1879.] liquid ellipsoid about its mean axis. 243 



To reduce the relation 



a^A-G'C h'B-c'G 



we must put 



where 



therefore 



b' + \={a'-c')^, 

 sn i« 



72 a'^-S^ 7 



k = 2 2 > a > > c ; 

 (X ^ c 



and c^ = (a^ — c^) — „- , 



^ ^ sn^a 



sn a 



^ ^ sn^a 



cn^a = -5 , dn^a = -5 ; and 



A = ;- sn w du, 



„ SM r^sn^M , 



B = J I 3-^- du, 



(a^-c')^Jodii'u 



SM r» sn^t 



c=-^^r^^dt.. 



Therefore to determine a, 



/ sn w aw — en a — ^ du = -t-^- du — t-o- / — ^ dii, 

 Jo J en u Jo dn'^M dn aJo en w 



/"" 2 7 . ToSn^acn^a r^sn^M , f<^sn^u j _ 

 Jo dn-'a Jo c^u Jo dnu 



