334 WAVE RESISTANCE OF A CYLINDER 
The coefficient of é is an effective mass for this particular problem, 
taking account of the free surface and assuming no wave formation and 
noting that the square of the fluid velocity has been neglected. 
As a special case, suppose the model to be started from rest with a 
velocity c which is then maintained constant. The finite resistance at any 
time after the start is given by the second term of (29), with c a constant 
ae a’ = {h'—h-+c(t—r7)}cos 0. 
The result can be reduced to the form 
mages [a J wo (I?+ J*)cos{xc(t—7)cos O}cos{g?x?(t—r)}« dx, 
(30) 
with rg | | OW e-wisicheos Odd. (31) 
Integrating with respect to 7, this gives 
47 es} 
9, i —aqtkt)tt inf bit) pt 
pit 2gpe do [ (2-402) sin{(«c cos 6 g’« é} intone rg i )e} oe 
xc cos 0—g' x? Kc cos 6-+-g?k? 
(32) 
It can be verified readily that the limiting value to which this tends as 
t becomes infinite is 
40 
R= smoke | (2-+J2)sec36 dO, (33) 
7 
0 
where J,+iJ, is given by (31) with « replaced by xy sec?6@. 
This result (33) is the known expression for the steady resistance at 
constant speed. 
REFERENCES 
1. L. Sretensxy, Joukovsky Cent. Inst. Rep. 319 (Moscow, 1937). 
2. T. H. Havetocr, Proc. Roy. Soc. A, 93 (1917), 520. 
3. H. Lamp, Proc. Roy. Soc. A, 111 (1926), 14 
544 
