212 INVESTIGATION OF THE SECULAR ACCELERATION [27 



Also, by the formulae of elliptic motion 



cos + e cos 



= n (f 1 - 1 e'A cos 2 (0 - \') + e' cos (20 - 2\' - 



l\ ^ / ^ 



- e' cos 2^ -2X' 



Li 



+ y 

 and 



m ' -, ia ar\ m ' > IO a>\ 



- am 2 - ^') = sin 2 - 



e' 2 cos (20 - 2V - 2<^') 1 , 



= w' 2 jfl -i e' 2 ) sin -2 (0 -\') + l e' sin (20 - 2\f - $ ) 

 l\ / ^ 



17 



The angles involved in these expressions are formed by combining the angle 

 20 -2X' with multiples of <'. 



For our present purpose we may omit the terms which involve 2<'. 

 Also, for the sake of brevity we may write 



n't instead of n't + e' CD' or <f>', 

 20-2n't instead of 20-2(n f t + J) or 29 - 2X', 

 20-3n't instead of 20-2X'-<', 

 20- w' instead of 20-2\' + <f>', 

 since no ambiguity can arise from this abbreviation. 



