106 COSMOS. 



bution of the fixed stars according to difference of magnitude, 

 down to the ninth, in about the following proportion . 



to -j-90), whence we should obtain 21,300 for the whole firmament. 

 According to the introduction to Weisse's Catal. e Zonis Regiomonta~ 

 nis, ded., p. xxxii., Struve fouud in the zone extending from 15 to 

 J 15 by the calculus of probabilities, 3903 stars from the first to the 

 seventh, and therefore 15,050 for the entire heaveus. This number is 

 lower than mine, because Bessel estimated the brighter stars nearly 

 half a magnitude lower than I did. We can here only arrive at a mean 

 result, which would be about 18,000 from the first to the seventh mag- 

 nitudes inclusive. Sir John Herschel, in the passage of the Outlines of 

 Astronomy, p. 521, to which you allude, speaks only of ' the whole num- 

 ber of stars already registered, down to the seventh magnitude inclu- 

 sive, amounting to from 12,000 to 15,000.' As regards the fainter stars, 

 Struve finds within the above-named zone (from 15 to -f-15), for 

 the faint stars of the eighth magnitude, 10,557 ; for those of the ninth, 

 37,739 ; and, consequently, 40,800 stars of the eighth, and 145,800 of the 

 ninth magnitude for the whole heavens. Hence, according to Struve, 

 we have, from the first to the ninth magnitude inclusive, 15,100-f- 

 40,800-f-145, 800=201,700 stars. He obtained these numbers by a 

 careful comparison of those zotiesor parts of zones which comprise the 

 same regions of the heavens, deducing by the calculus of probabilities 

 the number of stars actually present from the numbers of those com- 

 mon to, or different in, each zone. As the calculation was made from 

 a very large number of stars, it is deserving of great confidence. Bes- 

 sel has enumerated about 6 1,000 different stars from the first to the 

 ninth inclusive, in his collective zones between 15 and -j-45, after 

 deducting such stars as have been repeatedly observed, together with 

 those of the 9- 10 magnitude; whence we may conclude, after taking 

 into account such as have probably been overlooked, that this portion 

 of the heavens contains about 101,500 stars of the above-named magni- 

 tudes. My zones between -f-45 and -}-80 contain about 22,000 stars 

 ( Vurchmv sterling des nordl. Himmels, s. xxv.), which would leave about 

 19,000 after deducting 3000 for those belonging to the 9*10 magnitude. 

 My zones are somewhat richer than Bessel's, and I do not think we can 

 fairly assume a larger number than 2850 for the stars actually existing 

 between their limits (-^-45 and -f-80), whence we should obtain 

 130,000 stars to the ninth magnitude inclusive, between 15 and 

 -}-80. This space is, however, only 0*62181 of the whole heavens, 

 and we therefore obtain 209,000 stars for the entire number, supposing 

 an equal distribution to obtain throughout the whole firmament; these 

 numbers, again, closely approximate to Struve's estimate, and, indeed, 

 not improbably exceed it to a considerable (tent, since Struve reck- 

 oned stars of the 9-10 magnitude among thos<- of the ninth. The num- 

 bers which, according to my view, may bp asb imed for the whole firm- 

 ament, are therefore as follows: first mag. r 20 ; second, G5 ; third, 190; 

 fourth, 425; fifth, 1100; sixth, 3200; seventh, 13,000; eighth, 40,000; 

 ninth, 142,000; and 200,000 for the entire number of stars from the 

 first to the ninth magnitude inclusive. 



If you would contend that Lalande (Hist. C6lcste r p. iv.) has given 

 the number of stars observed by himself with the naked eye at 6000, 1 

 would simply remark that this estimate contains very many that have 

 been repeatedly observed, and that after deducting these, we obtain 

 only about 3800 stars for the portion of the heavens between 26 30* 



