103 
1914 - 15 .] Resistance to Motion of a Body in a Fluid, 
as is easily seen by putting 
~ iq ~ Vp ~ V7 ~ 
We will suppose that the axes of co-ordinates move with the system, so 
that we may write 
for u. and w/ , and ^ , for r. and v' , ^ and — 
‘'0 > 
dt 
^0 ’ dt 
dt 
respectively, neglecting the above infinite series in the expressions for 
and . We have not as yet supposed the f s and ^’s connected by any 
definite law. If, however, we suppose 
& = Vp = V,^ ( 24 ) 
4 = Vq = 'n(f^ ( 25 ) 
where P and Q are for the moment arbitrary functions of and q respect- 
ively, then the positions of the vortices will be assigned when we fix the 
functions P and Q, for all positive and negative integral values of and q. 
Equations (19) to (22) now become : — 
A%+B'f; + cv . . 
■ ■ (26) 
• • (27) 
-|f= . . 
• • (28) 
• • (29) 
+ ^ ■ ■ 
. (30) 
^ W(p + i)^ + ^ 
• • (31) 
(2i^ + l)P 
^WiP+hf+h-^Y ■ ■ ■ 
• • (32) 
(2g-l)Q 
^[i^ci-w+n ■ ■ ■ 
. . (33) 
“ ^[PYp+w+h-^r ■ ■ ■ 
■ . (34) 
. . (35) 
