He began by asserting what is self-evident—that faint stars are, “one with another,” more remote than bright ones; and he argued thence, reasonably enough, that the relative mean distances of the stars, taken order by order, might be inferred from their relative mean magnitudes. Next he pointed out that more space would be available for their accommodation in proportion to the cubes of their mean distances. Here lies the value of the method. It sets up, as Herschel said, “a standard of reference” with regard to stellar distribution. It makes it possible to compare actual stellar density, at a given mean distance, with a “certain properly modified equality of scattering.” By patiently calling over the roll of successive magnitudes, information may be obtained regarding over- and under-populated districts of space.
Herschel’s reasonings on the subject are perfectly valid, but for practical purposes far in advance of the time. Their application demanded a knowledge of stellar light-gradations, which, even now, has been only partially attained. His surprising anticipation of this mode of inquiry came, therefore, to nothing.
His device of “limiting apertures” was a simultaneous invention. It was designed as a measure of relative star-distances. Pointing two similar telescopes upon two unequal stars, he equalised them to the eye by stopping down the aperture of the instrument directed towards the brighter object. Assuming each to emit the same quantity of light, their respective distances would then be inversely as the diameters of the reflecting surfaces by which they were brought to the same level of apparent lustre. But the enormous real diversities of stellar size and brightness render this plan of action wholly illusory. Even for average estimates, proper motion is apparently a safer criterion of distance than magnitude.
Herschel employed the method of apertures with better success to ascertain the comparative extent of natural and telescopic vision. The boundary of the former was placed at “the twelfth order of distance.” Sirius, that is to say, removed to twelve times its actual remoteness, would be a barely discernible object to the naked eye. The same star carried seventy-five times further away still, could be seen as a faint light-speck with his twenty-foot telescope; and, transported 192 times beyond the visual limit, would make a similar appearance in the field of the forty-foot. These figures, multiplied by twelve, represented, in his expressive phrase, the “space-penetrating power” of his instruments. Their range extended respectively to 900 and 2,300 times the distance of his “standard star.” He estimated, moreover, that, through the agency of the larger, light might become sensible to the eye after a journey lasting nearly seven thousand years! So that, as he said, his telescopes penetrated both time and space.
His last observation of the Milky Way showed it to be in parts “fathomless,” even with the forty-foot. No sky-background could be seen, but only the dim glow of “star-dust.” This effect he attributed to the immeasurable extension, in those directions, of the stellar system. The serried orbs composing it, as they lay further and further from the eye, became at last separately indistinguishable. Herschel, as has been said, formulated no second theory of galactic structure after that of 1784–5 had been given up. What he thought on the subject, with ripened experience for his guide, can only be gathered piecemeal from his various writings. The general appearance of
That “broad and ample road, whose dust is gold,
And pavement stars,”
he described as “that of a zone surrounding our situation in the solar system, in the shape of a succession of differently condensed patches of brightness, intermixed with others of a fainter tinge.” And he evidently considered this seeming to be in fair accord with reality. The “patches of brightness” stood for genuine clusters, incipient, visibly forming, or formed. They are made up of stars not less lustrous, but much more closely collected than Sirius, Arcturus, or Capella. The smallness of galactic stars would thus be an effect of distance, while their crowding is a physical fact. The whole of these clusters are (on Herschel’s view) aggregated into an irregular, branching ring, distinct from, although bound together into one system with the brilliants of the constellations. “Our sun,” he emphatically affirmed in 1817, “with all the stars we can see with the eye, are deeply immersed in the Milky Way, and form a component part of it.”
He took leave of the subject which had engrossed so many of his thoughts in a paper read before the Royal Society, June 11th, 1818. In it he showed how the “equalising” principle could be applied to determine the relative distances of “globular and other clusters,” provided only that their component stars are of the rank of Sirius. It is improbable, however, that this condition is fulfilled. In open groups, such as the Pleiades, enormous suns are most likely connected with minute self-luminous bodies; but the stars compressed into “globular clusters” appear to be more uniform, and may, perhaps, be intermediate in magnitude. Yet here again, the only thing certain is the prevalence of endless variety. Celestial systems are not turned out by the dozen, like articles from a factory. Each differs from the rest in scale, in structure, in mechanism. Attempts to reduce all to any common standard must then prove futile. Disparities of distance are of course concerned in producing their varieties of aspect, coarse-looking “balls of stars” being, necessarily, on the whole, less remote than those of smoother texture. Finer graining, however, may also be due to a composition out of smaller and closer masses. The two causes concur, and the share of each in producing a certain effect cannot, in any individual case, be apportioned.
Herschel was indeed far too philosophical to adopt rigid lines of argument. His reasoning did not extend “so far as to exclude a real difference, not only in the size, but also in the number and arrangement of the stars in different clusters.” Nevertheless, the discussion founded upon it is no longer convincing. To modern astronomers it appears to travel quite wide of the mark. Its interest consists in the proof given by it that the problem of sidereal distances, the original incentive to Herschel’s reviews of the heavens, attracted his attention to the very end of his thinking life. Throughout his long career, the profundities of the universe haunted him. He sought, per fas, per nefas, trustworthy measures of the “third dimension” of celestial space. The object of his search was out of reach, and has not even now been fully attained; but the path it led him by was strewn with discoveries.