Sidereal science is, on its geometrical side, of modern development; on its physical side, of modern origin. The places of the stars, as referred to certain lines and points on the surface of an imaginary hollow sphere, are obtained now on essentially the same principles as by Hipparchus, only with incomparably greater refinement. And refinement is everything where the stars are concerned. Significant changes among them can only be brought out by minute accuracy. To a rough discernment their relative situations are immutable; and systematic inquiries into their movements hence became possible only when the grosser errors were banished from observation. Bessel's discovery of Bradley's exactitude gave the signal for such inquiries. It became worth while to re-observe stars already so well determined that discrepancies might safely be interpreted to mean real change.

Thus it is only within the last sixty or seventy years that the stars have been extensively catalogued for their own sakes, and no longer in the undivided interests of planetary or cometary astronomy. The scope of such labours now widens continually. For the objects of them are all but innumerable, and the nineteenth century has brought to bear on its large schemes of scientific ambition heretofore undreamt-of facilities for executing them by combination.

The strong presumption that the law of gravitation would prove truly universal has been fully borne out by investigations of stellar orbits. Binary stars circulate, it can be unhesitatingly asserted, under the influence of the identical force by which the sun sways the movements of the planets, the earth the movements of the moon. It is true that this does not admit of mathematical demonstration, but the overwhelming improbability of any other supposition amounts practically to the same thing. The revolutions of the stars are hence calculable, because conducted on familiar principles; their velocities have the same relation to mass, their perturbations may lead to similar inferences as in the solar system.

Observations, however, must precede calculations; and they are rendered arduous in double stars by the extreme minuteness of the intervals to be measured. Many revolving pairs never separate to the apparent extent of a single second of arc; yet this fraction of a second may represent, in abridgment, a span of some thousands of millions of miles. Infinitesimal errors, magnified in this proportion, become of enormous importance, and often impenetrably disguise the real aspect of the facts.

For determining the relative situations of adjacent stars, two kinds of measurement are evidently needed. The first gives their distance apart, the second the direction of the line joining them as regards some fixed line of reference.

We have seen, in the last chapter, that stars varying their light in periods of less than fifty days stand apart in several important respects from those undergoing slower changes. The distinction is accentuated by the tendency apparent in each class to group its members as far as possible from the frontier-line of separation from the other. Thus, long periods for the most part exceed three hundred days, while a large majority of short periods fall below ten. Thirty-eight stars in all are reckoned as variable within fifty days; of these thirty-two complete an oscillation in less than twenty, twenty-seven (including two with imperfectly ascertained periods) in less than ten days. A comparison of figures 17 and 18 shows that, among short periods taken en masse, those of three to four days predominate; those of five to eight days when Algol variables are excluded.

Variables of short period are, as we have said, nearly all white or yellow stars. A very few are reddish; and one—W Virginis—is suspected to possess a banded spectrum. R Lyræ, a star of about 4·5 magnitude, with a superb spectrum of the third type, is nominally variable in forty-six days, but its changes are so trifling and so imperfectly rhythmical as to suggest that its proper place is with β Pegasi and α Herculis among stars affected by abortive periodicity.

The further resolvability of a great many double stars is perhaps the most curious result of modern improvements in the optical means of observing them. With every addition to the defining power of telescopes, the visible complexity of stellar systems has increased so rapidly as to inspire a suspicion that simple binary combinations may be an exception rather than the rule. The frequency with which what appeared to be such have yielded to the disintegrating scrutiny of Mr. Burnham and others, suggests at any rate the presence of an innate tendency, and seems to show that the duplicity of stars is no accident of nebular condensation, but belongs essentially to the primitive design of their organisation. Although we can never become fully acquainted with all the detailed arrangements of stellar systems, we are then led to suppose them far more elaborate and varied than appears at first sight. Each, we cannot doubt, is adapted by exquisite contrivances to its special end, reflecting, in its untold harmonies of adjustment, the Supreme Wisdom from which they emanate.

The continuance of the process of optical dissociation, begun by the splitting-up of an apparently simple star, sometimes shows the primary, sometimes the satellite, not unfrequently both primary and satellite, to be very closely double. Ternary systems are accordingly of two kinds. In one, the smaller star consists of two in mutual circulation, and concurrent revolution round a single governing body; in the other, an intimately conjoined pair guides the movements of an unattended attendant.

The Milky Way shows to the naked eye as a vast, zoneshaped nebula; but is resolved, with very slight optical assistance, into innumerable small stars. Its stellar constitution, already conjectured by Democritus, was, in fact, one of Galileo's earliest telescopic discoveries. The general course of the formation, however, can only be traced through the perception of the cloudy effect impaired by the application even of an opera-glass. Rendered the more arduous by this very circumstance, its detailed study demands exceptional eyesight, improved by assiduous practice in catching fine gradations of light. Our situation, too, in the galactic plane is the most disadvantageous possible for purposes of survey. Groups behind groups, systems upon systems, streams, sheets, lines, knots of stars, indefinitely far apart in space, may all be projected without distinction upon the same sky-ground. Unawares, our visual ray sounds endless depths, and brings back only simultaneous information about the successive objects met with. We are thus presented with a flat picture totally devoid of perspective-indications. Only by a long series of inductions (if at all) can we hope to arrange the features of the landscape according to their proper relations.

To the uncritical imagination, the Milky Way represents a sort of glorified track through the skies—

The stars differ obviously in colour. Three or four among the brightest strike the eye by their ardent glow, others are tinged with yellow, and the white light of several has a bluish gleam like that of polished steel. Reddish tints are, however, in the few cases in which they affect lucid stars, the most noticeable, and were the only ones noticed by the ancients.

Ptolemy designates as ‘fiery red’ (ὑπόκιῤῥοι) the following six stars: Aldebaran, Arcturus, Betelgeux, Antares, Pollux, and—mirabile dictu—Sirius! all the rest being indiscriminately classed as ‘yellow’ (ξάνθοι). Now Pollux at present, though by no means red, is at least yellowish, but Sirius is undeniably white with a cast of blue. A marked change in its colour since the Alexandrian epoch might thus at first sight appear certain, the more so that Seneca makes express mention of the dog-star as being ‘redder than Mars;’ Horace has ‘rubra Canicula’ as typical of the heat of summer; and Cicero, in his translation of Aratus, speaks of its ‘ruddy light.’ Nevertheless the case is doubtful. The questionable epithet, in all probability, crept into the ‘Almagest’ by a transcriber's error, Ptolemy not being responsible for it. In the early Arabic versions of that work it evidently did not occur, for Arab astronomers of the tenth and subsequent centuries ignored the imputation of colour to the dog star, and Albategnius stated the number of Ptolemy's red stars as five.

The facts connected with the light-changes of stars are in the highest degree strange and surprising; and wonder is not lessened by our daily-growing familiarity with them. They are of everyday occurrence, they can be predicted beforehand, in many cases with nearly as close accuracy as an eclipse of the sun or moon, and they affect in manifold ways a great number of objects. Stellar variability is of every kind and degree. With the regularity of clockwork some stars lose and regain a fixed proportion of their light; others show fitful accessions of luminosity succeeded by equally fitful relapses into obscurity; many waver, in appearance lawlessly, about a datum-level of lustre itself perhaps slowly rising or sinking. The rule of change of a great number is that of an evident, though strongly disturbed periodicity; a few seem to spend all their powers of shining in one amazing outburst, after which they return to their pristine invisibility or insignificance.

The amount is as much diversified as the manner of fluctuation. Changes of brightness so minute as almost to defy detection are linked on by a succession of graduated examples to conflagrations in which emissive intensity is multiplied a thousand times or more in a few hours. The range of variation is in some stars sensibly uniform; they subside during each crisis of change to the same precise point of dimness, and recover, without diminution or excess, just so much light as they had before.

When all the stars blaze out on a clear, moonless night, it seems as if it would be impossible to count them; and yet it is seldom that more than 2,000 are visible together to the unaided eye. The number, however, depends very much upon climate and sharpness of sight. Argelander enumerated at Bonn, where rather more than eight-tenths of the sphere come successively into view, 3,237 stars. But of these no more than 2,000 could be, at any one time, above the horizon, and so many would not be visibly above it, owing to the quenching power of the air in its neighbourhood. Heis, at Münster, saw 1,445 stars more than Argelander at Bonn; Houzeau recorded 5,719 at Jamaica; Gould 10,649 at Cordoba in South America. The discrepancies of these figures, setting aside the comparatively slight effect of the increased area of the heavens displayed in low latitudes, are due to the multitude of small stars always, it might be said, hovering on the verge of visibility. If, indeed, the atmosphere could be wholly withdrawn, fully 25,000 stars would, according to a trustworthy estimate, become apparent to moderately good eyes.

Our system of designating the stars has come down to us from a hoar antiquity. It is a highly incommodious one. ‘The constellations,’ Sir John Herschel remarks, ‘seem to have been almost purposely named and delineated to cause as much confusion and inconvenience as possible.