ON RIFLED GUNS. ^d 



with the condition that, 



Vt + p>x, (2) 



without which the disturbance will not move fast enough to develop resistance by the time 



it is needed. 



The molecular resistance on a unit of surface, supposing every element of the unit to 

 exert a resistance equal to that on dx. dy, will be 



Sx 



and on the element dx. dy, 



M. 



x 



M. ' . dx. dii. 



x J 



The elementary quantity of work of this resistance, on a unit of length of the ring, will be 



Sx ,Sx 

 M. — . d — . dx. dy. 

 x x 



St* ox o c 



which integrated between the limits — =0 and — =— , will give the work of resistance in a 



unit of length of the ring. This integration gives 



ami in the entire ring 



dx 2 St? 



2- x.h M. -^-. dx. dy. = -. M. — T . xdx. dy. 

 ar xr 



Sx ... 



Replacing — by its value in the wave function (1), and indicating the integration within the 



limits of I and c, we get 



= 9 + c 



or 



3) 



(8) — In the incipient state of powder inflammation the gas pressure is zero, and this 

 pressure reaches a maximum when the bore is most enlarged. Denoting by p the varying 

 value of the pressure upon a unit of surface; by P its maximum value, and by (dp) the varying 

 value of dp, we may write 



,-p. *(»*!£) 



The pressure upon the interior surface of which the length is I is 



2,. / ,.;. i , = 2,. ( ,?.P. S m^.| ) ). 

 and the work of this pressure from the beginning till the bore has its greatest expansion is 

 Q D = f li °°2 tt. p. I. P. Bin ( I * ( 4^ d {dp) = 4. P . Sp. I. P 



J(i9)=ip V "." / 



5 ) 



