VARIATION OF NODE AND INCLINATION*. 



THE following method of finding the variations of the in- 

 clination and longitude of the node, is more convenient than 

 that given in Pratt's Mechanical Philosophy, p. 336. 



Adopting the notation usual in the lunar theory, we have 

 s = &sin(0-7) ........................ (1), 



, d*z IJLZ dR 

 also -j- +r jr + - r =Q ....................... (2). 



0F r dz 



In the disturbed orbit, (1) and its first derived equation will 

 be true, as if the elements were invariable ; which gives the 

 equation 



(3), 



and differentiating (1) a second time, there is 

 d's .d& d .J0 



' 



The second and third terms are those due to perturbation. 

 Also, the inclination being very small, the effect of perturbation 



n ~d? ' r w ^^ c ^ ^ s ^ e same tn ^ n S? on TT- > w ^ ^ e sensible 



only in the term p -^ . Hence, equating the perturbation and 

 its effect, we have 



* Cambridge MathemalicalJournal, No. IX. Vol. n. p. 113, May, 1840. 



