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allowance being made for the heat stopped in the atmosphere as the sun’s rays passed through it, an estimate was formed of the total amount of heat received annually by the earth from the sun, and hence of the total amount radiated by the sun in all directions, an insignificant fraction of which (one part in 2,000,000,000) is alone intercepted by the earth. But the allowance for the heat intercepted in our atmosphere was necessarily uncertain, and later work, in particular that of Dr. S. P. Langley in 1880-81, shews that it was very much under-estimated by both Herschel and Pouillet. According to Herschel’s results, the heat received annually from the sun—including that intercepted in the atmosphere—would be sufficient to melt a shell of ice 120 feet thick covering the whole earth; according to Dr. Langley, the thickness would be about 160 feet.169

308. With his return to England in 1838 Herschel’s career as an observer came to an end; but the working out of the results of his Cape observations, the arrangement and cataloguing of his own and his father’s discoveries, provided occupation for many years. A magnificent volume on the Results of Astronomical Observations made during the years 1834-8 at the Cape of Good Hope appeared in 1847; and a catalogue of all known nebulae and clusters, amounting to 5,079, was presented to the Royal Society in 1864, while a corresponding catalogue of more than 10,000 double and multiple stars was never finished, though the materials collected for it were published posthumously in 1879. John Herschel’s great catalogue of nebulae has since been revised and enlarged by Dr. Dreyer, the result being a list of 7,840 nebulae and clusters known up to the end of 1887; and a supplementary list of discoveries made in 1888-94 published by the same writer contains 1,529 entries, so that the total number now known is between 9,000 and 10,000, of which more than half have been discovered by the two Herschels.

309. Double stars have been discovered and studied by a number of astronomers besides the Herschels. One of the most indefatigable workers at this subject was the elder Struve (§ 279), who was successively director of the two Russian observatories of Dorpat and Pulkowa. He observed altogether some 2,640 double and multiple stars, measuring in each case with care the length and direction of the line joining the two components, and noting other peculiarities, such as contrasts in colour between the members of a pair. He paid attention only to double stars the two components of which were not more than 32″ apart, thus rejecting a good many which William Herschel would have noticed; as the number of known doubles rapidly increased, it was clearly necessary to concentrate attention on those which might with some reasonable degree of probability turn out to be genuine binaries (chapter XII., § 264).

In addition to a number of minor papers Struve published three separate books on the subject in 1827, 1837, and 1852.170 A comparison of his own earlier and later observations, and of both with Herschel’s earlier ones, shewed about 100 cases of change of relative positions of two members of a pair, which indicated more or less clearly a motion of revolution, and further results of a like character have been obtained from a comparison of Struve’s observations with those of later observers.

Fig. 101.—The orbit of ξ Ursae, shewing the relative positions of the two components at various times between 1781 and 1897, (The observations of 1781 and 1802 were only enough to determine the direction of the line joining the two components, not its length.)

William Herschel’s observations of binary systems (chapter XII., § 264) only sufficed to shew that a motion of revolution of some kind appeared to be taking place; it was an obvious conjecture that the two members of a pair attracted one another according to the law of gravitation, so that the motion of revolution was to some extent analogous to that of a planet round the sun; if this were the case, then each star of a pair should describe an ellipse (or conceivably some other conic) round the other, or each round the common centre of gravity, in accordance with Kepler’s laws, and the apparent path as seen on the sky should be of this nature but in general foreshortened by being projected on to the celestial sphere. The first attempt to shew that this was actually the case was made by ξ Ursae, which was found to be revolving in a period of about 60 years.

Many thousand double stars have been discovered by the Herschels, Struve, and a number of other observers, including several living astronomers, among whom Professor S. W. Burnham of Chicago, who has discovered some 1300, holds a leading place. Among these stars there are about 300 which we have fair reason to regard as binary, but not more than 40 or 50 of the orbits can be regarded as at all satisfactorily known. One of the most satisfactory is that of Savary’s star ξ Ursae, which is shewn in fig. 101. Apart from the binaries discovered by the spectroscopic method (§ 314), which form to some extent a distinct class, the periods of revolution which have been computed range between about ten years and several centuries, the longer periods being for the most part decidedly uncertain.

310. William Herschel’s telescopes represented for some time the utmost that could be done in the construction of reflectors; the first advance was made by Lord Rosse (1800-1867), who—after a number of less successful experiments—finally constructed (1845), at Parsonstown in Ireland, a reflecting telescope nearly 60 feet in length, with a mirror which was six feet across, and had consequently a “light-grasp” more than double that of Herschel’s greatest telescope. Lord Rosse used the new instrument in the first instance to re-examine a number of known nebulae, and in the course of the next few years discovered a variety of new features, notably the spiral form of certain nebulae (fig. 102), and the resolution into apparent star clusters of a number of nebulae which Herschel had been unable to resolve and had accordingly put into “the shining fluid” class (chapter XII., § 260). This last discovery, being exactly analogous to Herschel’s experience when he first began to examine nebulae hitherto only observed with inferior telescopes, naturally led to a revival of the view that nebulae are indistinguishable from clusters of stars, though many of the arguments from probability urged by Herschel and others were in reality unaffected by the new discoveries.

Fig. 102.—Spiral nebulae. From drawings by Lord Rosse.

[To face p. 400.

311. The question of the status of nebulae in its simplest form may be said to have been settled by the first application of spectrum analysis. Fraunhofer (§ 299) had seen as early as 1823 that stars had spectra characterised like that of the sun by dark lines, and more complete investigations made soon after Kirchhoff’s discoveries by several astronomers, in particular by Sir William Huggins and by the eminent Jesuit astronomer Angelo Secchi (1818-1878), confirmed this result as regards nearly all stars observed.

The first spectrum of a nebula was obtained by Sir William Huggins in 1864, and was seen to consist of three bright lines; by 1868 he had examined 70, and found in about one-third of the cases, including that of the Orion nebula, a similar spectrum of bright lines. In these cases therefore the luminous part of the nebula is gaseous, and Herschel’s suggestion of a “shining fluid” was confirmed in the most satisfactory way. In nearly all cases three bright lines are seen, one of which is a hydrogen line, while the other two have not been identified, and in the case of a few of the brighter nebulae some other lines have also been seen. On the other hand, a considerable number of nebulae, including many of those which appear capable of telescopic resolution into star clusters, give a continuous spectrum, so that there is no clear spectroscopic evidence to distinguish them from clusters of stars, since the dark lines seen usually in the spectra of the latter could hardly be expected to be visible in the case of such faint objects as nebulae.

312. Stars have been classified, first by Secchi (1863), afterwards in slightly different ways by others, according to the general arrangement of the dark lines in their spectra; and some attempts have been made to base on these differences inferences as to the relative “ages,” or at any rate the stages of development, of different stars.

Many of the dark lines in the spectra of stars have been identified, first by Sir William Huggins in 1864, with the lines of known terrestrial elements, such as hydrogen, iron, sodium, calcium; so that a certain identity between the materials of which our own earth is made and that of bodies so remote as the fixed stars is thus established.

In addition to the classes of stars already mentioned, the spectroscope has shewn the existence of an extremely interesting if rather perplexing class of stars, falling into several subdivisions, which seem to form a connecting link between ordinary stars and nebulae, for, though indistinguishable telescopically from ordinary stars, their spectra shew bright lines either periodically or regularly. A good many stars of this class are variable, and several “new” stars which have appeared and faded away of late years have shewn similar characteristics.

313. The first application to the fixed stars of the spectroscopic method (§ 302) of determining motion towards or away from the observer was made by Sir William Huggins in 1868. A minute displacement from its usual position of a dark hydrogen line (F) in the spectrum of Sirius was detected, and interpreted as shewing that the star was receding from the solar system at a considerable speed. A number of other stars were similarly observed in the following year, and the work has been taken up since by a number of other observers, notably at Potsdam under the direction of Professor H. C. Vogel, and at Greenwich.

Fig. 103.—The spectrum of β Aurigae, shewing the K line single and double. From a photograph taken at Harvard.

[To face p. 403.

314. A very remarkable application of this method to binary stars has recently been made. If two stars are revolving round one another, their motions towards and away from the earth are changing regularly and are different; hence, if the light from both stars is received in the spectroscope, two spectra are formed—one for each star—the lines of which shift regularly relatively to one another. If a particular line, say the F line, common to the spectra of both stars, is observed when both stars are moving towards (or away from) the earth at the same rate—which happens twice in each revolution—only one line is seen; but when they are moving differently, if the spectroscope be powerful enough to detect the minute quantity involved, the line will appear doubled, one component being due to one star and one to the other. A periodic doubling of this kind was detected at the end of 1889 by Professor E. C. Pickering of Harvard in the case of ζ Ursae, which was thus for the first time shewn to be binary, and found to have the remarkably short period of only 104 days. This discovery was followed almost immediately by Professor Vogel’s detection of a periodical shift in the position of the dark lines in the spectrum of the variable star Algol (chapter XII., § 266); but as in this case

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