Many other departments of sidereal work are best left to the professional astronomer. The derivation of accurate star-places, proper motions, distances, &c. requires instruments of great refinement and trained hands to use them. Researches such as these do not come within the scope of ordinary amateurs. But a vast field is open to them in respect to double and variable stars; and the physical relations of many of the former greatly intensify the interest in this branch, and make it necessary to secure frequent observations. FOOTNOTES: [47] There are several forms of this instrument: for particulars of construction and use the reader is referred to Thornthwaite’s ‘Hints on Telescopes,’ and Chambers’s ‘Astronomy,’ 4th ed. vol. ii. [48] Mr. George Knott, of Cuckfield, mentions that the radius of the first bright diffraction-ring of a stellar image, for a 7-1/3-inch aperture, is 1″·01, and for one of 2 inches 3″·70 (‘Observatory,’ vol. vi. p. 19; see also vol. i. pp. 107 and 145). Mr. Dawes is quoted as giving 1″·25 for a 7-inch, 1″·61 for a 5½-inch, and 3″·57 for a 2·4-inch. These figures exceed the theoretical values, if the latter are adopted from Sir G. B. Airy’s ‘Undulatory Theory of Optics,’ where, for mean rays, we have:— Radius of object-glass in inches × radius of bright ring in seconds = 3·70. [49] The number visible to different persons varies according to eyesight. Some observers see thirteen or fourteen stars in the Pleiades, while others cannot discern more than six or seven. [50] About 2 seconds. Sir W. Herschel found the diameter of α Lyræ with a power of 6450 to be 0″·3553. Tycho Brahe, before the invention of telescopes, estimated the diameter of Sirius as 120″. J. D. Cassini, with a telescope 35 feet long, found the diameter of the same star 5″. [51] Dr. Doberck gives some valuable information with reference to the computation of binary star-orbits in ‘The Observatory,’ vol. ii. pp. 110 and 140. [52] The star α Canis Minoris (Procyon) was also inferred to be a binary and to have a similar period. Several close companions appear to have been discovered (Ast. Nach. no. 2080). But Prof. Hall, using the 25·8-inch refractor at Washington, says:—“I have never been able to see any of these companions that would stand the test of sliding and changing the eyepiece, turning the micrometer, &c., and am therefore doubtful of their existence. This is an interesting star for the powerful telescopes of the future.” It has been surmised that the companion is a non-luminous one, and therefore invisible. [53] It is remarkable that nearly all the temporary stars have appeared in the region of the Milky Way. [54] This expert comet-finder would appear to have more acute, sensitive vision on faint stars than Burnham (see ‘Monthly Notices’, vol. xlix. p. 354). CHAPTER XVII. _NEBULÆ AND CLUSTERS OF STARS._