10] PERTURBATION OF THE ORBIT OF THE NOVEMBER METEORS. 195 



"corresponding to these portions, we may find the total secular changes 

 "of the elements produced in a complete period of the meteors. 



" In this manner I have found that during a period of 33'25 years, 

 "the longitude of the node is increased 20' by the action of Jupiter, nearly 

 " 7' by the action of Saturn, and about 1' by that of Uranus. The other 

 ''planets produce scarcely any sensible effects, so that the entire calculated 

 " increase of the longitude of the node in the above-mentioned period is 

 "about 28'. 



" As already stated, the observed increase of longitude in the same 

 " time is 29'. This remarkable accordance between the results of theory 

 ' ' and observation appears to me to leave no doubt as to the correctness 

 " of the period of 33'25 years. 



"In order to attain a sufficient degree of approximation it is requisite 

 " to break up the orbit of the meteors into a considerable number of 

 " portions, for each of which the attractions of the elliptic rings corre- 

 " spending to the several disturbing planets have to be determined; hence 

 "the calculations are necessarily very long, although I have devised a 

 " modification of Gauss's formulae which greatly facilitates their application 

 " to the present problem." 



The following exti-acts from MSS. give a sketch of the mathematical 

 details of this remarkable calculation.] 



Let NAP be the orbit of the disturbed body, and NA' that of the 

 disturber ; 



A, A' are the perihelia ; 



NP = 6, NA=a>, NA' = u', ANA' = i; 



S the force at P perpendicular to the orbit ; 

 N the longitude of the node ; 

 then as in Lectures on the Lunar Theory, XV., 



dN Sr sin 6 



dt ~~ H sin i ' 



252 



