to B B«, 



^/= ^''i (3) 



The rate of change of velocity with distance across the contours is ^t - '•« 



■J 

 where J is the distance between contours, and therefore the velocity Q-^ 

 at A' is greater than that at A by the amount c, - Cj, . g. 



similarly the velocity C2' at B' is greater than that at B by the amount 



^/ ~ ^ d sin (oc-jia)^ The velocity C" between A' and B' is therefore 

 J- 



and, as before 



./?z=c"i (5) 



From equation (1) 



From equation (2) and (3), t^^t - ^l~ .a^jj 



Z 



It may be noted that if a±n(oc-Ao() is assiuned approximately equal to sin fir , 

 the equation derived by Isaacs resul.ts. However, with the more accurate 

 approsdmation of sin(a-^Jcr) = sin Of cos4a - cos of sin ^or «= sin or- J^ eas c( t 

 then Aoc becomes 



Acc^^ Bi^Lma^ ^^L^£L£i) (8) 



An 

 Now angle 0" AO — —- and from triangle A 0«J 



Z 



.^-«-r-^/> 



/ 



J ' ^ / ooacx +^ 



Z 



Substituting into equation (8) and reducing terms, than 



oo3CX + 1i3. sir) a. 



A<x=-^ 2^^^cc-/itx (10) 



^ar. 2-t-Aa ian oc 



Letting - — » K and solving for J^ 



2 ioin cc 

 25 



(U) 



