Vortex Theory for Bodies Moving in Water 
is the deficiency of Py, that is the difference between the ® ¢ deter- 
mined in the steady case for the present velocities VE(0, t,) and 
la 
2 (to) at t, andthe true @ in the real motion at t, 
Let Be, and at denote two points infinitely close to B}, 
but located on 3 and 53 ’ respectively. We have 
! = ! = ! . 
u (Bi, t.) HAP ans ts) Big t) (7. 31). 
Mis the solution of the integral equation 
-H(M', t.) Nie a _ d Lu (P!) 
Sy 
= @ (MM! it ) <4@ 
! . ! My 
a (Mit, 30+), M! being on pide (7232) 
We have 
u(M',t )= u(t) u,(M) -G o (Ms, t 3 0+) ) (7.33). 
Ae a linear and wee eneous functional the argument of which 
is the function ® ¢ ( (M', ; O+) : it may be written in the form 
GC (M' me KUM, P) OP eG +) dd (P').) ees 
Let us substitute (7. 27), into (7.33), and take into account 
(7.26) and also the condition 
(1) K is the resolvent kernel of equation (7. 32). 
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