GENERAL PERTURBATIONS OF MINERVA (93), BY JUPITER, INCLUDING 



TERMS ONLY OF THE FIRST ORDER WITH RESPECT TO THE 



MASS, TOGETHER WITH A CORRECTION OF ELEMENTS. 



By W. S. Eichelberger, Ph. 1>. 



( 1872 



The method used iu computing the perturbations is that developed by FTansen in "Ausein- 

 anderselzung einer zweekmpissigen Methode zur Berechnung der absoluten Storungen der Ideinen 

 Planeten. r 



The elements of Jupiter were obtained from Hill's Theory of Jupiter and Saturn, and those 

 of Minerva from a special discussion, by the author, of the observations from 1SC7 to 1S79 

 inclusive. These elements are as follows • 



Elements of Jupiter and Minerva. 



Epoch, 1872, Nov. 2.0, Greenwich M. T. 



(93) U 



O / /; 



0=.- 108 37 18. 4 



^•=274 17 11.4 



6 = 5 5 25.0 



•/=■ 8 36 21.6) 



cp= 8 5 0.5 



n = 776. 51130 



n' 



The first step in determining the perturbations was to develop the reciprocal of the dis- 

 tance between the two planets and, in the case of the first order perturbations, its cube, in 

 terms of the sines aud cosines of the sum of the different multiples of the eccentric anomalies of 

 the two planets. The coefficients of the terms in these developments are functions of the following 

 six quantities:* 



log a=0. 271)3315 J= 8 47 42.5 



e=sin <p=0. 1406156 77=278 17 16.4 



e'=sin tp'=0. 0482551 77'= 15 36 37.8 



The square of the mutual distance ( ) was thrown into the form 



D— /'cos (t'—F)-i-h' 2 cos 2e' 

 where e' is the eccentric anomaly of Jupiter, y 2 =a z e' 2 , and D, F and / are functions of the 

 elements aud the eccentric anomaly * of Minerva. 



*The notation and formulas are those of Hansen in the work referred to above. 



59 



