With every decrease in magnitude there is a great increase in numbers, and if this is extended to still smaller magnitudes down to the 15th or 16th we can readily understand that there exist vast multitudes of fainter stars. Paul Henry, of the Paris Observatory, says there are about 1,500,000 stars of the 11th mag., and Dr. Schönfield, of Bonn, gives 3,250,000 as of the 11½ mag. It is probable that by means of photography and the largest telescopes considerably more than 50 millions of stars may be charted, but this is a mere approximation. Roberts has photographed 16,206 stars within an area of four square degrees in a very rich region of the Galaxy near η Cygni, and Gore computes that were the distribution equal to this over the whole firmament the number of stars would reach 167 millions. He also remarks that in the Paris photographs of the Pleiades, 2326 stars are shown in a space covering about three square degrees, and this gives for the entire sky a total of 33 millions. It is, however, manifest that unusually plentiful spots in the heavens cannot be accepted as affording a criterion of the whole. _Magnitudes._—According to Argelander’s figures, above quoted, each magnitude exhibits a rise of about 300 per cent. But authorities rarely agree as to scale, as the following comparison between Sir J. Herschel and Struve will show:— H. S. 4·0 3·6 4·5 4·1 5·0 4·6 5·5 5·05 6·0 5·5 6·5 5·95 7·0 6·4 7·5 6·85 8·0 7·3 8·5 7·7 9·0 8·1 9·5 8·5 10·0 8·8 10·5 9·1 11·0 9·3 11·5 9·6 12·0 9·8 12·5 10·0 13·0 10·18 13·5 10·36 14·0 10·54 14·5 10·71 15·0 10·87 16·0 11·13 17·0 11·38 18·0 11·61 19·0 11·82 20·0 12·00 Argelander’s magnitudes come between those of Herschel and Struve. Such disagreements are perplexing to observers, and it is fortunate that in regard to the naked-eye stars we are now furnished with a more consistent and accurate series of magnitudes. Photometric determinations of the light of 4260 stars not fainter than the 6th mag., and between the N. pole and 30° S. declination, were made at Harvard College Observatory, and similar measures of 2784 stars between the N. pole and 10° S. declination were effected at the Oxford University Observatory, and the results published in 1885. The two catalogues are in very satisfactory agreement, the accordances within one tenth of a mag. being 31 per cent., within one quarter of a mag. 71 per cent., and within one third of a magnitude 95 per cent. The photometers used in the two independent researches were constructed on very different principles, and the substantial agreement in the results indicates that “a great step has been accomplished towards an accurate knowledge of the relative lustre of the stars” (‘Monthly Notices,’ vol. xlvi. p. 277).