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336 mirror appear equally bright, then the second star is—on the fundamental assumption—six times as far off.

In the same way the size of the mirror necessary to make a star just visible was used by Herschel as a measure of the distance of the star, and it was in this sense that he constantly referred to the "space-penetrating power" of his telescope. On this assumption he estimated the faintest stars visible to the naked eye to be about twelve times as remote as one of the brightest stars, such as Arcturus, while Arcturus if removed to 900 times its present distance would just be visible in the 20-foot telescope which he commonly used, and the 40-foot would penetrate about twice as far into space.

Towards the end of his life (1817) Herschel made an attempt to compare statistically his two assumptions of uniform distribution in space and of uniform actual brightness, by counting the number of stars of each degree of apparent brightness and comparing them with the numbers that would result from uniform distribution in space if apparent brightness depended only on distance. The inquiry only extended as far as stars visible to the naked eye and to the brighter of the telescopic stars, and indicated the existence of an excess of the fainter stars of these classes, so that either these stars are more closely packed in space than the brighter ones, or they are in reality smaller or less luminous than the others; but no definite conclusions as to the arrangement of the stars were drawn.

259. Intimately connected with the structure of the sidereal system was the question of the distribution and nature of nebulae (cf. figs. 100, 102, facing pp. 397, 400) and star clusters (cf. fig. 104, facing p. 405). When Herschel began his work rather more than 100 such bodies were known, which had been discovered for the most part by the French observers Lacaille (chapter, § 223) and Charles Messier (1730–1817). Messier may be said to have been a comet- hunter by profession; finding himself liable to mistake nebulae for comets, he put on record (1781) the positions of 103 of the former. Herschel's discoveries—carried out much more systematically and with more powerful instrumental appliances—were on a far larger scale. In 1786 he presented to the Royal Society a catalogue of 1,000