174-176] Adiabatic Model 177 



Again, as must in general be the case, there is no error in the terms 

 multiplied by 7. In the remaining terms, the errors in l y M and N t the 

 coefficients which determine the smallest cross-section, are seen to be less 

 than two per cent, but the errors in the remaining coefficients L, m and n 

 are very much greater, being respectively 34, 26 and 24 per centr 



176. Having determined L, M, N, I, m, n, we complete the solution by 

 finding p, q, r from equations (469), which, written out in full, become 



F 



2r<9 





At this stage it is convenient to extend the notation already introduced 

 in 35. By analogy with the integrals J defined in equation (56) we shall 

 write 







With this notation the value of 4c^ is readily found to be 



4dj = ZpJ AA z I AA i I AB ~ ~ 9 I AC + ^i (478), 



in which 



r/. M AT 



i x _ _ a hr 77- 4-77 4_ 



*1 4 X^^AAA ~T~~H I2 ABB~T~ ~T 

 |_u> O 



3Z 

 I- ft2 ^^ 



The value of B l can be determined as soon as the values of the coefficients 

 L, M, N, I, m, n have been found, and equations (475) etc. assume the form 



2^(9 p 



-^ _ 9r.T 4- SL 



0? 



These linear equations determine p, q and r. The solution may be 

 regarded as the sum of two solutions, the first arising from the terms 4^, 4S 2 

 and 48 3 on the right, and the second from the terms in Ao> 2 . The second 

 solution represents merely a step along the ellipsoidal (or spheroidal) series 

 corresponding to a small change Aw 2 in the value of o> 2 . To obtain a com- 

 pressible solution we may give any value to Ao> 2 , the zero value, which is of 

 course most convenient, giving a solution which corresponds to the same 

 rotation as the incompressible figure from which it is derived. 



j. c. 12 



