″ 1·0 4·56 1·6 2·85 2·0 2·28 2·25 2·03 2·5 1·82 2·75 1·66 3·0 1·52 3·5 1·30 3·8 1·20 4·0 1·14 4·5 1·01 5·0 0·91 5·5 0·83 6·0 0·76 6·5 0·70 7·0 0·65 7·5 0·61 8·0 0·57 8·5 0·536 9·0 0.507 9·5 0.480 10·0 0·456 12.0 0·380 15·0 0·304 20·0 0·228 25·0 0·182 30·0 0·152 Dallmeyer, the optician, confirmed these values by remarking:—“In all the calculations I have made, I find that 4·33 divided by the aperture gives the separating power. Thus, 4·33 inches separates 1
″.” But a good deal depends upon the character of the seeing and upon other conditions. A large aperture will sometimes fail to reveal a difficult and close _comes_ to a bright star when a smaller aperture will succeed. This is due to the position of the bright diffraction-ring, which in a large instrument may overlap the faint companion and obscure it, while in a small one the ring falls outside and the small star is visible[48]. Dawes concluded that “tests of separation of double stars are not tests of excellence of figure,” and he gave much valuable information with regard to micrometers and double-star observations generally in the ‘Monthly Notices,’ vol. xxvii. pp. 217-238. This paper will well repay attentive reading. _Number of Stars._—In the northern hemisphere there are about 5000[49] stars perceptible to the naked eye. This is less than an observer would suppose from a casual glance at the firmament, but hasty ideas are often inaccurate. The scintillation of the stars and the fact that many small stars are momentarily glimpsed but cannot be held steadily have a tendency to occasion an exaggerated estimate of their numbers. Authorities differ as to the total of naked-eye stars. Sir R. S. Ball says “the number of stars which can be seen with the unaided eye in England may be estimated at about 3000.” Gore gives 4000. Backhouse mentions 5600 as visible in the northern hemisphere. Argelander, who has charted 324,188 stars between 2° S. of the equator and the N. pole, gives the following numbers of stars up to the 9th magnitude:— 1st. 2nd. 3rd. 4th. 5th. 20 65 190 425 1100 6th. 7th. 8th. 9th. 3200 13,000 40,000 142,000