422 T. H. Havelock 
where we have used the abbreviation 
(q, Y) = Ko sec? 9 (q cos 8 + y sin 0). 
In (15) the wave pattern is analysed into simple constituents associated 
with the bow, amidships, and the stern; putting the expression into the 
form 
1/2 
C= | {A, sin (ox sec 0) + Ag cos (yx sec 0)} 
0 
cos (yy sin 8 sec? 0) d8, (16) 
the wave resistance is given by* 
7/2 
=} pre? | (A,2+A,”) cos® 60. (17) 
0 
Carrying out the reduction we obtain 
_ 16eb%2 (21 + 6) , 166? , 128(1 — BF , 28 
RX \ 3p? vy ‘epee 35p5 a P P, 2p) 
eas 2 a -* 
ee ae ae DP. 2p) 
ieee s@= 8 (1 — BP 
-40= 2, +B SCP}. (18) 
In terms of P functions which have been tabulated this becomes, for 
the particular case 8 = 0-6, 
“GeBRE DD OBR BOMB gfe? 9-32) 
me \ 3p? cy p a 35p% i ie P, 2p) 
3s) 
Tp? P; (p) 
18 
-88 14:4 7-68 
ie OO! a Tp 
R 
2:88 0:8 2ESz 
— (7 — 22) Pate) + Se Por) + 
Pp 
)P,(@)f- 09) 
This is to be compared with the value for the same model without any 
reducing factor, that is, with (18) when § = 1, or 
l6eb7c? ( 4 16 2 4 2 ; 
a OS) Sa OD) = = =. 
R= WORE (oat spt phe CP) = han) + Ps (2p)}- 20) 
The curves are given in fig. 2, and show the variation of R/c* with the 
quantity c/\/(g/); in addition to the smaller value of the resistance from 
(19) compared with (20), there is also a relative decrease in interference 
effects. 
* © Proc. Roy. Soc.,’ A, vol. 144, p. 519 (1934). 
403 
