Lord Rayleigh : Ilydrodynamical Notes. 193 



^ = CV 3 (cos#- cos30) + D^sin0-|sin~30), . (9) 



VY=8r(Ccos0 + Dsin0) = 8(C« + Dy). . . . (10) 



In rectangular coordinates 



t=4CV + 4% 3 , (11) 



solutions which obviously satisfy the required conditions. 



When 5 — 2, a — 27T, the boundary consists of a straight 

 wall extending from the origin in one direction (fig, 2). In 



Fig. 2, 



4\ 



S= 2 



this case (C) and (7) give 



<f=:C^ l {c0S(i?^-2(9)-C0s|72^} 



4-D ? i ^sin(^6'-26>)-('l-^jsin|/^[, (12] 



7^= {2n-4:)r hn - 2 { C cos (\n0-20) 



+ D sin Hn0-20)}. .,/„.,. (13) 



Solutions of interest are afforded in the case ?i — l. The 

 C-solation is (C = £) 



^r=i^(cos|^~cos|(9)=-7- l cosJ^sin 2 |^ . (14) 



vanishing when 0=w, as well as when # = 0, 8 = 2tt, and 

 for no other admissible value of 6. The values of yjr are 

 reversed when we write 2 y ir^-0 for 0. As expressed, this 

 value is negative from to it and positive from it to 27T. 

 The minimum occurs when = 109° 28'. Every stream- 

 line which enters the circle (?' = 1) on the left of this radius 

 leaves it on the right. 



The velocities, represented by d^rjdr and r~ 1 dtyld0, are 

 infinite at the origin. 



FJdL Mag. S. 6. Vol. 21. No. 122. Ftb. 1911. 



