Brard 

 This ejqjression being linear with respect to 0, we would obtain 



with 



(5) 



Pi(m^,t') 



pP'C-^e't') = 



L3t 



Ve grad 



- - Ve grad 





'Poo(">e) + L V-^e't') 



(6) 



PiCmg, t') generates the set of forces (?■) when the fluid is quite perfect, 

 say when there is no wake; p '(nig, t ') gives the contribution of the wake in the 

 hydrod5niamic forces. 



In order to use the density of the distribution of normal doublets on S and 

 the equation 



it is, however, easier to consider the streamlines C of the relative motion on 

 Sg. These streamlines are the orthogonal trajectories of the curves y = con- 

 stant, where 7 is the total density of the normal doublets on S . Because all the 

 components of 7 are small with respect to ygg, that is, with respect to the 

 density of normal doublets which generate $00, we may consider that the unit 

 vector i^ tangent at m^ to the streamline C passing through m^ at t' is practi- 

 cally independent of t ' . We choose i^ positive downstream and also the ele- 

 ment of arc da' on C. Consequently, the relative velocity Vj.(mg,t') is approxi- 

 mately given by 



V.Cm^.t') = V/mg,t') i;(m^) 



2 -| 



)0('-e) + E 1'okC'^e) fokCt') - [VeI;] 



3 

 'ha' 



m , t ' 



Hence, 



2_ 



'da' 



7 \\o(^e) + E ^("'e't')] 

 k = J 



- V ^ (m ,t') 

 o ' r ^ e' '' 



is the sum of the three following terms: 



846 



