A. MATHEMATICS AND ASTRONOMY. 59 



differences that may exist in the special ratios between any 

 two successive orders of magnitudes, he conchides that the 

 observations are, as yet, only sufficient to justify the belief 

 that this ratio is smaller for the stars visible to the naked 

 eye than for telescopic stars. BuU. Imp. Acad, of Sciences^ 

 8t.Fetersburg^ vol. xviii., 34. 



biela's comet. 



The various hypotheses as to the formation of comets and 

 the groups of meteoroids, with which certain comets are in- 

 timately associated, have received somewhat further elucida- 

 tion from a recent communication of Professor Kirkwood. 

 Two theories have been broached, which respectively require 

 that the different bodies moving together in the orbit of 

 Biela's comet have entered the solar system, either as a sin- 

 gle mass, subsequently broken up into portions, or as a group 

 of cometary bodies. The latter hypothesis has been advo- 

 cated by Kirkwood, who adduces the following facts in its 

 support : 



1. There is nothing improbable in supposing that the bod- 

 ies now known as the Biela comet, or the Biela group of 

 comets, were originally distinct and separate masses while 

 they were moving in straight lines through space, and be- 

 fore their orbits were changed into ellipses, with the sun as 

 a focus. 



2. It is improbable that, had they originally been imited, 

 they would have escaped observation until the year 1845. 



3. It is highly probable that the comet of 1818 is intimate- 

 ly related to that of Biela, and that that of 1Y72 belongs to 

 the same group, if, indeed, it be not identical with that of 1818, 

 whence it would follow that the Biela group of comets began 

 to separate from each other long before the year 1845, when 

 the first actual observation of their separation was made. 



4. It is probable that the comet whose discovery is due to 

 Klinkerfues and Pogson on the 2d of December, 1872, and 

 which has by some been regarded as identical with the long- 

 lost companion of Biela's comet, is, on the other hand, an- 

 other member of the same family. 



5. If we trace back the position of Biela's comet and the 

 planet Jupiter, we shall find that they Avere in the vicinity 

 of each other in September, 1734. This is the most recent 



