109M The Wave-making Resistance of Ships. 285 
This indicates two pressure systems, one of excess and the other of defect 
of pressure ; each distribution is of the type already used, and their centres 
are separated by a distance 7. Fig. 3 shows the character of the disturbance. 
In the rear of the whole disturbance there is interference between the 
regular wave-trains due to the two parts. With the same methods as before 
we find that the resulting waves are given by 
= 2g?) , ~ age? a Z J (x—3l) lt) 2gP2 e7agl? sin 
we 
g(e@+3l) 
ee ay? uv 
2 a emoglen poe sin SEs P2) sin t cos: ue ae (16) 
CO) 
Hence the average energy per unit area is proportional to 
ov *e~ Peal {P12 + Po? — 2 PsP cos (g1/v2)}. 
Now, assuming as before that P, and P2 vary as v*, we find that as regards 
variation with the velocity the effective resistance R, which is the expression 
of the energy cm to feed the wave-trains, is given in the form 
= {A?+B?—2AB cos (gl/v2)} ¢~ 229!” (17) 
A more general expression might have been obtained by taking two 
quantities a and a in (15), corresponding to some difference in wave- making 
properties of entrance and run; this would have led to different exponential 
factors being attached to the bow and stern waves. However, we find (17), 
with a common exponential factor, sufficiently adjustable for present 
purposes. 
In Froude’s experiments in 1877 the effect of inserting different lengths 
of parallel middle body between the same entrance and run was examined ; 
it was found that a hump in the residuary resistance curve corresponded to 
a trough of the bow waves being in the vicinity of the middle of the run 
and a hollow to a crest being in that position. 
43 
