Vortex Theory for Bodtes Moving in Water 
® (Mi, t.) =@ 
4 (M:, t) + u(M',t ) = Zou (t,) Jey + M; wy) on Lu. 
d 
(7.17), 
Hence, with the above notation, we have : 
(M,) + ¥ (0%) | yr (M!,t.).v,(M!, t,) 
t 
fe) 
The second term on the right side only depends on the instan- 
taneous velocities. It is the same in cases a,and a, for equal velo- 
cities Vp(0) and QE . But, in case ay the first term on the right 
side is null ; the term on the left side is null also by virtue of (7. 15), 
Hence we obtain : 
3 ! = = if 
a ® (Mi, t.) = pede fo, + H (00) (ire 18). 
Let us put 
dvi {* = a dM AN (M) dv (M) (7. 19) 
The system of forces exerted on the bound vortex sheet is 
that of the elementary forces 
[F| 
| 
— 
“e) 
= 
x 
es 
| 
ue) 
ee 
s 
o 
=} 
s 
Qu 
Kd 
| 
4 
i] 
> 
=) 
. 
oa 
s 
iS 
BY 
uM 
iS 
umes 
+ 
1 
a. 
we 
Lge a 
The system of forces exerted on the set E of fluid points 
is that of the elementary forces 
1239 
