236 T. H. Havelock. 
We shall consider two cases, one a sharp-ended form which is symmetrical fore 
and aft, while in the second case the aft end is curved to a fine point. 
4. For the first case we take a spindle-shaped body which has been used for 
experimental work at the National Physical Laboratory; for this form the 
source distribution is 
F(A) = af(h/l) — (h]l)"}; —l<h<l. (5) 
The shape of the surface for this case has been given by Perring.* It is sufficient 
to state here that it is a surface of revolution symmetrical about the middle 
cross-section and having pointed ends with finite angle of entrance ; it can be 
made to have any required ratio of breadth to length. 
We can, in this case, carry out the integration in (2) and obtain the equation 
of the longitudinal section. It is found that with 2b as the breadth of the 
model, 2/ its length, and 8 the ratio of 6 to Ll, then the constant a of (5) is equal 
to 4.abe, where 
a=d/1(1+57j2(3+252)+ 57(14+- 487) log (6/f 14(14+-52)2})]. (6) 
The equivalent distribution of doublets, given by the conditions stated in 
(3), is 
b(t) = — gal (l — #/P). (7) 
Substituting in (4) we obtain the wave resistance 
R = 4ag'plta’e all TP? sec! go Paes dy, (8) 
where = 
i ja — u?)? cos (glu/c* cos ¢) du. (9) 
After evaluating (9), the ey (8) can be reduced to standard form as 
9 2]ey2 pale 
a Se |e s$+ 5 ie = cos" 
; 0 
— (cos ¢—--> 80 os? d+ oe i cos (p sec ¢) 
cos*@ 12cos'd)\ . =H 
+ 12 se ae sng sin (p sec #) |e RB eee Shp, (10) 
where 8 = f/l, p = 2gl/c?, and « is given in (6). 
An asymptotic expansion suitable for large values of p could be obtained, 
but calculation from it is very tedious ; the particular point under consideration 
can be made by comparison with the similar expression for the second case. 
*W.G.A. Perring, ‘Trans. Inst. Nav. Arch.,’ vol. 67, p. 95 (1925). 
