Brard 





VE(m^,t') i;(mj + — l'oo('^e) 



3a 



-, yi(m,t') 



or by 





v; * ^ *oo 



+ J 5P (?) ,5r>,f-r')dr' 



"^ 



Let us consider firstly the particular case "aj," when 



(^).. = (^l + » 



for t ' > . Let 



be the expression of pjCm^.t') in this case. Equation (10) gives: 



(10) 



U 3 



i ^'"e.t') = - L bT Sr;(m,t') + 



V; + 3^ <^oo 



Therefore, one has 



1 1 ,* 



V; + ^ ^00 



3a 



X —, [7*Cm,0+) + S7*(m,t')] 



7 [yl(m,0+) + S7*(m,+oo)] . (H) 



Now consider the difference in the case "b^," when (w/U)^., is an arbi- 

 trarily given function, between the pressure pg i(me)(w/U)^, in the quasi-steady 

 motion and the pressure pj(m^,t') in the real motion. Assuming that (w/U)^, 

 is continuous for t ' >0, we have: 



where 





(12) 

 (12') 



848 



