Leathem — On Tioo- Dimensional Fluid Motion. 35 



For the same obstacle and the same limit velocity at infinity, the 

 theoretical and the actual flow may be said to correspond. It is doubtful 

 whether a good case has been made out* for believing that the resistance of 

 the obstacle to the flow is the same in corresponding motions ; nevertheless 

 the correspondence may help towards estimating the resistance in the. actual 

 flow. 



It seems to be established as an experimental fact that in actual flow 

 the resistance is greater when the wake or region of rotational motion is 

 extensive than when it is small. Thus, in such a problem as the designing 

 of the cross-section of a strut for an aeroplane, attempt is made to secure 

 a form such that the lateral spreading of the wake, and its area, shall be as 

 restricted as possible. Now it may be argued with a certain degree of 

 probability that, the less divergent are the free stream-lines at their points 

 of departure in the theoretical flow, the less spreading will be the wake 

 in the actual flow, and therefore the less will be the actual resistance. 

 For different shapes of prow the capacity to produce divergence of the 

 two branches of the divided stream is likely so to correspond in the 

 theoretical and the actual flow that where it is relatively small in one it 

 is also relatively small in the other. In both kinds of flow divergence of 

 the wake is evidence of the capacity of the prow to screen the region 

 behind it from the force of the adverse stream. 



If this be true it is important to enquire how. in theoretical flow, 

 the divergence of the free stream-lines can be made as small as possible. 

 And it may be surmised that, in theoretical flow, the most probable points 

 of departure of the free stream-lines are those points which (as discussed 

 in articles 17 and 18, above) are the most forward points of the obstacle from 

 which departure is possible ; or, at least, that the degree of divergence for 

 these most forward points of departure is relevant for purpose of comparison 

 with the corresponding actual flow. 



When the flow is symmetrical the most forward possible points of 

 departure correspond to the value of a which satisfies the equation S=6, 

 that is 



{ = » 



** + ai J <n? = 0; ("J 



where there is a functional relation between % and £ whose form determines 

 or is determined by the shape of the obstacle. Assuming p to be assigned, 

 the question of design with a view to minimizing the divergence of the wake 



* See a foot-note near the beginning of paper A. 



R.I.A. PROC, VOL. XXXIV, SECT. A. [6] 



