MR. J. H. MICHELL Off THE THEORY OP FREE STREAM LINES. 
421 
Therefore, in terms of and c, this distance is I where 
TT = 
--X -T- + :: log + V —t-‘ si 
Vj + Vi ro 
z>3 + 
sin 
For example, let the stream have half the velocity of the issuing jet, so that 
Vy=- \ % Then the jet makes an angle of 60° with the plane, and its breadth is Z: 
approximately, while I is about 5 h. 
Case IV .—Jet from a pipe along which liquid is flowing. 
The liquid is flowing along a pipe bounded by the plane walls AC, DE, and there is 
an aperture AB in the former. 
The left boundary of the jet is i// = 0 , the right boundary is a stream line if/ = tt, 
which branches at a point C on BC, and DE is ifj = tt. 
The w diagram is as in the figure, consisting of two infinite lines, xp = 0, xjj = tt, 
with a semi-infinite line xfj = zs between them. 
xj/- — TT 
y = US 
y = 0 
In transforming to the u plane, we suppose that </> = — 00 corresponds to 
u = — 00 , and that u = — 1, u = 1 are the edges of the aperture. 
The constants of the transformation are then determined, and we take u — a for 
the branch point, u —h for the jet at an infinite distance, u — c for ^ = co in the pipe. 
Then 
where 
dw . u — a , 
ddi~ ^ ^ 
A I' ~~ C 
A - TT — TT 
. c — a 
— A , - - TT 
0 — c 
rj' — 77, 
