LECTUBE VIII. 



THE PARALLACTIC INEQUALITY. 



WE shall now apply the method of the last lecture to find the terms 

 in the Moon's coordinates which depend upon the parallax of the Sun. 



The values of I, found in Lecture IV are 



4 = log e (?'/) = <&. cos 2\jj, 

 o = n t + t + l > ., sin 2i/, 



and these satisfy the equations of motion in which the terms involving 

 the Sun's parallax are omitted. Hence the residuals they leave from the 

 complete equations are 



X = - \ n T - I| cos (0 -0') + ~ cos 3 (0 t - 6')} , 



Ct/ |^o o J 



F= An* T - jf sin (0. -0') + - sin 3 (0. - ff) 



where 



E-M a 



._ 

 ~ a 



Now from above 

 hence we have 



sin (^ 6'} = sin ^ + - 6., (sin x/> + sin 



cos (0 0') = cos\li - b., (cos i/ cos 3t/), 



M 



3 

 sin 3 (0 - 0') = sin 3</> + - b, (sin \)t + sin 5t/>), 



u 



3 



cos 3 (^ - &} = cos 3t/> - - b, (cos i/ - cos 



A. II. 



