THE ROYAL ARTILLERY INSTITUTION. 
185 
The following table shows the ranges (in feet), calculated in the 
above manner, compared with those given in the tables - 
Gun. 
Elev. 
Range. 
Gun. 
Elev. 
Range. 
calculated. 
in table. 
calculated. 
in table. 
1 fi.pr. 
o 
1 
175051 
2100 
9-nr. . 
o 
1 
1723*855 
2000 
2 
3155*35 
3500 
// .MMI Ml Ml 
2 
3117*12 
3300 
4 
5448*34 
5700 
4 
5278*964 
5400 
// ... 
6 
7685*685 
7650 
// .. 
6 
7098*09 
7050 
The calculated ranges are less than those given in the range tables,* 
owing to the height of the muzzle of the gun above the level of the 
horizontal plane not having been considered. Of course the difference 
is considerably more for low elevations than for high ones, when it 
becomes immaterial. This will be evident after studying the accom¬ 
panying diagrams of the calculated trajectories. For a drop of 5J ft. 
at the end of the trajectory we have for increase of range about 300 ft. 
when firing at 1° elevation, but only 35 ft. at 6°. 
It will be interesting to make some comparisons between the trajec¬ 
tories of the two guns. For short distances from the muzzle, it would 
appear (vide diagram) that the 9-pr. has the flatter trajectory, owing 
to its higher initial velocity, but afterwards the greater weight of the 
16-pr. gives it the advantage ; for 
resistance of air varies as —, 
w 
and io varies as eft, 
resistance varies as 
a 
i,e. } the greater the calibre the less the resistance. 
Thus in every case here calculated the 16-pr. has the longer range, 
but in cases (1) to (4) it attains a lower vertical height than the 9-pr.; 
so also it descends at a less angle—except when firing at so high an 
angle as 6°, when, in consequence of the great difference in range 
(about 600 ft.), it is natural to expect a greater angle of fall; but the 
difference is very slight. This illustrates the very great advantage to 
be derived by diminishing the proportions between calibre and weight 
of projectile. 
Some slight inconsistencies may be observed in these diagrams— 
seldom, however, amounting to more than a decimal of a foot. They 
are due to the values selected for K not having been absolutely correct. 
In some instances, K was required for lower velocities than those 
given in Table I. The following values were used, which were esti¬ 
mated from the average law of variation in the table. They may be of 
* Except at 6° elevation. 
