22 ON RIFLED GUNS. 



repeated firing, by which it becomes heated and thrown into a new set, is not the same as 

 before the firing began. 



(4) — It is by the propagation of molecular disturbance that the forces of resistance are 

 developed and brought into action, and the rate of this propagation is measured by the velocity 

 of sound in the gun material. 



(5) — When powder is burned behind a projectile, the first action of the expanding gas is 

 to enlarge the bore and compress the metal in the direction of the radius, and this action may 

 be so intense and sudden as to break up the molecular structure within, before the outer 

 portion can come to its support, and tear the gun as an ordinary force would a piece of cloth 

 applied to its edge. This would be the case, for instance, with an active fulminate, in which 

 the limits of stable equilibrium of the chemical forces are very narrow. 

 (6) — -Take the following notation, viz: 

 M = Modulus of the gun's material. 

 p = Pressure of the gas on unit of surface. 

 ft = Radius of bore. 

 c = Thickness of gun. 

 I = Length of bore on which p is exerted. 

 V = Velocity of sound in the gun material. 



t — Time since the beginning of the explosion to the instant of greatest action. 

 Q r = Quantity of work of gun resistance. 

 Q p = Quantity of work of the expanding gas on gun. 

 (7) — Take the axis of the gun for the axis of y; a line at right angles thereto for that of .''. 

 The circumference of the bore before firing will be 



2*.p; 

 and at any time after the explosion begins 



2 * (p + dp) 

 in which dp is the increase of p. And the expansion of the circumference will be 



2- ((> + dp) - 2 tz p = 2 it. dp 

 and on a unit of length 



2 ~ (">p S/> 

 2r.,, = J 



Conceive a circular ring of radius x, and of which the plane is perpendicular to the gun's 

 axis, and let the area of a section of this ring, by a plane through the axis, be dx. dy. 



When the circumference of the bore is expanded by 2 tz dp, that of this ring will be 

 2 7z. ox; and on a unit of length 



2 -x x ' 

 By the principles of wave propagation, 



(334) 



