256 Mr. Thompson's Experiments 
Of the method made ufe of for computing the velocities of the 
bullets. 
As the method of computing the velocity of a bullet from 
the arc of the vibration of a pendulum into which it is fired is 
fo well known, I fhall not enlarge upon it in this place, but 
fhall juft give the theorems that have been propofed by different 
authors, and fhall refer thofe who wifh to fee more on the fub- 
je£t to Mr. Robins’s New Principles of Gunnery ; to Profeflor 
euler’s Obfervations upon Mr. robins’s Book ; and, laftly, to 
Dr. hutton’s Paper on the initial Velocities of Cannon Balls, 
which is publifhed in the Tranfa&ions of the Society for the 
year 1778. 
If a denote the length from the axis of the pendulum to the 
ribbon which meafures the chord of the arc of its vibration ; 
g , the diftance of the center of gravity below the axis ; 
f the diftance of the center of affiliation ; 
h , the diftance of the point ftruck by the bullet ; 
c , the chord of the afcending arc of the pendulum ; 
P, the weight of the pendulum ; 
b , the weight of the bullet, and 
v, the original velocity of the bullet , 
v= C - K-fb + J x a ^eorem for finding the velocity 
upon Mr. robins’s principles. 
= - x y- -f x \j^y is the theorem propofed by Pro- 
feffor euler, who has corrected a fmall error in. Mr.- robins’s 
method ; and 
* Put the rational part — X — ^ -|r 
r a bb 2/ 
~ n r and exp refs /in the thoufandth 
parts of a Rhynland foot ; then the velocity with which the ball ftrikes the pendu* 
lum will be 
4 ^ 2 - 
Rhynland feet in a fecond*. 
V — 
