^s-K^p{r,^'ify 



[9] 



Thus the problem has been reduced to the case of a body at rest in space or in rotation 

 about some point fixed in space. This is the case which will be considered in the remainder 

 of this paper. 



HYDRODYNAMIC FORCE 



We suppose the singularities generating the surface of the body to be enclosed at time 

 t^ by a control surface, S', which everywhere lies within S (see Figure 2). At present we 



Figure 2a 



Figure 2b 



Figure 2 



specify only that S' possess a clearly defined normal at each point. This control surface is 

 considered fixed with respect to S. The portion of the body between S and S'is designated by 

 v. The body being in rotation, the space occupied by 7' changes with time, and we designate 

 this region by V'{t). In the following discussion we consider the particular set of fluid parti- 

 cles which at time t occupy the region V '{t^). Since the fluid is also in motion, the region 

 occupied by this set of petioles is also a function of time, V r{t). By definition then 



but at any other time, in general 



V'(to)-= VfitJ 



V'(tJ^Vj(t) 



The net force acting on this set of fluid particles at any time is dTH/dt where 772 is the 

 total momentum of the fluid in Yr(t). At time t^, then 



