421 
TRAJECTORIES OF THE 9-PR, 18-PR, AID 
16-PR. I.L.R. GENS.. 
BY 
LIEUT. P. A. MACMAHON, R.A. 
la the calculation of these trajectories the approximation given by 
Major Sladen, R.A., at p. 67, of “Principles of Gunnery/' has been 
employed. 
The angles of elevation being low, the resistance of the air has been 
considered to act only horizontally, so that its effect upon the vertical 
component of the velocity has been neglected. This amounts to the 
substitution of ~ for ~ in the expression — 2 h (-^ for the atmos- 
dt 
dt 
pheric resistance. 
This method is satisfactory for flat paths, but as the elevation is 
increased, it tends to make the path less curved at the commencement 
than it should be, and if carried beyond certain limits, it would actually 
cause a convexity of the path at the beginning. The remaining 
velocities at every hundred yards from the muzzle were first obtained 
from the formula— 
S v 
w 
The differences of these velocities were found to be irregular, about 
the region where they were very nearly equal to the velocity of sound. 
This might be expected, as the air just in front of the projectile 
becomes disturbed by the propagation of the whirring sound of the 
shell— as the velocity of' the shell falls below that of sound. These 
velocities were tabulated, and the times from the muzzle to each 
distance, thence calculated from the time-integral formula 
52 
