Resistance of a Ship among Waves 303 
The resistances R,, R, of the two models when far apart are given by (5) 
with P, +2, in terms of 7, and P,+7Q, in terms of a5. 
In addition the rear model experiences a resistance Ry. which, from (7) 
and (13) of the paper just quoted, is given by 
Ry. = 327K? | {a dx, dz, | | O,dx, dz» 
an . 
x I errata) Se*9 cost{k g(a, — a) sec O} sec? 0d0, (13) 
0 
the integrations extending over the two distributions. This may be put into 
a form involving the same quantities P,, Q,, P,, Q, as are required for R, 
and R,, namely, 
an 
Ry = S2mnip| (P,P, + Q, Q.) sec? 0d0. (14) 
0 
We now simplify the problem by supposing the two models to be similar 
in all respects; then if / is the distance from the bow of the leading model to 
the bow of the rear model, we have 
12 +7Q = (U2 +7Q ) etxok sec 0 15 
2 2 1 1 
37 
This gives Ry, = S2nnip| (P}+ Q?) cos(kyk sec A) sec? 6d0. (16) 
0 
Finally, we carry out the integrations for a model of great draft and of 
uniform horizontal cross-section given by 
y = b(1—2?//?). (17) 
The results may be expressed in terms of P functions used in previous 
investigations and defined by 
an 
P3y(p) = (= yf cos?” @ sin(p sec 8) dé, 
d 
47 
PanualP) = (= 1] “cos 9 cos(p see 0) 0. (1s) 
0 
(I am indebted to the Superintendent of The William Froude Laboratory 
for graphs of the first nine of this series of functions.) We obtain then for 
433 
