OF WHICH IS MOVING ROTATIONALLY AND PART IRROTATIONALLY. 395 
stant A can always be chosen so as to make the absolute terms equal. The elimination 
of k from the two equations for C, D in which it occurs will leave the one relation 
between them which must be satisfied. 
/ X * 'll * 
Adding k [ — +wr— 1 
to the right-hand side, the conditions are 
/ cb a *-b\ Tx a*-F , k 
a/ 2 2 2a 2 cr 
¥ -Z = -C.— 2 - D.ab.~zp-+p 
and an equation to determine A. 
The velocity parallel axis of x' inside cylinder =^q==^~— <b \ y'. 
clA. /2 f y 
The velocity parallel axis of y' outside cylinder = — —=—[^ —w) x 
ClX \ CL 
From the assumed value of A for space outside cylinder 
dA 
dy 
= -G(a?-b^'-T>(a?-¥)y ^ 
+ e 
6 2 + e 
dy' 
2^/(a*+ €)(& + €) 
B+D 
( a/ 2 
r 
2 \a 2 -f-e 6 2 -fe 
dA 
dxf 
-C(a 2 -&V-D(a 3 -& 2 >F 
h l±l 
a~ + e 
de 
dx' 
2 v / (a s + e)(6 2 + 6) 
a? + e & 2 + e 
For the continuity of the values of at the surface e=0, it is evident that the 
coefficients of —, must vanish. Therefore 
Also 
B+D^ V^ o 
/-*6=-C(a»-6*)-D^(a»-6*) 
^-■5= C(«»-4»)+D^(a*-6») 
3 E 2 
