A. MATHEMATICS AND ASTRONOMY. 37 



integral in place of the discontinuous variable, by means of 

 which, it is said, he is able to compute the perturbations 

 with ease, even in the most difficult cases. 6 B, LXXX., 808, 

 907, 1070. 



SPECTRUM OF COGGIA's COMET. 



Some accurate observations of the spectrum of Coggia's 

 comet of 1874 were made by Bredichin, of jMoscow. The 

 greater part of his work was done by means of a spectro- 

 scope by Merz. The values of the scales used by him were 

 determined each night by comparison with a Geissler's tube. 

 The channels observed in the cometary spectrum coincide 

 with those of the bands in the spectrum of the hydrocarbons, 

 whose wave lengths are respectively 563.3, 51G.4, and 474.2. 

 Bullet, de la Soc. Imp. des Naturcdistes de Moscou, 1874, 

 146. 



THE PERIODIC COMET OP d'aRREST. 



The periodic comet of D' Arrest was discovered in 1851 by 

 that astronomer. Its orbit about the sun was computed 

 with considerable precision by Villarceau, who allowed for 

 some of the perturbations to which it was subjected by the 

 attractions of the planets. His work has been recently taken 

 up by Le Veau, and carried to a considerable degree of re- 

 finement ; the inclination of the plane of the comet's orbit to 

 the plane of the ecliptic is only fourteen degrees. A special 

 difficulty, however, arose from the fact that in 1861 the com- 

 et approached very near to the planet Jupiter, and the in- 

 fluence of this great body was so considerable that the vari- 

 ations in the perturbations were sensibly of the same order 

 as the changes in the elements of the comet's orbit, so that, 

 in order to obtain the corrections to the latter, the ordinary 

 equations of condition would not suffice. This difficulty was 

 overcome by employing the method of false position. The 

 twenty-two resulting equations were resolved by the method 

 of Cauchy. The mass of Jupiter employed in these computa- 

 tions is that deduced by Bessel from observations of the sat- 

 ellites of that planet ; and the results of Le Veau's observa- 

 tions show that no material change in the mass of Jupiter is 

 needed, although the new observations of this comet at its 

 successive apparitions will probably enable the astronomer 



