1894.J On a Spherical Vortex. 223 



the components of the molecular rotation are first found, viz., 



4 1 



-+ 

 or c 



Then the potentials L, M, N" of distributions of matter of densities 

 f/27r, 1//27T, /2?r respectively throughout the ellipsoid are deter- 

 mined. 



These are, outside the ellipsoid, 



/4 1\ f r 2 -Z 2 \ du 



L = -i^c+ 



N = o, 



where e is the parameter of the confocal ellipsoid through x, y, z. 

 Then 



3N 9M . / 4 , 1 \ r . f" 



5 -- ^~ = * ac ( + l x ( z ~ Z ) T~ 

 dy 82 \- c 2 / y j (a 



L N / 4 l \ f d 



o ^- = &a*c H - h/ (2 Z) -r-3 - ^7-2 - r7 

 8 9a; \a~ c i / J y j e (a 2 + )-(c 2 + %)t 



To obtain the corresponding expressions inside the ellipsoid it is 

 necessary to replace e by zero. 



, 8N 3M aL 3N 8M 8L 

 Uutside the ellipsoid -^- , -^-^-, -= -- 5 are the differ- 



Oy cz oz ox Ox oy 



ential coefficients of the potential function 





which, with a suitable value of fc, gives the potential of the irrota- 

 tional motion outside the ellipsoid moving parallel to the axis of z 

 with velocity Z. 



. , 3N oM. 3L 3N 3M 3L 

 Jut inside the ellipsoid -^ -- 5-, - , -^ -- ~- are not re- 



o?/ oz oz ox ox oy 



Rpectively equal to the values of u, v, w from which the investigation 

 commenced. 



VOL. LV. B 



