1' low from a Disturbed Area. 447 



Resultant Pressure 



^ -r^ o i 1 ^ w dw /TO . . i' 1 ^ ID 



0>=irF o -2p\ +^_1) 



Jo v l — w J o v/l_^ 



dw 



to 6" — m; 



= TrPo-Tr/ajja-^^Tf. 



This has been obtained on special assumptions as to units 

 of length and time. 



:...*— ^^_^p=ij + ^, . (13> 



where <? = velocity of undisturbed stream, 

 L= CB, 

 b = tt/4 .£t^, where r=CB : C'B. 



Hence (13) gives the resistance of a flat plate with a 

 straight after-body. 

 As b— >1, 



9_p ^ 



c^ 5 — > j -f (Twice the pressure on a plate of 



length L as given by the discon- 

 tinuous stream-line theory) . 



This is in better agreement with experiment than the 

 discontinuous stream-line results (Kelvin, Collected Papers, 

 vol. iv.). 

 . As b increases the resistance diminishes. 



However, since this will soon make the velocity, relative 



to the plate, q = rqo small compared with q , the solution 



soon ceases to represent an approximation to the actual 

 motion . 



VII. Effect of the shape of the after-bod//. 



That the resistance will depend on the shape of the after- 

 body can be seen as follows : — 



Replace c by a suitable function of w, 



e. g. c(w) = {{d + w l l 2 )(f+wV*) } l \ 



c, d, and /'all >0. 



c(ic) has no singularities in the finite part of the upper 

 half-plane. 



