MR. J. H. MICHELL ON THE THEORY OF FREE STREAM LINES. 
413 
Hence when xjj = i.e., at the edge of the aperture 
y ^(1 - c) 1 - v'Cl - «) 
therefore the ratio of the jet to the aperture is 
t + \/(l — ft) 
\/(l — ft )I — {I — a) 
IT + 
log 
The velocity at <^ = — co is 
therefore the width of the vessel is 
3. - 
1 + Ct 
— ^ /I + \/« \* 
1 — y/a 
d = TT 
therefore 
From which we obtain 
d /I “f~ ft\^ 
d — a/« 
1 + \/ ft 1 
c~ 
5+1 
d- 
1 — y^ a 1 
?+I 
C" 
therefore 
k = c 
1 /c . d 
1 + 5; b + ; '°g 
j-i- + -' 
’(Me 
‘Iiryd c j 1 2 
or 
'l TT \c ' d/ ^ d — c_ 
This is for the vessel considered. For the pipe 
k = c 
' 1 /2d c \ . 2d + c 
’■ + ,r(7+2J ^°^2d-c 
