196 PERTURBATION OF THE ORBIT OF THE NOVEMBER METEORS. [10 



but if u be the eccentric anomaly of the disturbed body, n its mean 

 motion, and a its semi-axis major, and the square of the disturbing force 

 is ignored, we may put 



dt \ , . r 



- T - = - (1e cos tt) = , 

 du n v an 



or taking the Sun's mass unity, so that 



n~a 3 = 1 , 

 dN S'r sin 



we get 



-, - = i . 

 du /] e' 2 } sin l 



Now the quantities which Gauss has shewn how to compute are the 

 components of the whole attraction at P of the disturbing ring of matter 

 NA', resolved parallel to the major and minor axes of this ring and 

 perpendicular to its plane. Call these components X, Y, Z respectively; 

 then in the above formula 



S X sin a)' sin i Y cos CD' sin i + Z cos i. 

 [2 March, 1867.] 



Take the origin at the centre of the orbit of the disturbing body 

 and the axes parallel to the above-mentioned directions ; 



let A, B, C be the coordinates of P; 



a', V, e', u' refer with the usual meanings to the disturbing body; 



then by Gauss's formulae the elements of X, Y, Z, due to the attraction 

 of that portion of the ring into which the disturbing body is distributed 

 which lies between u' and u' + du', are given by 



, y _ (A a' cos u') (l e' cos u') du' 

 ITT!? 



i V _(B b' sin u'} ( 1 e' cos u'] du' 

 2*& 



(C )(l-e'cosu')du' 



~ 



