Voh. 6, 1920 
PHYSICS: A. G. WEBSTER 
289 
ON THE SPRINGFIELD RIFLE AND THE LEDUC FORMULA* 
By Arthur Gordon Webster 
Clark University, Worcester, Mass. 
Read before the Academy, April 26, 1920 
One of the formulae of interior ballistics found most useful, at any 
rate by practical ballisticians in the United States, is the formula of 
Leduc, which says that the velocity of a shot in the bore of a gun is graphi- 
cally represented in terms of the distance travelled by a rectangular 
hyperbola, giving the formula : 
as 
V = 
where v is the velocity, 5 the distance travelled by the shot. 
The writer had the curiosity to try this formula on the Springfield 
rifle. The observations were made by the gauge described in these 
Proceedings, 5, July, 1919 (259-263). The mode of deducing the Leduc 
formula is decidedly open to criticism since it assumes the combustion to 
be instantaneous, and the expansion adiabatic, neither of which is true 
and it is perfectly obvious that powders giving curves so different as those 
published in the paper quoted cannot possibly give v, s curves of the same 
shape. Nevertheless, it turns out that for the rifle the Leduc formula 
answers very well indeed. 
Observations were made on the time of reaching different points in the 
barrel by Mr. H. C. Parker, assistant in the Ballistic Institute of Clark 
University. The method was to put a fine wire insulated with enamel 
down the barrel of the rifle to a certain distance. When the shot reached 
it a circuit was made which made a current passing through the oscillo- 
graph. The motion of the oscillograph was photographed on a rotating 
drum and thus the times were obtained. The curve obtained for the 
actual times of reaching ten or a dozen distances was exactly similar to 
that shown in the paper cited above, obtained by a double integration 
of the pressure- time curve. The velocities were obtained from Mr. 
Parker's curve by a graphic differentiation, and from the known velocities 
and distances the formula was obtained. Even without the method of 
least squares the formula v = ^^^^^ answers very well where the dis- 
19.8 + ^ 
tances are given in centimeters and the velocities in meters per second. 
* Contribution from the Ballistic Institute, No. 7. 
