86 



THE TIDAL PROBLEM. 



The units are so far arbitrary. We shall choose them so that 



unit of time = mean solar day 

 2TiCja^ = 1 



(27r)Hmi+m2)'~ 

 Then equations (6) and (7) become 



Tir Til l~, '■, • . Wli cost, . C^fCL'A 



\ Di Ci \ai/ 



m^ cos i^ 

 D, 



(8) 



(9) 

 (10) 



If we represent the ascending nodes of the planes of the orbit and of the 

 equators of m^ and wig by Q,, Qi, and 0,2 respectively, the moment of 

 momentum equations for the x and y-Skxes are similarly 



M'=Pi-^l-e2sinisin Q 



rrii sin i\ sin 0>i c^ fo^zV ^2 sin ij sin ft. 



D, 



+ 



2 /M 



D, 



Tir,, nx n ^ • • r^ , ^1 sinr, COS ^1 , Cj /a^Vm. smi, cos Q. 



M" = Pi Jl— 6 smt cos ^-^ — ^ ~ -* + -—) ^ ^ ^ 



(90 



