1909. ] The Wave-making Resistance of Ships. 299 
velocity—the resistance being zero after that point. In practice, we know 
that there are no such discontinuities in the resistance curves, and there are 
certain considerations which go to account for this difference. First, as 
regards the transverse waves alone, the preceding formule show that the 
amplitude tends to become infinite at the critical velocity, although the 
corresponding resistance at uniform velocity remains finite ; but, even apart 
from the effects of viscosity, there is a highest possible wave with a velocity 
depending partly upon the amplitude. Secondly, we have left out of 
consideration the diverging waves; but these must become more important 
in the neighbourhood of the critical velocity, for we may regard the two 
systems as coalescing into one solitary wave in the limit as the critical 
velocity is reached. After this point the diverging waves persist, so that 
the effect of these would be of the order of halving the drop in the resistance 
as the critical velocity is passed. 
Finally, we must consider the frictional resistance, which increases steadily 
with the velocity ; so that the fall is finally a smaller percentage of the total 
resistance than might appear at first. The curves given in fig. 11 give 
an estimate of a maximum effect of this kind, considering only the transverse 
wave system. 
§7. Further Types of Pressure Distribution. 
The preceding formule have been built up on the effect of a travelling 
pressure disturbance of simple type; we consider now another type which 
we may use as an illustration. 
Let the pressure system be given by 
P =f (2) = A (2%) (0? +H 
The type of distribution is graphed in fig. 12. 
Proceeding as in §2, we have 
” h?—w? 
(x) = 2A | (or PO Ko dw = wAxKe-*, (30) 
0 
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