The Initial Wave Resistance of a Moving Surface Pressure. 252 
system as if the surface elevation were that due to the stoppage of a negative 
system, as represented in fig. 3. 
For a concentrated pressure system, the value of the integral (13) will be 
given approximately by the Kelvin group method, if the time is sufficiently 
large ; that is, if C is sufficiently far in advance of G for us to neglect the 
contribution of the applied pressure acting on the surface to the rear of G. 
Without attempting to specify these conditions more precisely, we shall 
apply the method to the type of system used in the previous sections; from 
the previous exact solution we have been able to estimate somewhat the 
degree of accuracy of the group approximation. 
The group value of (13) is given in (26). Hence the wave resistance, for 
sufficiently large values of ¢, is given by 
2 1/2 42) 12 
B= (8) } Geechee em tlse+ im, (0) 
9. Apply this to the pressure distribution 
TE (x) = V (3) (r2-+.22)-* cos {2 tan (w/r)} (31) 
for which («) = «*/4e-™, with « = g/c. The graph of this distribution is 
shown in curve (3) of fig. 1. 
We have 
ae 2gr/c2 i —g7|2c? 
pR= aaa =] ae gle" cos (gt/4c +41). (32) 
The value of R oscillates about the final steady value. The relative 
deviation is given by the ratio of the two terms, namely, 
Q-W2qp— 1p 1/26377 Ao agg 4(2n+ 1)z7, 
where 2» is the wave-length of the regular train and cf =A)n- We may 
obtain numerical values by using the two cases of the previous sections. 
For Case i we have r= 1, X» = 2, and we find the following comparison 
between Rj, the tinal steady resistance, and Re, the deviation given by the 
second term of (32):— 
Hence, after the system has moved through nine wave-lengths, the devia- 
tion is less than 5 per cent. 
117 
