TRAJECTORIES OF FIELD GUNS. 
423 
These formulae are very accurate, and may be relied upon for results, 
differing very slightly from those obtained from the most exact methods. 
They have certainly the great advantage of being independent of tables, 
and of all knowledge of velocities and times for their calculation. 
A reliable statement of the trajectory of the shell for the last two or 
three hundred yards of the ranges is undoubtedly of much assistance 
to the officer recording results in the range report during practice. 
By means of pegs and flags there is no difficulty in telling how far 
short or over a shrapnel shell bursts, but the height above plane is so 
very deceptive that the conjectures of practised observers often widely 
differ. It will, therefore, I think be of use in such a case to know at 
what height above the plane a shell should burst at a given distance 
from the target, supposing the gun to be correctly laid. 
For an instance, suppose the practice is with the 13-pr. at 2500 yds. 
range, and that the shell is judged to burst 90yds. short; from the 
table we see that at a hundred yds. from the target, the height of the 
shell is 33 ft., and moving the decimal point one place to the left we 
obtain 3*3 ft. for the vertical height due to 10 yds. distance from the 
target; thus 9 x 3*3 ft. or 29*7 ft. is the height of the burst, presuming 
that the gun is well laid. A moments reference to the table thus 
forms a good guide to the judgment, and if the laying be not reckless, 
a very wrong guess could not be given. 
The height of the bulks eye of the target must of course be added 
to the numbers in the tables. 
We can also find how far in front of the point of impact a man would 
be struck; taking his height at 5*5 ft. we have— 
3‘3 : 10 :: 5*5 : x (required distance in yards), 
550 „ , 
*’ x = 33" = 16 3 yds. 
A shell striking twenty or twenty-five yds. over at this range would 
thus pass over the heads of a line of men. 
Approximate Rule for Rinding the Highest Point of the Trajectory. 
If h be the height in feet, and t the time of flight in secs., then, 
h = ft x 4. 
