10] PERTURBATION OF THE ORBIT OF THE NOVEMBER METEORS. 199 



plane of the disturbed orbit, that is in the plane of which the direction 

 cosines of the normal are 



sin &)' sin i, cos to' sin i, cos i, 

 we have 



= (^4 afe') sin w' sin i B cos &/ sin i + C cos i, 

 we get 



S = a' sin (w' + /3) sin i - 1 - - a'e' sin &>' sin i ^ - a'e' sin (&>' + 2/8) sin i ^~ 

 = a' sin (w' + /3) sin i ( Q - P) + 3a'e' sin /8 cos (a/ + /8) (P + $) 



- a'e' sin (to' + 2/8) sin i f a + -} (Q - P). 



\ a/ 



[13 March, 1867.] 



We substitute this value of S in the right-hand member of the 

 equation for dN/du. The right-hand member is thus expressed as a 

 function of known quantities and the co-ordinates of the disturbed 

 body. Taking n the eccentric anomaly in the disturbed orbit to define 

 what is variable in these co-ordinates, we compute the value of dN/du 

 for a sufficient number of different values of u. Thus for instance we 

 find 



Perturbations by Jupiter. 



dN 



u -j 



du 



270 31-54 

 281i 79-5 

 263-59 

 495-32 



303f 642-1 

 309* 414-04 



o 



315 194-14 

 45-1 



9-93 

 360 0-04 



To deduce from these figures the change in N while u ranges from 



