Brard 
s = ! 
Pp eh i eh es , t). (7. 34). 
Then we obtain for determining M(B} ; t, 10+) a_Volterraintegral 
equation. This shows that the fluid motion time _t,. does depend 
not only on the present velocities VE(0, t,) and ‘-@ Q R(t), but also on 
the history on the motion during the whole interval t < ty 
Let us consider now the system aoe of hydrodynamic forces 
exerted on the body. We readily obtain 
Ey ee cae WA +Z, (7.350 
where 
Fe = [ar | 3 - pT(M) AV, (M) aX (on 
2 
E 
1 
eal 
Q 
i 
I 
> 
=) 
by © 
H 
ro¥ 
'o) 
pay 
iI 
ae) 
nN] 
es (t) r (M, t) #422000], 
EF. . fs pia )(® 45) + ou a )a,, ads (vo |. 
A 
; AS D(M', t 5 0+) ve an ax’ | ; (7. 36) | 
The definition of "| and of ee are exactly the same 
asin formulas (7.20), and (7.22), , respectively. But the system 
of forces [dF ] does not coincide with that defined in case a. This 
is due to the effect of potential ®, on potential ®gy. On the con- 
trary, the systems of forcesY 4 coincide in both cases if the sys- 
tems of the six accelerations u;(t,) are identical. 
Let Sf op denote the system of forcesH evaluated at t, 
under the assumption that Ve (0) and {2 FE coincide with VE (@,t a 
and f(t.) in the time interval (t',t,), with t'< to. Then the 
difference 
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