131 
OH THE 
MOTION OF A PROJECTILE IN A RESISTING MEDIUM. 
BY 
A. G. GREENHILL, M.A. 
(Professor of Mathematics to the Advanced Class of Artillery Officers.) 
It is assumed tliat the resistance of the medium acts through the 
centre of gravity of the projectile in the tangent to the trajectory, and 
consequently it follows that the trajectory will lie in a'Vertical plane. 
Resolving normally, supposing v the velocity at the point where the 
tangent is inclined at an angle i J/ to the horizon, 
difr 
v = — g cos $; 
the negative sign being required because ^ is diminishing, and there¬ 
fore is negative. 
If we put u = v cos (the horizontal component of the velocity), 
and p — tan then 
dxj/ 
dt 
and the first equation becomes 
V COS 2 l jr 
dp 
dt 
— (J cos l/,. 
or 
dt u 
dp~ g ' 
( 1 ) 
Since ^ = n, therefore multiplying equation (1) gives 
and since % 
dx 
dx 
dp 
p, therefore 
dy 
dp 
pu i 2 
0 
(V 
(3) 
