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no doubling of the lines can be seen, the inference is that the companion star is nearly or quite dark, so that as the two revolve round one another the spectrum of the bright star shifts in the manner observed. Thus the eclipse-theory of Algol’s variability received a striking verification.

A number of other cases of both classes of spectroscopic binary stars (as they may conveniently be called) have since been discovered. The upper part of fig. 103 shews the doubling of one of the lines in the spectrum of the double star β Aurigae; and the lower part shews the corresponding part of the spectrum at a time when the line appeared single.

315. Variable stars of different kinds have received a good deal of attention during this century, particularly during the last few years. About 400 stars are now clearly recognised as variable, while in a large number of other cases variability of light has been suspected; except, however, in a few cases, like that of Algol, the causes of variability are still extremely obscure.

316. The study of the relative brightness of stars—a branch of astronomy now generally known as stellar photometry—has also been carried on extensively during the century and has now been put on a scientific basis. The traditional classification of stars into magnitudes, according to their brightness, was almost wholly arbitrary, and decidedly uncertain. As soon as exact quantitative comparisons of stars of different brightness began to be carried out on a considerable scale, the need of a more precise system of classification became felt. John Herschel was one of the pioneers in this direction; he suggested a scale capable of precise expression, and agreeing roughly, at any rate as far as naked-eye stars are concerned, with the current usages; while at the Cape he measured carefully the light of a large number of bright stars and classified them on this principle. According to the scale now generally adopted, first suggested in 1856 by Norman Robert Pogson (1829-1891), the light of a star of any magnitude bears a fixed ratio (which is taken to be 2·512 ...) to that of a star of the next magnitude. The number is so chosen that a star of the sixth magnitude—thus defined—is 100 times fainter than one of the first magnitude.171 Stars of intermediate brightness have magnitudes expressed by fractions which can be at once calculated (according to a simple mathematical rule) when the ratio of the light received from the star to that received from a standard star has been observed.172

Most of the great star catalogues (§ 280) have included estimates of the magnitudes of stars. The most extensive and accurate series of measurements of star brightness have been those executed at Harvard and at Oxford under the superintendence of Professor E. C. Pickering and the late Professor Pritchard respectively. Both catalogues deal with stars visible to the naked eye; the Harvard catalogue (published in 1884) comprises 4,260 stars between the North Pole and 30° southern declination, and the Uranometria Nova Oxoniensis (1885), as it is called, only goes 10° south of the equator and includes 2,784 stars. Portions of more extensive catalogues dealing with fainter stars, in progress at Harvard and at Potsdam, have also been published.

Fig. 104.—The Milky Way near the cluster in Perseus. From a photograph by Professor Barnard.

[To face p. 405.

317. The great problem to which Herschel gave so much attention, that of the general arrangement of the stars and the structure of the system, if any, formed by them and the nebulae, has been affected in a variety of ways by the additions which have been made to our knowledge of the stars. But so far are we from any satisfactory solution of the problem that no modern theory can fairly claim to represent the facts now known to us as well as Herschel’s earlier theory fitted the much scantier stock which he had at his command. In this as in so many cases an increase of knowledge has shewn the insufficiency of a previously accepted theory, but has not provided a successor. Detailed study of the form of the Milky Way (cf. fig. 104) and of its relation to the general body of stars has shewn the inadequacy of any simple arrangement of stars to represent its appearance; William Herschel’s cloven grindstone, the ring which his son was inclined to substitute for it as the result of his Cape studies, and the more complicated forms which later writers have suggested, alike fail to account for its peculiarities. Again, such evidence as we have of the distance of the stars, when compared with their brightness, shews that there are large variations in their actual sizes as well as in their apparent sizes, and thus tells against the assumption of a certain uniformity which underlay much of Herschel’s work. The “island universe” theory of nebulae, partially abandoned by Herschel after 1791 (chapter XII., § 260), but brought into credit again by Lord Rosse’s discoveries (§ 310), scarcely survived the spectroscopic proof of the gaseous character of certain nebulae. Other evidence has pointed clearly to intimate relations between nebulae and stars generally; Herschel’s observation that nebulae are densest in regions farthest from the Milky Way has been abundantly verified—as far as irresoluble nebulae are concerned—while obvious star clusters shew an equally clear preference for the neighbourhood of the Milky Way. In many cases again individual stars or groups seen on the sky in or near a nebula have been clearly shewn, either by their arrangement or in some cases by peculiarities of their spectra, to be really connected with the nebula, and not merely to be accidentally in the same direction. Stars which have bright lines in their spectra (§ 312) form another link connecting nebulae with stars.

A good many converging lines of evidence thus point to a greater variety in the arrangement, size, and structure of the bodies with which the telescope makes us acquainted than seemed probable when sidereal astronomy was first seriously studied; they also indicate the probability that these bodies should be regarded as belonging to a single system, even if it be of almost inconceivable complexity, rather than to a number of perfectly distinct systems of a simpler type.

318. Laplace’s nebular hypothesis (chapter XI., § 250) was published a little more than a century ago (1796), and has been greatly affected by progress in various departments of astronomical knowledge. Subsequent discoveries of planets and satellites (§§ 294, 295) have marred to some extent the uniformity and symmetry of the motions of the solar system on which Laplace laid so much stress; but it is not impossible to give reasonable explanations of the backward motions of the satellites of the two most distant planets, and of the large eccentricity and inclination of the paths of some of the minor planets, while apart from these exceptions the number of bodies the motions of which have the characteristics which Laplace pointed out has been considerably increased. The case for some sort of common origin of the bodies of the solar system has perhaps in this way gained as much as it has lost. Again, the telescopic evidence which Herschel adduced (chapter XII., § 261) in favour of the existence of certain processes of condensation in nebulae has been strengthened by later evidence of a similar character, and by the various pieces of evidence already referred to which connect nebulae with single stars and with clusters. The differences in the spectra of stars also receive their most satisfactory explanation as representing different stages of condensation of bodies of the same general character.

319. An entirely new contribution to the problem has resulted from certain discoveries as to the nature of heat, culminating in the recognition (about 1840-50) of heat as only one form of what physicists now call energy, which manifests itself also in the motion of bodies, in the separation of bodies which attract one another, as well as in various electrical, chemical, and other ways. With this discovery was closely connected the general theory known as the conservation of energy, according to which energy, though capable of many transformations, can neither be increased nor decreased in quantity. A body which, like the sun, is giving out heat and light is accordingly thereby losing energy, and is like a machine doing work; either then it is receiving energy from some other source to compensate this loss or its store of energy is diminishing. But a body which goes on indefinitely giving out heat and light without having its store of energy replenished is exactly analogous to a machine which goes on working indefinitely without any motive power to drive it; and both are alike impossible.

The results obtained by John Herschel and Pouillet in 1836 (§ 307) called attention to the enormous expenditure of the sun in the form of heat, and astronomers thus had to face the problem of explaining how the sun was able to go on radiating heat and light in this way. Neither in the few thousand years of the past covered by historic records, nor in the enormously great periods of which geologists and biologists take account, is there any evidence of any important permanent alteration in the amount of heat and light received annually by the earth from the sun. Any theory of the sun’s heat must therefore be able to account for the continual expenditure of heat at something like the present rate for an immense period of time. The obvious explanation of the sun as a furnace deriving its heat from combustion is found to be totally inadequate when put to the test of figures, as the sun could in this way be kept going at most for a few thousand years. The explanation now generally accepted was first given by the great German physicist Hermann von Helmholtz (1821-1894) in a popular lecture in 1854. The sun possesses an immense store of energy in the form of the mutual gravitation of its parts; if from any cause it shrinks, a certain amount of gravitational energy is necessarily lost and takes some other form. In the shrinkage of the sun we have therefore a possible source of energy. The precise amount of energy liberated by a definite amount of shrinkage of the sun depends upon the internal distribution of density in the sun, which is uncertain, but making any reasonable assumption as to this we find that the amount of shrinking required to supply the sun’s expenditure of heat would only diminish the diameter by a few hundred feet annually, and would therefore be imperceptible with our present telescopic power for centuries, while no earlier records of the sun’s size are accurate enough to shew it. It is easy to calculate on the same principles the amount of energy liberated by a body like the sun in shrinking from an indefinitely diffused condition to its present state, and from its present state to one of assigned greater density; the result being that we can in this way account for an expenditure of sun-heat at the present rate for a period to be counted in millions of years in either past or future time, while if the rate of expenditure was less in the remote past or becomes less in the future the time is extended to a corresponding extent.

No other cause that has been suggested is competent to account for more than a small fraction of the actual heat-expenditure of the sun; the gravitational theory satisfies all the requirements of astronomy proper, and goes at any rate some way towards meeting the demands of biology and geology.

If then we accept it as provisionally

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