RESISTANCE OF A SUBMERGED CYLINDER 427 
of 0-975 near c/(gf)! = 1, falls to a minimum of 0-91 near ce/(gf )t = 2:5, 
and then rises gradually towards 0-95. It is of special interest to notice 
that while the coefficient begins with the free surface value its rise towards 
the rigid surface value occurs before the wave resistance fk, has become 
appreciable. A few calculations were also made for a very small accelera- 
tion, with y/g = 0-035, to confirm the general trend of the variation; in 
this case, the coefficient p has risen to a value of 1-05 at about cl(gf )? = 0-2. 
Referring to (37), some of the approximate values found in these 
calculations are given for reference. 
For y/g = 0-1418, the quantity 32k6%) has the value —0-52, —1-2, —1-1, 
0:92, 1-66, 0-4 for B equal to 40, 10, 4, 1, 0-5, 0-25 respectively. For 
y/g = 1-276, the values of 3282) are —0-04, — 0-24, 0-3, 0-4 for B equal to- 
10, 1, 0:25, 0-125 respectively. 
The motion which has been examined in detail is uniform acceleration 
starting from rest. Similar calculations could be made for other cases of 
variable velocity, in particular for motion with uniform acceleration with 
a given initial velocity. In the latter case the results are not likely to be 
much different in general character; it appears that in any case the initial 
value of R, would be the inertia resistance for a free surface without 
gravity, and its subsequent variation would be similar to that shown by 
the present calculations. 
REFERENCES 
. H. Havetock, see above, pp. 325-34. 
. M. MitnE-Tuomson, Theoretical Hydrodynamics, p. 239. 
- H. Havetock, Proc. Roy. Soc. A, 157 (1936), 532. 
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