36 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



Dr. Bredichiii will shortly publish a complete discussion of 

 this interesting subject. 38 G, LXXXVIL, 239. 



OEBIT OF COMET II., 1840. 



This comet was discovered by Galle, of Berlin, January 25, 

 1840, and was observed until the end of March. Dr. Ko- 

 walczyk, of Warsaw, has recently reinvestigated its orbit 

 from a good number of observations, and finds it to be an 

 ellipse, the periodic time being 3789 years. The agree- 

 ment of observation with his theory is very close. Plan- 

 tamour and Loomis had previously investigated this orbit, 

 and their results may be found in Astronomische Nachrich- 

 ten, No. 476, and Transactions of the American Academy of 

 Arts and Sciences, \6\. viii. Plantamour's orbit was parabol- 

 ic, and represented the Geneva observations well ; Loomis's 

 was an ellipse, which corresponded to a periodic time of 

 2420 years; Kowalczyk's, however, agrees so well with all 

 the observations that this orbit may be considered as settled. 

 38 C, LXXXVIL, 225 ; 12 A, March 16, 1876, 386. 



ON" THE CALCULATION OF THE ABSOLUTE PERTUEBATIONS OF 



COMETS. 



Professor H. Gylden, Director of the Astronomical Observ- 

 atory at Stockholm, communicates to the Paris Academy of 

 Sciences a method of calculating the absolute perturbations 

 of comets. He states that in all cases where the solution of 

 the problem of these bodies can possibly be effected by de- 

 veloping the expression for the perturbing forces into a series 

 depending upon their powers and products, the principal dif- 

 ficulty is experienced in the evaluation of two consecutive 

 quadratures, the first of which is ordinarily performed by 

 means of a series depending upon the sines and cosines of 

 the eccentric anomaly. This method, however, becomes in- 

 applicable in the case of comets whose orbits are ordinarily 

 very eccentric. Li order to meet this case, Hansen has in- 

 vented the method of partitions, in which he divides the 

 comet's orbit into successive portions, and introduces into 

 them new variables called partial anomalies; the variables 

 for one partition being connected with those of the next by 

 a discontinuous function. Professor Gyiden's method con- 

 sists in modifying that of Hansen, by introducing an elliptic 



