37 



The difference of the forces of S on P and on E in a direction 

 parallel to SE ^ S (^^ — i^) 

 The effect of this difference in direction EP opposite to E = 



s (Hi - y) '^^^ c^-'') 



and in direction perpendicular to PE = S f^p-^ — s£^) ®"^ 0~'') 

 also the force of S in direction PE = S x -p-^^ 

 Hence R = — + « (g.) _ S (g, — L_) cos (v-0 

 and P = S (1^ — ^) sin (.— '.) 



or in consequence of the substitution m = ^3— i, if we represent 

 M the sum of the masses of the earth and moon by unity 



T> I m'a' CPE /SE I \ ^ /N 7 



-^ = ?£i+-— [Wi — isT^ — sw) COS 0-0 ^ 



D »n^^^ /SE I \ • ^ 'X 



^= — (5F3 - ^) «"> 0-") 



Now SP :r. V-^,^ - ? (cos ^^ = « \/l"^^W^(^ 

 hence neglecting quantities of the order t^ 



I \_ f, , Scos(,-^) \ 



Spi — a^ \ u.i J 



Therefore if we neglect quantities of the order -^ 



fi - ,^2 + i!iL__ ?!!' cos^ 0-v) =71^ — "^n +3 cos (?>—2'A) 



= — -^ COS (v-v) sm (v- ^) = — 271: ^'» (2i'-2») 



„ /'Per. Time Moou\„ ■ 1 i 



now as m- — I -r. tjt. — ,, -. r nearly = — - nearly 



— \Pdr. Itmc hurthj J lit) •' 



, , . .,1 Purnllnx Sun ,1 ,1 . 



and a being unity j = p^,^^^jj-,- nearly = j^ near,y ; - may be 



