in which we may write

w′ = φ + ψi.

(12)

Along the stream line xABPJ, ψ = 0; and along the jet surface APJ, −1 > φ > −∞; and putting φ = −πs/c − 1, the intrinsic equation is

πs/c = cot2 nθ,

(13)

which for n = 1 is the evolute of a catenary.

Fig. 7.

43. When the barrier AA′ is held oblique to the current, the stream line xB is curved to the branch point B on AA′ (fig. 7), and so must be excluded from the boundary of u; the conformal representation is made now with

dΩ= − √ (b − a·b − a′)
du (u − b) √ (u − a·u − a′)