109 
1914-15.] Kesistance to Motion of a Body in a Fluid. 
Differentiating with respect to a, and proceeding as in the case of 
(68) and (69), it follows that 
^ (2M-l)2-a2 
V' ' — cos 
1 \ cos 
pn-l)x=2,r^ 
^ oos (271 - l)x _ ^ cos{2n-l)x 
^[{2n-lf + a‘^f 
^{2n — 1 )‘^ + ci^ 
7T^ cosh ax 
8 cosh^ ^ 
7tx cosh a[x — - 
4 cosh 
air 
(73) 
C)h 
Put x = and a = and we obtain finally 
V 
-00 
2 7 ,_ 
P C0Sh2 ^ 
i 
(74) 
(67), (70), and (74) embrace as particular cases all the series that arise in 
the discussion. 
{Issued separately April 8, 1915.) 
