Studies in Wave Resistance. 577 
Here 2/ is the constant length, and 301 the constant area of horizontal 
section of the ship; the beam is 
2b (1—?/6d?)/(1—P/5d?). (17) 
The points of inflection in the curve are at « = +d. For d = 0., we have 
the ordinary parabolic form with beam 2b. With d =/the bow and stern 
lines are still straight, but the ship has a finer entrance and a slightly larger 
beam. With d<l, the lines at bow and stern are hollow, that is, the sides 
are concave outwards. We shall study in detail later four values of 1/d, 
namely, 0, 1, 1:25 and 1:5. 
From (15) and (16) we have 
4b y : 
= ae _ 173) q2 TE 
J = Pd TES |e 4x3/d?) sin ma de. 
Evaluating and putting in (14) we obtain 
R = 64n71gpb71-4(1 -1?/5d?)-? x 
<a l [3 21 1 2 2 ; 2 
Sj fs hs m 
ie {(4 Bari =) SUE (= Fates) sin ml } 
dm 
m? (mc! [g?—1)v* re) 
We shall use the notation 
o— ae IL, = Ye p=gL fe. 
Altering the variable in (18) and expanding the terms, it can be expressed in 
the form 
512Qgpb"l re 
4 
= Uap |, [Fos [35+ 5 142545 c0s2 
0 
+57 Beast p+ Boosh b 4d costg {1p 
4 Z 
Te (1-6 B+ Fd 4eos! p—T 8 (1-254) cost g 
256 6t 6 2 2 4 §2 1 §4 
Rian cos® @ - cos(p sec d)—cos? & Ae +4 5*) cos b 
oe 5? (1—3 6?) cos? p+ = 64 cos? an sin (p see 6) | dd. (19, 
J 
5. The integrals in (19) which do not seem to have been studied explicitly 
are of the following forms 
Pos (p) = (—1)* [cost sin (p see @) dg (20) 
1/2 
Ponti (p) = (—1)"#2 | cos*"*1 ¢ cos (psec d) dd, (21) 
0 
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