60 ON RIFLED GUNS. 



(2 tan £ „)■*. W 



By repeated trials with different weights but with the same cutter and copper, a series of 

 values for m and A may be found, and these being treated by the principle of least squares, 

 will give the most probable values for the constants m and A. The copper should not be 

 beaten or rolled, but simply cast and planed to a smooth surface with a very sharp tool. 



(31) — To apply these preliminaries to the finding of gas pressures, it is to be observed 

 that when the powder begins to burn, the pressure is nothing, and at the close of the action it 

 is also nothing; that is, the initial and terminal values of the pressure are zero, having a 

 maximum value somewhere between. The simplest law of continuity which connects these 

 varying values with each other is expressed by the equation 



i = P. sin 



(* •') <"> 



in which p denotes the pressure, in pounds, upon tho plug head, P the maximum pressure 

 upon the same, and I the greatest value for x, or the entire penetration. 

 The quantity of work of this pressure will be 



Jr»x = / x\ 2 1 



^ P. Bin. (*. ? ) <** = -. P; 



The quantity of work of the copper resistance will be 



Jf*z=o A 

 Ai". dx = -. l m + l ; 



(32) — But these quantities of work must be equal; whence 



2 I t, A , 



— .P = -. l m + l 



iz m 4- 1 



or 



A. l m (23) 



' re, the maximum value of ?/, or the 

 have, Eq. (19), 



■ 2(m+l) 



and denoting by re, the maximum value of y, or the entire length of the cut, answering to I, we 



1-. 



2 tan ^ <p' 

 which in Eq. (23) gives 



P = . k.( V. (24) 



2(m+l) \2tani p/ V ; 



A and m are known, Eqs. (20) and (21); re may be measured by the Filar Micrometer 

 with great accuracy; whence P becomes known. The value of P, multiplied by the ratio of the 

 area unity to that of the plug head, gives the pressure on unit of surface, or P in Eq. (7). 



(34) — At page 38 of Major Rodman's work is a table giving a series of actual pressures, 

 varying from 1.000 to 14,000 pounds, and the cuts produced, ranging in length from 0,21 to 

 1,11 of an inch. These, by Eq. (17), give a mean value for m— 1,5957; say 



m = 1,G. 

 (342) 



