Brard 
fluid motion would be steady at t, if mw ¢(By,t) were constant during 
the infinitely large interval (- » , tj). 
One may write 
®, (M',t. 3) 04) «= aff u (Ph, to ; 0+) om ae ad, (Pj). (7.27). 
f 
This expression is the velocity potential due to the normal dipole 
distribution on )/,. 
The expression 
! é Sel Bela ye ! , at 3 1 ! 
JOBS RG aa Ss | Ae a a) np, M'P} ad (Ps) 
‘ f (7.28), 
is the difference between the true expression of D(M', t, ce +) given 
by (7.27), and that which would be reached at t, if the motion of 
the body had been uniform in the interval (t', to),the velocities 
Vz (0) and E— during this interval being constant and equal to those 
of the real motion at Bee 
Obviously : 
+O; (7.29) 
@,(M',t, ; t+ oo ) is the limit reached when t' ——~- © . This 
limit defines the steady case b when Vp(0) and Qf are constant 
(since t<t.) and equal to the velocities which determine u (BE, t.) 
and u,(Pf,t,) = #;,(By,t,) for every — > 0! 
The difference 
5@,(M', t 3) foo prey 
Z piM'.t, 3 +0 )- @(M',t. 5 0+) (7. 30). 
1242 
