it may be observed, of the most approved constitutional type; deprivation, rather than increase of influence accompanying the office of chief dignitary. But while we are still ignorant, and shall perhaps ever remain so, of the fundamental plan upon which the Galaxy is organised, recent investigations tend more and more to exhibit it, not as monarchical (so to speak), but as federative. The community of proper motions detected by Mädler in the vicinity of the Pleiades may accordingly possess a significance altogether different from what he imagined.
Bessel's so-called "foundation of an Astronomy of the Invisible" now claims attention.[95] His prediction regarding the planet Neptune does not belong to the present division of our subject; a strictly analogous discovery in the sidereal system was, however, also very clearly foreshadowed by him. His earliest suspicions of non-uniformity in the proper motion of Sirius dated from 1834; they extended to Procyon in 1840; and after a series of refined measurements with the new Repsold circle, he announced in 1844 his conclusion that these irregularities were due to the presence of obscure bodies round which the two bright Dog-stars revolved as they pursued their way across the sphere.[96] He even assigned to each an approximate period of half a century. "I adhere to the conviction," he wrote later to Humboldt, "that Procyon and Sirius form real binary systems, consisting of a visible and an invisible star. There is no reason to suppose luminosity an essential quality of cosmical bodies. The visibility of countless stars is no argument against the invisibility of countless others."[97]
An inference so contradictory to received ideas obtained little credit, until Peters found, in 1851,[98] that the apparent anomalies in the movements of Sirius could be completely explained by an orbital revolution in a period of fifty years. Bessel's prevision was destined to be still more triumphantly vindicated. On the 31st of January, 1862, while in the act of trying a new 18-inch refractor, Mr. Alvan G. Clark (one of the celebrated firm of American opticians) actually discovered the hypothetical Sirian companion in the precise position required by theory. It has now been watched through nearly an entire revolution (period 49·4 years), and proves to be very slightly luminous in proportion to its mass. Its attractive power, in fact, is nearly half that of its primary, while it emits only 1/10000th of its light. Sirius itself, on the other hand, possesses a far higher radiative intensity than our sun. It gravitates—admitting Sir David Gill's parallax of 0·38′ to be exact—like two suns, but shines like twenty. Possibly it is much distended by heat, and undoubtedly its atmosphere intercepts a very much smaller proportion of its light than in stars of the solar class. As regards Procyon, visual verification was awaited until November 13, 1896, when Professor Schaeberle, with the great Lick refractor, detected the long-sought object in the guise of a thirteenth-magnitude star. Dr. See's calculations[99] showed it to possess one-fifth the mass of its primary, or rather more than half that of our sun.[100] Yet it gives barely 1/20000th of the sun's light, so that it is still nearer to total obscurity than the dusky satellite of Sirius. The period of forty years assigned to the system by Auwers in 1862[101] appears to be singularly exact.