OF WHICH IS MOVING ROTATIONALLY AND PART IRROTATIONALLY. 381 
From the first 
therefore 
But 
whence 
therefore 
But 
therefore 
A= 
&F(\, f) b f f rbr 
bt bt J 
M0 + # r - 
dA_ b*F(\, t ) N d b[^ [rbr , d 
dr bXbt 
\ o? off rbr ,d 
d £> b 
&r~br'^ Xr bx 
d_ b 
dz ~b\ 
A 
dt bt ' 1 b\ 
b d \t d 
bt dt X 2 dz 
rfA_6 8 F(\, t) x bCrbX b [ rbr , b . . 
dr~ b\bt K 
Xtz , 
i >* 
ip 
v 21 
r a/ y 
d V d \ 1 
dt X 2 dz jx, 
Xt 
X , dz\ X 
=[ r!, A(-i;) = - r £+ 4> ( r - < ) 
dA fb°F(X, t ) i f rbr \ , \ t . , b , 
* =H _ »r ! “s Jvj) +r ( > 
Hence, choosing xfj(r, t ) so that 
and therefore 
Ur, t)=\i(r, <)»r=jrtr^ + {>r 0+Q(n 0 
the required form for — is obtained. 
dr 
A— 
&F(\, t) 
bt 
+ JrSr/—'Y+P(\, «) + Q(r, t) 
