Wu and Whttney 
where the integral with symbol C signifies its Cauchy principal 
value, and also defines the finite Hilbert transform of I(t) , as 
denoted by Hy [r] 
From this parametric description of the flow we derive the 
physical plane by quadrature 
Z(¢ ) = i et) ae dg (10) 
With the solution (7) - (10) in hand, we see that the chord 3 
wetted arc-length S , angle of attack a , as wellas the drag D, lift 
L, etc. can all be expressed as integral functionals with argument 
functions [(&) and £8(£&), which are further related by (9). 
III. THE VARIATIONAL CALCULATION 
The general optimum problem considered here is the mini- 
mization of a physical quantity which may be expressed as a function- 
al of the form 
under M isoperimetric constraints 
i 
tg [T, Bic, ... o] = i Fg(T,8, &3c),... e) dé =Ap 
(12) 
where si are constants, L i ee eee 
