80 66 



In the resultant motion of the fluid as a whole, this volume is carried out- 

 ward from the surface by the normal component of the resultant particle ve- 

 locity v„. Hence 



v„ 6S = NV^ dS = -^^ f{t)6S 



The velocity y„, however, must be the same as the normal component of veloc- 

 ity of the target. Hence, if z is a coordinate of position for the element 

 6S, measured perpendicularly to the initial plane and, for convenience, in 

 the direction away from the fluid, 



_ _ dz^ _ _ . 



^^ dt ^ 



The proper particle velocity will exist, therefore, at the target if f{t) is 

 such a function that 



— r-/(«) = v„= - z 



Then 



ru) = ^fit) = -^z 



where z = d'^z/dt^; and 



where z .± denotes the value that the acceleration z has, not at time t, but 



c 



at the earlier time ( - s/c. 



The pressure at a distance s from the element dS, due to all sources 

 on it, is, therefore, by [98] 



(N6S)p. = J [*■ ~ VI ~o ^(--s- 



and at any point on the face of the target the pressure due to all sources is 



2 



-f--z,.^dS [99] 



where s denotes distance from the point to the element dS. Here p^ refers to 

 a particular point on the target and to time t, z ^ _ j_ is the value of z at dS 



C 



but at a time t - s/c, and the integration extends over the face of the 

 target. 



The pressure at any point on the target due to all causes is then 



p = 2p. + p, + Po = 2p. + po - -^fj z,,^ dS >[100] 



Here even p^ may vary from one point of the target to another. 



