w 
420 MR. J. H. MtCHELL OR THE THEORY OP FREE STREA.M LIRES. 
therefore 
So that 
and 
therefore 
Hence 
'ViN®_ _ (I 
~~ (a + 2)2 ^ 
a = 
j 
- V, 
v/ — 
— « -f h 
2v^ (^3 - 
r.d — 
* - 9’’/+V , 
^=2"v '. + ^n 
^’2 
O' 
V., ^ V^ — V^ 
+ ^ 
V- 
and the inclination of the jet to the plane is 
-1 
cos ' - • 
'^■2 
An interesting element not yet calculated is the distance of the branching of the 
stream line xp = tt from the edge of the aperture. 
This distance is 
1 
’«+iri („ + 1)^ _ 52 + _ py 
Ji 
b p — (I. 
a + 1 a 1 
dp 
O+if g + 1 _ g 1 I f 2a ] 1 
J4 _ h b p — a b ^ P ~ dip!^ — 
dp. 
where we have used the relation between a and h to simplify the expression, 
ad-1 
P-1 log {p “ «) + r \/(p" - ^') + T log (p + \/p2 - IP) 
, \/2ff, . _n \ P - ap 
+ - sm - 1 —-- 
b [0 (p — a) 
1 / I -I 7 \ ^ 1 n \ ^ I ^ 1 + 2 
—y^ {a + 1 - z>) + - log (6 - a) + - + ^ log 
+ r j - 2 
