Ship Resistance. 497 
Working out the numerical values from (22) we obtain for the resistance, 
omitting a constant factor, 
R = 516e7* 4 353e-116% — 857 cos (10 «—e) e~ 98%, (27) 
with K = g/v. tane = 0-017. 
We verify that in this case ¢ is, in fact, very small, consequently the simple 
relation between speeds at which there are humps is not appreciably altered. 
The absolute position of these humps on the R,v curve may be slightly dis- 
placed. For instance, the final hump occurs when 10x is equal to 7, that is 
when the half wave-length is equal to 10; on the other hand, the distance / 
between the maximum and minimum on the pressure curve is 10:66 units. 
8. We turn now to more complicated distributions of pressure similar to 
those obtained by Baker and Kent, to which reference has already been made. 
We can build up a rational algebraic fraction which has at least the salient 
features of these curves; for instance, the graph of fig. 2 is represented by 
26 =p? (28) 
EA (+ pw?) +3 Att pt) 
where \ and yw are constants. We have, on the curve, 
p= 
OA=2, OB=V[}0'+), OC =p, AE = CD =2/(u2—a’), 
OF = 2(a2+2)/(at+ 4). 
With different values of > and p, one could obtain variations in the 
relative prominence of OF compared with CD, and in other features. 
If the roots of the denominator in (28) are + (a+7b), we have 
2(a?—2) = 0? + p?, 
2 (a? +07)? = A 
Using these relations in evaluating the integral y, we obtain 
9 (2 —a? ct b?) eixé 
(29) 
ss ec aMeR Gey R= OO 
ei 2 (E2— a? +08) 
{E—(a+1b)} {E—(a—1b)} {E+ (a+%d)} |-a+iv 
102 
