THE FIGURES OF EQUILIBRIUM OF ROTATING LIQUID MASSES. C,7 



The values of P!, P 2 , P 3) P 4 originating from these terms are 



, o3 /^ , 3 y 2 , o3 /3 , 3. y , ii /3yl 

 ' i 34 243 



-4- J4- Kl 



B 2 1 A 



p - r^ + JL -Z- UK ~M ir > op y , ' )cco L oc *y py 



U s AB AC.y 4 4 V " A 3 2AB 2 2 AC 2 A 2 B A^'C ABC 



a ., K, .. 



C 



3 :i 



" 



1 have evaluated independently the three contributions to d l} <L,, d s and find for 

 them 



-(26ia 2 J AAAA + 2i/8 2 J AA 



, J AA + ^K 2 J AB + K 8 J AC + iK 5 J A ), 



and there are corresponding values for the contributions to 4(7;, and 4'?.. The 

 numerical values found by independent computations are 



4^ = 0-032398, 4d a = -O'Ol 1175, 4rZ, = -0'021223. 



As a check on the computations, the sum of these contributions ought to be zero ; 



we find 



= O'OOOOOO. 



The six contributions to c u , c, 2 , ... have also all been calculated separately. The 

 values obtained are' 



4c n = 0-0722711, 4c 22 = 0'0271162, 4c ffl == 0'0274693, 

 4c 12 = -G'215756, 4c I3 = -Q-217869, 4c 23 - 0'053056, 



as regards the checks which ought to be satisfied by these values, I find 



6c u + c ia +c 13 = 0'000002, 6c 22 +c 12 +c 33 = -O'OOOOOS, 6033+^+^= +0'000003. 



K 2 



