The Initial Wave Resistance of a Moving Surface Pressure. 250 
are inthis case. Hence the slowness with which the steady state is attained 
and the probable lack of stability of the steady state. 
To compare the group approximation with the exact solution, we have 
from (27) 
—m gp R = 9 x 2-74 —-W2¢—n!2 cos 1 (Qn + 1)z. (28) 
The following is a comparison of the values of 10°7rigpR, as given by (28) 
and the exact formula (21): 
Case iiiAs a second numerical example, we take one which might 
correspond more to practical conditions, in that the pressure system is 
similar to that associated with the motion of a ship model in an experimental 
tank. Using foot-second units, we take 
GSH5 PSAs 6S 20s ko = 0°08; Ay = 25m. 
The pressure system is graphed in curve (2) of fig. 1, from the expression 
8 cos* 6 cos $9—125 cos” @cos 20. We notice the contrast between this and 
the previous case. We should now expect the steady state to be attained 
quickly and to be much more stable. This is brought out very clearly by 
the resistance curve, which has been graphed from (21), and is shown in 
curve (2) of fig. 2; after the initial peak, the subsequent oscillations can 
searcely be shown on the scale of the diagram. 
A comparison of the exact formula and the group approximation gives 
similar results to the previous case, for in both the numerical value of the 
ratio (23) is of the order 1/n, in spite of the difference in the values of r]ro 
for the two cases. 
It should be remarked that the two cases cannot be compared as regards 
absolute values from the curves shown, because the scale for the ordinates 
has been chosen arbitrarily in each case. The maximum value of R, that is, 
the value at the prominent peak on curve (2), is given by gpR = 7 x 1073. 
We can obtain some idea of the magnitude by the following comparison : 
We have chosen the pressure system so that it is waveless at a particular 
velocity, namely, 20 feet per second. Now, imagine the same system to be 
