342 



Mr. A. Mallock. 



it does only on the elasticity and mass of the weapon, but t n and A. n 

 depend on the rapidity and rate of the explosion. 



Suppose that in place of assumed explosive a slower burning explosive 

 were used, with a charge sufficient to give the same muzzle velocity. 

 This would cause an increase in © and t n • that is, q nm would be dimin- 

 ished, and, owing to the greater terminal pressure (see (15) et seq.) all 

 the values of A n for n odd would be increased in relative importance 

 compared with those for n even. The result in the case of a small 

 variation of this kind in the Lee-Enfield would be an increased upward 

 jump. 



A lower muzzle velocity would also correspond to an increase of % y 

 and would give an increased upward jump in this rifle, and at some 

 particular range it should be found that the variation of jump and 

 variation of initial velocity compensate one another, and that for 

 moderate variations of charge the sighting at this range does not 

 require alteration. 



The natural periods of the rifle may be altered either by adding 

 mass, or shortening the barrel. In the first case % will remain un- 

 altered, and q mn will increase ; thus the tendency of a small mass added 

 near the muzzle will be to make the rifle shoot low. 



If the barrel is shortened both T m and & are diminished, but the 

 alteration in T m (which depends on the square of length of the 

 equivalent rod) is much more important than the alteration in % ; 

 hence a small shortening of the barrel may be expected to cause a 

 considerable diminution in q nm and a corresponding increase in 

 upward jump. 



The most important factors in these changes (as regards the Lee- 

 Enfield) are </i-2 and ^.3, that is the effect of the first term of the 

 harmonic expansion of the explosion curve in exciting the 2nd and 

 3rd mode vibration of the rifle. 



If ammunition could be made absolutely uniform in its action, 

 " jump " would be of comparatively small importance, but the 

 ± 40 feet per second by which the initial velocity of the service 

 bullet varies may, by altering the factors on which " jump" depends, 

 exaggerate with some classes of rifles, and diminish with others, the 

 variation of the trajectory due to the effect of gravity and the altered 

 initial velocity. 



Suppose a rifle to be aimed and shot from P x , fig. .12, so as to hit 

 the centre of a target T 1 at range R, when the initial velocity is V. 

 What will be the effect on the aim of a variation of the initial 

 velocity 1 



Let oi be the angle of elevation of the rifle and f3 the angle of 

 descent of the bullet at Ti. Let P' be the place in the trajectory of 

 the shot (whose initial velocity is V) where the velocity has fallen to 

 V - v. If a shot is fired from P 2 with the same sighting as was used 



