^mvi-a^<\K•?>A^'^ ' in the Pendulum Oval ,, -/^jf 'iiifi W^ 



"' 'Also to Sn3 -jT and -j-, we have the equations of motibri dbdui 

 A, ^, y being the cooidinates of N, 



■ dt^ 

 \ (vel)^ in disturbed orbit 







'.)t(/ 'iO 



,M 



>??/^ 



But (vel)^ in undisturbed ellipse 

 And these by the theory are equal j 



Also^ from the equations of motion. 



</jf 



'^4. 



« 9?iii/uiiKd Xi 



Hence from (2.) and (3.) we have ' ,^ 



(/«_ /aW^ dr db ^ /jJbr^ dr ■i^\ 



'di'^fi{(v'-b^) 'Jt ' Tt^''fM{a^-b^)'Tt' 



Hence substituting in (1.), and calling 0—'Cj = (j), we have, re- 

 membering that 



^=-/^sm<Acos0.(^^^^j.^, 



^ fJ'' a fcos^rf) sin^<f)"l 5., 



This is at once integrable by making the usual assumptions, r 

 y:^y>- r cos (J) = a cos yjr; r Bm <l>=zb sin yjr, 



