68 MR. J. H. JEANS ON THE POTENTIAL OF ELLIPSOIDAL BODIES, AND 



Formation and Solution of the Equation. 



32. We proceed to form and solve the final equations. It is convenient to deal 

 with the equations in c u , c 12 ... first. 



By comparison of coefficients in equation (123), we obtain 



L = L'+^-lOm = L' +50-01206. (144) 



a 



= M'+ 0-01178109 .... (145) 



a 



2 



a 2 



a 



= N'+ 0-001297113 .... (146) 

 = V + Q'003909145 .... (147) 



m = m' + ^f + '^ -5 K y = m'- 0*3538936 ..... (148) 



f.t (' 



5 Kj Q =ri- T0060520 ..... (149) 

 o 



K a = p' - 2-800420 ..... (150) 



ct 

 ^ = q' + G'02913935 .... (151) 



a 



2 



= /' + Q'009668880 . . . . (152) 

 = s' + 0-07207330 .... (153) 



These coefficients can he checked hy comparing the sums of the coefficients in the 

 two values of ' (equation (123)) ; i.e., taking 2 = ,, 2 = 2 = 1. For the difference of 

 the sums which, ought to vanish, I find 41'8G192-4r86191 = O'OOOOl. Using the 

 values just obtained, 



- L = 0'002585G75L/ + 0-1293149, 



8 



' + 0-02503914, 



- 8 N = 12-87541N' + 0-01670087. 



Collecting the various contributions to c u , c 22 , c 33 , equations (102) to (104) now 

 become 



0'002585675L' + 0-1293149 



= 0-001359233L' + 0-01278935M' + 0'04066156N / 



+ 0-01515472Z / -0-01251121m'-0 > 006581149w'+0-0722711, 



