THE FIGURES OF EQUILIBRIUM OF ROTATING LIQUID MASSES. 69 



2-I25367M' + Q'02503914 



12'8754lN' + 0'01670087 



while equations (115) to (117) give 



L' = -23-52190w'-9-55G72ji'-32-0732G, 



M' = -- 0'8204313Z'-0-01162649n'- 0-00329142, 



N' = - 0'1354301/ / -0'00472373m'-0'000154830. 

 The solution of this set of six equation is 



L' = -6172711, M' = -0-01761613, N' = -0'002105706, 



V = -- 0-006053622, m' = +0'5865530, n' = + TG59250 . . (154) 



No check is needed on the accuracy of these values beyond the fact that they 

 satisfy the equations. On substituting directly into the equations, I find that they 

 are all satisfied accurately to the last place of decimals. 



The corresponding values of L, M, N, /, m, //- (see opposite, page) are 



L= -1171505. M= -G'00583504, N = -0-000808592, 



1=-- 0-002144477, m= 0'2326594, n- 0'653I98,. . (155) 



and the values of c n , r 1L ,, ..., calculated directly from equations (102) to (107) are 

 4e n = -0-03029132, 4c,, = -()'() L2401GO, 4c :w = -O'Ol .0410956, 

 2c 2;i = -0-01121809, 2c :u = 0'04245102, 2c, 8 = 0'0484230L. (156) 



These ought to satisfy the checks afforded by equations (108) to (I 10). In point 

 of fact, I find 



6c n + c ia + c i:! = +0-00000007, Gc^ + c^ + c^ = +0'00000012, 



'Gc3a+cia+c K = +O-QOOOOOOG. 



33. The first use which must be made of these numbers is to determine the 

 contributions to d lt d 2 , d 3 , evaluated on p. 64. We have by separate computation. 



L' M' N' 



G'085375 ^L-o-073783^0-089893.-... =-0'3412367, 

 4 l> 1 c 



-0-041149^+.. =+0-1672652, 



a 



-0'044227^+... -+0-1739738, 



