Experiments upon Gtmpowder. 27 



is Dr. Hutton's theorem, which is sufficiently accurate, 

 and far more simple and expeditious than either of the 

 preceding. It is to be remembered that ^, /z, and c may 

 be expressed in any measure; but f must be English 

 feet, and v will be the velocity of the bullet in English 

 feet in a second. 



The velocities of the bullets in most of the foregoing 

 experiments were first computed by Euler's method, as 

 I had not then seen Dr. Hutton's paper; but in going 

 over the calculations a second time, I made use of Dr. 

 Hutton's theorem. Both these methods gave the same 

 velocity very nearly, but the Doctor's method is by 

 much the easiest in practice. 



In these computations care was taken to make a proper 

 allowance for the bullets that were lodged in the pendu- 

 lum, and also for the velocity lost by the bullet in pass- 

 ing through the screen. 



The corrections necessary on account of the bullets 

 lodged in the pendulum were made in the following 

 manner : — 



b was continually added to the value of P, 

 ^^^ X -^ " " " to the value of ^, and 



^-=^ X ^ " " " to the value of/. 



Of the Spaces occupied by the different Charges of Powder. 



The heights of the charges of powder, or the lengths 

 of the spaces which they occupied in the bore, were 

 determined by measurement ; and in order that this 

 might be done with greater accuracy, inches and tenths 

 of inches were marked upon the ramrod, and the charge 





yi^yj^ A <=.<=>■ 



