Wave Resistance: Effect of Parallel Middle Body. 87 
velocity, in contrast to R. E. Froude’s results. The expression for R corre- 
sponding to (21) is now 
R = A+B sin (gPL/c*), (25) 
and instead of the sequence (22) we have 
ites ae nee 
GB" Vf of 
for the ratios of the significant velocities. 
(26) 
The authors of this formula based it upon observations over a certain inter- 
mediate range of velocities. If we omit the first two or three terms in the 
sequences (22) and (26), there is a range in which the ratios do not differ very 
much ; further, if we are considering a resistance-velocity curve, the points 
in quéstion are not defined with precision. However, these remarks do not 
apply to the final hump on such a curve, and in that case the available evidence 
seems to favour the first sequence (22). 
It is different when we turn to,resistance curves, such as those given by 
W. Froude and by Baker and Kent, in which the base line is length of parallel 
middle body. In these curves we may follow the position of a certain maximum 
as the velocity is increased. If the wave-making length Z is constant, it follows 
from (21) that if (is the wave-length and 2k the length of parallel middle body 
at which the maximum occurs, we should have 
9) 
“t >—2k = constant; 20 
while, on the other hand, from (23) and (25) we should have 
wt A—2k = constant, (28) 
where n is zero or an assigned positive integer. 
It is certainly the case that over the range which has been examined the 
second relation (28) fits the data very well. For comparison with present 
calculations we may take one example from the results of Baker and Kent. 
The figures are given by Kent, in a recent discussion already quoted, for the 
case n = 2. They relate to models ranging in length from 11-2 feet to 20-5 feet 
by the insertion of parallel middle body ; and the velocities vary from 290 
to 370 feet per minute. We transform the results to apply to ships with entrance 
and run equal to 160 feet by multiplying all lengths, including wave-lengths, 
by the factor 160/11-2. In the present notation we obtain thus Table IT. 
224 
