THE EOYAL ARTILLERY INSTITUTION. 
189 
pressure, and the only effect of either of the above experiments would be to 
increase the time during which that pressure acted. Experiments have 
shewn that the initial velocity of a shot will depend upon the point at which 
the charge is ignited, all other things remaining the same. And Daniel 
Bernouilli, who gave the common formula for the calculation of initial 
velocity in 1738, at that time expressed his belief that the whole charge 
was not fired instantaneously, and more than a century ago a Committee of 
the Royal Society, appointed to examine this question, came to the conclu¬ 
sion that the whole of the powder is not fired before the ball is sensibly 
moved from its place. Why then are we to retain a mathematical formula 
which is manifestly based on an erroneous assumption ? The thorough con¬ 
tradiction between the results of this formula and of the experiments with 
the 70-pr. Armstrong and Whitworth guns with charges of 10 lbs., ought to 
be the death blow to the formula. The length of bore of the Armstrong 
muzzle-loader was 10 feet 3*25 inches, and length of cartridge, 12*81 inches. 
The ratio of weight of powder to weight of ball was *1403; and the initial 
velocity was 1336 f.s. Substituting these values in the formula 
-75 
/* . M 
~Y~T~ lo S — > 
+ 3 ^ /* 
1836 
-*/r+i 
1403 
+ J X *1403 
log 
123*25 
12*81 5 
which gives = 3680*3. 
As the powder was the same in quality in the two cases is a constant. 
Now apply the formula to calculate the initial velocity for the Whitworth 
gun, the bore of which was 9 feet 11 inches = 119 inches long. The 
length of cartridge was 14*5 inches, and the ratio of weight of powder to 
weight of shot was *1427. We find by the formula the initial velocity 
= mn * 
whilst the velocity found by experiment was 1338 f.s. Thus the formula 
gives for the Whitworth gun a velocity decidedly less than that for the 
Armstrong, whereas experiment gives a velocity slightly greater * The formula 
gives 1298*7 feet as the velocity at the gun, whereas experiment shews that 
this would be the velocity at a point about 600 feet from the gun. 
Under these circumstances it is quite plain that this formula is perfectly 
useless in determining the stress upon the gun. Captain Rodman used his 
pressure gauge in very numerous experiments, but as might have been 
expected from the shortness of the time during which the pressures were 
applied, the instrument did not give results sufficiently regular. Major 
Navez has proposed to use his pendulum to measure the times occupied by 
the shot in traversing different parts of the bore of the gun, but inasmuch as 
these intervals of time must be very short, and as every measurement must 
depend upon the action of three electro-magnets, it may very naturally be 
doubted whether the results would be of any value. The only method 
which appears to me to hold out any prospect of success, is one to which 
Captain Rodman gave a very partial trial. He mounted a gun in the old 
gun pendulum. A cylinder was placed with its axis parallel to the bore of 
[vol. v.] 25 
