18 ON RIFLED GUNS. 



At the instant the plug stops, V = 0; and 



A = B x n 



2(m + l) 1-cos (i k.-\ 



or 



B; 



a 2(m+l) 1- cob (**.?) 



The first member is the ratio of the maximum elastic force of the gas to the copper resistance 

 at the instant the plug stops, or at the instant of greatest penetration; and it is apparent that 

 we can neither take the first member equal to unity nor x=za, since x has already been taken 

 to satisfy the condition of V — 0. The penetration or width of the cut cannot, therefore, 

 indicate, directly, the maximum gas pressure. 



If we make m=l, that is, the copper resistance proportional to the plug penetration, 

 then will 



A _ ~ x 1 



B* ~ 4' a ~ 



-cos (A,.*) 



still indicating the same difficulty. 



It seems to have been taken for granted, in Major Rodman's experiments, that the gas 

 pressure is constant during the time the cutter is making its way to the stopping point. This 

 certainly cannot be true; but if it were, then would 



f A dx — / B x m dx- — . V 2 = ; 



2g 



or 



B W 



Ax x m + 1 . V 2 = ; 



m+l 2g 



and the instant the plug stops, V=0, and 



(m + 1) A — B x m = 



or 



»v< 



A 



and making m=l, which supposes the resistance to vary directly as the penetration, 



A 



or 



Bx = 2A, 



That is, the resistance of the copper at the stopping point of the cutter is twice the pressure 

 of the gas. 



(20) — Major Rodman seems not to have recalled the distinction between the measure for 

 inte.nnity and that for its work. The real difficulty lies in our ignorance of the laws which connect 



the intensity of copper resistance and of gas elasticity with the plug penetration. If these 

 (330) 



