583 T. H. Havelock. 
Curves are shown in fig. 2 (p. 590) for the variation of resistance with velocit iy 
in three cases—when the draught is infinite, and when it is one-tenth and one- 
twentieth of the length of the model. The latter values cover approximately 
the usual ratios in practice. On the same diagram are reproduced experi- 
mental curves for three models of different types, the data being reduced to 
the same non-dimensional co-ordinates. Making allowance for the differences 
of form between these models and for the simplified form for which the calcula- 
tions have been made, the results show that the calculated values are of the 
right order of magnitude over a considerable range of velocity. Differences 
in the two sets of curves, such as the greater prominence of interference effects 
in the theoretical curves, are discussed. 
The first sections of the paper deal with the mathematical expressions for 
the resistance, and their transformation into forms suitable for calculation ; 
graphs of certain integrals are given in fig. 1 (p. 586). 
2. Take axes Ox, Oy in the undisturbed surface of a stream flowing with 
uniform velocity ¢ in the negative direction of Oz, and take Oz vertically 
upwards. If there is a distribution of doublets in the liquid in the plane y = 0, 
with axes parallel to Oz, and of moment w (h, 0, f) per unit area, the corre- 
sponding wave resistance is given by* 
R= lergipe* | an a | aif an |” O4/Oh. Ou'/AK’. sec? d 
x € UU IME} see°$ cos [fg (h — hi’) )/e*} sec d]dé (1) 
Over the plane y = 0 the normal fluid velocity at the point (h, 0, f) is 2x0 p/Oh. 
Taking y= 0 as the fore-and-aft median plane of the ship, we assume the 
action of the ship to be equivalent to a distribution of normal velocity over 
its section by this plane, the distribution being such that if y —F (x, z) is 
the equation of the ship’s surface, we substitute in (1) 
by _ ¢ 
ane = en Ff). () 
To simplify the calculations as far as possible, we shall assume the ship 
to be symmetrical fore and aft, and to have vertical sides so as to be of constant 
horizontal section. The water-plane section is taken to be of parabolic form, 
the equation for y positive being 
y = 6b (1 — 2? /l). (3) 
The length of the ship is 2/, its beam 2b, and it is of constant draught d. 
* «Roy. Soc. Proc.,’ A, vol. 108, p- 79 (1925). 
231 
