4 
THE SMALL-ARMS OE EUROPE. 
(g) Dangerous trajectory .—Tlie angle of elevation giving a trajectory 
wkicli catches a height of 6 ft. throughout is got as follows :— 
The trajectory which nowhere rises more than 6 ft. above the level 
is always one of short range; one may therefore substitute a simple 
parabola (Fig. 2) for it, of which the highest ordinate h is given by 
the formula 
To calculate the range which is all dangerous, assume the firer holds 
his arm at B' at a given height above the ground, which we will 
consider horizontal, and aims at the enemy's middle at C'; if B'C' 
be assumed horizontal, no part of the trajectory should rise more than 
3 ft. above it, and if in (7) we make 7i= 3 ft., 
R j n , = </2 X 9-81 x 0*9 _ 4*202 
Vl v ~ V ’ 
V being expressed in metres ; and by means of a table of elevations, 
the range BC due to the angle is readily obtainable by interpolation. 
The total range AD due to the angle calculated with h = 6 ft., 
is similarly deduced. In this case we have 
• . __ \/2 x 9*81 x 1*8 
sm (j) q —- 
5*9427 
V 
BDy the real space swept, can then be found approximately by means 
of AD; for 
BD = BC + CD. 
If it is seen that CD = AB, it follows that 
AD = 2CD + BC, 
and as BC = B'C' 3 we have 
BD = B’C + 
2 
