IN A RESISTING MEDIUM. 
139 
The horizontal component of the velocity 
s/ (4 + a 2 ) 1 — cn x h' + 1* cn a ( . 
1 + a 2 1 — cn a h' + h cn x 
The velocity v in the trajectory is a minimum when ~ 
leads to the equation & 
= 0, which 
or 
and therefore 
1 + p (3 a + a s ) —/» 2 = 0 , 
<f (1 + « 2 ) 2 - aq (1 + a?) + 1 = 0 , 
_ a ± s/tcfi + 4) 
q 3 + 2a« 
Therefore 
and 
2^3 
= ± 3 , 
X = H- 
at the points of minimum velocity, and at these points the tangents 
are at right angles. 
