Wave Resistance: Some Cases of Unsymmetrical Forms. 239 
b/ 
janet armel oy apnean Sate 
a 
Fia. 1. 
7. Taking the symmetrical case first, we obtain from (20), 
R = 90°01 * ( J* cos d dd, (22) 
where : 
J= \ (2u + wu?) sin (glu/c* cos d) du. (23) 
0 
From these we have, after reduction, and writing p for 2gl/c?, . 
__ 324gob2l fe Pes WO Sew 
BSG ea GE OO) ee relly 
112 1 128 1 64 1 32 1 
eee ep pe Cee PNG), oe BG 
+ HPA, Ps(@) + sPo (e) + 5 ar ®) — FaPs Oo) 
256 1 256 1 1 
== = 1 3 Sow 74 ine) 2 
+ 2B Ea (bp) — 7 SP (| (24) 
with the notation 
Ps, (p) = (= 1)” fe cos*" ¢ sin (p sec ¢) dd, 
Poss (p) = (— 1)" | cos! # $008 (p see 4) dd. 
J0 
Using sequence relations for the P functions, we reduce (24) to a form 
involving only P3, Py and P; ; tabulated values of these have been given 
previously,* and in addition large-scale graphs of the three functions were 
available over the range of p from zero to 40. These graphs have been used 
also in the present calculations ; the reduced form of (24) from which these 
have been made is 
2 Ah (2 -9482 , 9-752 . 
R= Shgeb (2 4 0-048? 5 TO? + (1 + SF) Paw) 
z \3 p p 
5-333 , 11:684 
— (FS Pe to) + ( 
14-98 
246 
