MR. J. H. MICHELL ON THE THEORY OF FREE STREAM LINES. 
401 
Case I, A Single Jet from a Vessel. 
There will be but two bounding stream lines, which we may take to be = 0 . 
xjj = TV, both extending from + co to — oo. 
The diagram in the plane consists merely of two parallel infinite straight lines, 
AB, CD, at a distance tt apart. 
C F D 
A ]<] B 
A portion of each, say EB, ED, will correspond l.o the boundaries of the jet. 
If now we transform to the u plane so that the ends D, B go to p = dz > we 
may choose the points w = — 1, w = l,to correspond to the edges of the aperture 
from which the jet issues. 
The point (C, A) will then be in a definite position, u = c, and the formula 
of transformation from w to u is 
(ha _ A 
(In K. — r. 
Remembering that 
A = 1, and therefore 
TT is the distance between the two stream lines, we see that 
(ha 1 
(lit, u — c 
Let u = a„ correspond to an angle a„ of the vessel, then the points along q — Q are 
arranged in the manner of the figure 
free stream line. 
ri"id. 
rigid. 
free. 
U — — 1 u — a„ U — C y = 0 M = 1 
The appropriate formula is then that of Problem II. (b), viz., 
fh 
= n 
and therefore 
(ha 
<h _ 1 
(Ik, u — 
4 — a„n -j- J(1 — a,r) ^(1 — 
U — ((„ 
n 
1 — a„n + Jil — a,~) 
U — On 
3 r 
MDCCrxC.—A. 
