426 T. H. HAVELOCK 
given by A,+A,. It is seen, from (35) and (37), that the part of the total 
resistance which is simply proportional to the acceleration is 
mpa*y(1—a?/2f?). 
If we define the effective mass as the coefficient of y in this term, then 
the inertia coefficient is the same as for a free surface neglecting gravity. 
We could, on the other hand, divide the total resistance by y and so define 
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the effective mass at each instant. However, from the way in which R, 
and #, arise and from their variation, it seems convenient to refer to R, 
as the wave resistance and to regard &, as the product of the effective 
mass and the acceleration; with this convention, the inertia coefficient for 
motion with uniform acceleration from rest is given by the quantity p 
of (37). It can be seen from (37) that p converges to 1—a?/2f? for both 
c—+>0O and coo. In the particular case being considered, the inertia 
coefficient would be 0-95 for a free surface without gravity, and 1-05 for 
a rigid surface. Its variation with velocity can be seen from the curve A,, 
which gives the resistance R,. The coefficient p begins with the value 
0-95, rises to a maximum of about 1-07 near c/(gf)? equal to 0-4, falls to 
a minimum of 0-78 near c/(gf) = 1-4, and then rises towards. the value 
0-95 with increasing velocity. 
Similar calculations were made for the case y/g = 1-276, for which the 
wave resistance is shown in the curve B,. The curve for R, in this case 
is not shown in the diagram, because on the scale its magnitude would be 
nine times that of A,. However, the curve, in its relation to B,, is of the 
same type as in the case of the curves A, and A,, but with less variation 
in the inertia coefficient; this coefficient begins at 0-95, rises to a maximum 
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