THE FIGURES OF EQUILIBRIUM OF ROTATING LIQUID MASSES. 59 



= ^-TS + 3 *AB + t AfT 2 +3 A~ 2 



A -\.J_> -TXl_/ .\_ 



L'B 



BK, 

 A 



AC 



N'B 



BK, 



L/p M'P XT' 



+ ^ ^ + 3. 1V1< ^ + 3|. L . j.i 



jrx O 



+ 



'G 



A 4 AB 



r l^- '35 -"33? 



/I/ /' K ] 



A 2 C ABC!, 



A B ' C 

 If the value of ^> is taken to he e(/>i + i'''<j> 2 , we have as the value of 9^, 



B 



C 



A 



A 



B G 



(129) 



(130) 



(131) 



^ 4 + M V + NT + 2ZV 8 + 2m 1 ' 2 f + 2n'? n * + 2 



(132) 



and we have already supposed (25) that 



f 



- ' 



+ c l2 x V + c 13 a; 

 I 2 



t . (133) 



