(5)

w = −2Ua1/2z1/2,

(6)

and the resistance of the liquid is 2πρaV2/2g.

A relative stream line, along which ψ′ = Uc, is the quartic curve

y − c = √ [ 2a (r − x) ],   x = (4a2y2 − (y − c)4,   r = 4a2y2 + (y − c)4,
4a (y − c)2 4a (y − c)2

(7)

and in the absolute space curve given by ψ,

dy= − (y − c)2, x = 2ac− 2a log (y − c).
dx 2ayy − c

(8)