86 T. H.. Havelock. 
for the ratios of the velocities at which these occur, beginning with the final 
hump on the curve of R plotted on a velocity base. 
This was the sequence verified experimentally by R. E. Froude. It should 
be noted, however, that these points are not actual maxima or minima on the 
resistance-velocity curve ; although their approximate position is fairly obvious 
from inspection, they cannot be defined accurately without a knowledge of the 
mean resistance curve. 
Turning to W. Froude’s work, it is obvious we should have similar phenomena 
if the effect of introducing parallel middle body is simply an addition to the 
wave-making length. his is the case if we consider any curve of R on a base 
of parallel middle body for a given speed. Here we are dealing with actual 
maxima and minima; and Froude’s curves show that, within experimental 
error, the separation between consecutive maxima is approximately equal 
to the wave-length 4. On this theory the quantity Z derived from each curve 
should be the same for all velocities, but Froude did not examine that point. 
The second approximate theory, which we shall consider now, asserts in fact 
that Z is not constant in these curves. 
From a study of various model results, a formula connecting Z with ship 
form was given by G. 8. Baker and J. L. Kent*; the formula was later asso- 
ciated with direct observation of wave profiles in certain cases. For a recent 
critical account of this formula, reference should also be made to two papers 
by J. Tutin} and to the discussions published in connection with them. 
The formula is equivalent to defining the wave-making length Z by the 
equation 
Z= PL+4A = PL+2c?/2g, (23) 
where L is the total length of the ship, and P is the prismatic coefficient of 
form. Since P is the ratio of the volume of the ship to the volume of a prism 
of the same length and with section equal to the midship section of the ship, 
we have in the present notation 
PL = 2k+9P,I, (24) 
where P, is the coefficient for the entrance or run; and at any given speed 
there is a similar relation between R and 2k as on the previous theory. The 
chief interest of (23) lies in the second term, which makes Z increase with the 
* G.S. Baker and J. L. Kent, ‘Trans. Nav. Arch.,’ vol. 55, Pt. I, p. 37 (1913) ; also 
J. L. Kent, ‘Trans. Nav. Arch.,’ vol. 57, p. 154 (1915). 
{ J. Tutin, ‘Trans. Nav. Arch.,’ vol. 66, p. 240 (1924); also ‘ Trans. N. E. Coast Inst. 
Eng. and Ship.,’ vol. 41 (1925). 
223 
