THE ROYAL ARTILLERY INSTITUTION. 
367 
making the variations winch the pressures undergo more readily com¬ 
parable, I have laid down in the Plate the curves derived from equations 
(15) and (17) for the battering charge of pebble powder. 
Prom these diagrams the pressures on the driving-surface at any 
point of the bore, both for the uniform and parabolic twists, can be 
seen by simple inspection. The line of abscissae gives the travel of the 
shot, and the ordinates give the corresponding total pressure on the 
studs. 
The curves show that with the uniform spiral the pressure on the 
studs reaches nearly 70 tons after a travel of *3 ft., rapidly falling to 
about 9 tons at the muzzle; while with the parabolic rifling the 
pressure at *3 ft. of travel, corresponding to the point of maximum 
pressure, is only 31 tons. The pressure then falls slightly, and amounts 
to 28 tons at about 1 ft. travel; thence it gradually increases to a 
maximum of 36 tons at the muzzle. 
By way of comparison, I have added in the engraving a curve 
showing the pressures required to give rotation to a 400-lb. projectile 
fired from the 10-in. gun with uniform twist when R.L.Gr. instead of 
pebble powder is used. 
The curve in this case is of the same nature as that derived from the 
pebble powder; but the variation is greater, the maximum pressure 
being much higher, and the muzzle-pressure, owing to the smaller 
charge, somewhat less. 
27. To one more point it is worth while to call attention. • 
If the gun were a smooth-bore gun, the equation of motion would be 
M . 
(24) 
and comparing this equation with (10), we have, on the supposition* 
that the velocity increments in both cases are equal. 
G = G' + R . 
{ 
2z . sin 8 
+ 
s/ 4 z 2 (sin S) 3 + k 2 n/ 4 z 2 -}- k 2 
or, in the case of the Woolwich gun, where 8 = 90°, 
G = G' + R . 
}. .( 25 ) 
f \ . 
,(26) 
and the interpretation of these equations is that the gaseous pressure in 
the rifled guns (rifled with the parabolic twist) is greater than that in 
the smooth-bored gun by the second term of the right-hand member of 
the equation. 
28. The corresponding equations for a uniform twist are 
G==G' + R 
or, if 8 = 90°, 
{ 
sin 8 
+ 
Mil- 
\/£ 3 + (sin 8) 3 ‘ «/l -M 3 
G = G' + R { fo*- + -l X 
In/I + k 2 J 
>} 
.(27) 
.(28) 
* Were tlie velocity increments not supposed equal, the reduction of pressure due to the sup* 
pression of rifling would be less than that given in the text. 
