Herschel meantime kept them under watch and ward, and after the lapse of a score of years found himself in a position to speak decisively. On July 1, 1802, he informed the Royal Society that “casual situations will not account for the multiplied phenomena of double stars,” adding, “I shall soon communicate a series of observations proving that many of them have already changed their situation in a progressive course, denoting a periodical revolution round each other.” A year later he amply fulfilled this pledge. Discussing in detail the displacements brought to light by his patient measurements, he made it clear that they could be accounted for only by supposing the six couples in question to be “real binary combinations, intimately held together by the bond of mutual attraction.” His conclusion was, in each case, ratified by subsequent observation. The stars instanced by him—Castor, Gamma Leonis, Epsilon Boötis, Delta Serpentis, Gamma Virginis, and Zeta Herculis—are all noted binaries. Not satisfied with establishing the fact, Herschel assigned the periods of their revolutions. But he could only do so on the hypothesis of circular motion, while the real orbits are highly elliptical. His estimates then went necessarily wide of the mark. For one pair only, he was able to use an observation anterior to his own. Bradley had roughly fixed, in 1759, the relative position of the components of Castor, the finest double star in the northern heavens; and the preservation of the record in Dr. Maskelyne’s note-book extended by twenty years the basis of Herschel’s conclusions regarding this system.
He continued, in 1803, his discussions of double stars; announced a leisurely circulation of both the pairs composing the typical “double-double star,” Epsilon Lyræ; and conjectured the union of the two into one grand whole—a forecast verified by the evidence of common proper motion. The Annus Magnus of the quadruple system cannot, according to Flammarion, be less than a million of years.
The discovery of binary stars was, in Arago’s phrase, “one with a future.” In itself an amazing revelation, it marked the beginning of a series of investigations of immense variety and importance. By it, a science of sidereal mechanics was shown to be possible; the sway of gravitation received an unlimited extension; and the perception of order, which is the precursor of knowledge, ranged at once over the whole visible creation. Herschel, it is true, had not the means of formally proving that stellar orbits are described in obedience to the Newtonian law. His affirmative assertion rested only on the analogy of the solar system. But the rightness of his judgment has never seriously been called in question.
His research into the transport of the solar system through space proved, as Bessel said, that the activity of his mind was independent of the stimulus supplied by his own observations. It was one of his most brilliant performances.
The detection of progressive star-movements was due to Halley. It was announced in 1718. The bright objects spangling the sky are then “fixed” only in name. “But if the proper motion of the stars be admitted,” asked Herschel, “who can deny that of our sun?” The same idea had occurred to several earlier astronomers, but only one, Tobias Mayer, of Göttingen, had tried to test it practically; and he had failed. “To discern the proper motion of the sun between so many other motions of the stars,” Herschel might well designate “an arduous task.” Yet it was not on that account to be neglected. The conditions of the problem were perfectly clear to him. If the sun alone were in motion, the stars should unanimously appear to drift backward from the “apex,” or point on the sphere towards which his journey was directed. The heavens would open out in front of his advance, and close up behind. The effect was compared by Mayer to the widening prospect and narrowing vista of trees to a man walking through a forest. On this supposition, the perspective displacements of any two stars sufficiently far apart in the sky would suffice to determine the solar apex. For it should coincide with the intersection of the two great circles continuing the directions of those displacements. But the question is far from being of this elementary nature. The stars are all flitting about on their own account, after—to our apprehension—a haphazard fashion. The sole element of general congruity traceable among them is that “systematic, or higher, parallax,” by which each of them is, according to a determinate proportion, inevitably affected. If this can be elicited, the line of the sun’s progress becomes at once known.
Herschel treated the subject in the simplest possible manner. Striking a balance between the proper motions of only seven stars, he deduced, in 1783, from simple geometrical considerations, an apex for the sun’s way, marked by the star Lambda Herculis. But while he seemed to proceed by rule, he was really led by the unerring instinct of genius. His mode of conducting an investigation, small in compass, yet almost inconceivably grand in import, distances praise. Its directness and apparent artlessness strike us dumb with wonder. Eminently suited to the materials at his command, it was summary, yet, within fairly narrow limits, secure. And the result has stood the test of time. It ranks, even now, as a valuable approximation to the truth. He himself regarded his essay as nothing more than an experimental effort. In a letter to Dr. Wilson, of Glasgow, he expressed his apprehensions lest his paper on the sun’s motion “might be too much out of the way to deserve the notice of astronomers.”
Provided with Maskelyne’s table of thirty-six proper motions, he resumed the subject in 1805. He now employed a graphical method, drawing great circles to represent the observed stellar movements, and planting his apex impartially in the midst of their intersections. It was, however, less happily located than that of 1783. The constellation Hercules again just included it; but it lay certainly too far west, and probably too far north. The memoir conveying the upshot of the research is, none the less, a masterpiece. Philosophy and common-sense have rarely been so fortunately blended as in this discussion. Without any mathematical apparatus, the plan of attack upon a recondite problem is expounded with the utmost generality and precision. The reasoning is strong and sure; intelligible to the ignorant, instructive to the learned.
In his earlier paper, Herschel, while venturing only to “offer a few distant hints” as to the rate of the sun’s travelling, expressed the opinion that it could “certainly not be less than that which the earth has in her annual orbit.” That is to say, his minimum estimate was then nineteen miles per second. A direct inquiry, on the other hand, convinced him, in 1806, that the solar motion, viewed at right angles from the distance of Sirius, would cover yearly an arc of 1″. 112. This he called “its quantity;” the corresponding velocity remained undetermined. We can, however, now, since the real distance of his assumed station has been determined, translate this angular value into a linear speed of about nine miles a second. The mean of his two estimates, or fourteen miles a second, probably differs little from the actual rate at which the solar system is being borne to its unimaginable destination.
His conclusions regarding the solar translation obtained little notice, and less acceptance from his contemporaries and immediate successors. His son rejected them as untrustworthy; Bessel, the greatest authority of his time in the science of “how the heavens move,” declared in 1818 that the sun’s apex might be situated in any other part of the sky with as much probability as in the constellation Hercules. Not until Argelander, by a strict treatment of multiplied and improved data, arrived in 1837 at practically the same result, did Herschel’s anticipatory efforts obtain the recognition they deserved. Scarcely in any department has there been put on record so well-directed a leap into the dark of coming discovery.
The systematic light-measurement of the stars began with the same untiring investigator. He described in 1796 the method since named that of “sequences,” and presented to the Royal Society the first of six Photometric Catalogues embracing nearly all the 2,935 stars in Flamsteed’s “British Catalogue.” They gave comparative brightnesses estimated with the naked eye; classification by magnitudes was put aside as vague and misleading. The “sequences” serving for their construction were lists of stars arranged, by repeated trials, in order of lustre, and rendered mutually comparable by the inclusion in each of a few members of the preceding series. Their combination into a catalogue was then easily effected. “Simple as my method is in principle,” he remarked, “it is very laborious in its progress.” On a restricted scale it is still employed for following the gradations of change in variable stars.