602 



After the introdnclion of nndimensioned variables, we make use 

 of the abbreviations: 



1 



I dy y uv ■=:■ 

 

 1 







1 r - 

 12J ^' 



The equations (50) and (51) now reduce to: 



X 1 



ÖT H =: — . . 



R" R 



(52) 



1 JA _ C _ 1 



(53) 

 (54) 



Distribution of the vortices over the jiuid. 



clU 



As aopears from equation (49) the value of /< —^ will be small 

 compared to that of ^^ ( ;r — .V ) (as is the case for the real motion) 

 onlj- if — Quv becomes approximately equal to J I - 



.yj. Or, 



using the nndimensioned variables introduced above, we may say 

 that — uv aught to be proportional to ^ — y. 



Hence the quantity uv must take a negative value in the neigh- 

 bourhood of the wall y = 0, and it must lake a positive value at 

 the other wall. This can be obtained if we use two groups of 

 vortices whose positions are symmetrica! with respect to each other. 

 In the first place a group of elliptic vortices having the same 

 position as those described in paragraphs 4 and 5 (i.e. with the 

 long axis extended from the second to the fourth quadrant) is put 

 ill against the wall y = Q. The contiibution of these vortices to the 

 field of values of uv will be denoted by 



— {uv)i = \\> (y). 

 Then a second group is put in, situated symmetrically against 

 the other wall: the contribution of the latter to uv will be: 



— ("r)u= - t|'(l— y)- 



