274 Remarks on the Central Forces of Bodies 



the theory. If an ounce ball of lead, with a small hole drilled 

 through it, be firmly secured by a catgut string close to the perime- 

 ter of a fly-wheel, or any other wheel that can be rapidly revolv- 

 ed, it may be discharged from the vertical point of the circumfer- 

 ence, whilst the wheel is revolving, by interposing a sharp knife 

 well fixed in a slide. When the velocity necessary to project the 

 ball horizontally at a given short distance has been ascertained, 

 then by increasing the velocity and taking care to discharge the 

 ball from the same point of the circle, and at an equal distance 

 from the centre of the wheel, its elevation will be found to in- 

 crease with the increased projectile force. And the experiment 

 may be varied by having a number of balls prepared of the same 

 weight, and varying the velocities and the distances from the cen- 

 tre. The effects of gravity, however, and the difficulty of re- 

 presenting by a straight line what may be considered the direc- 

 tion of the circle, have prevented me from determining geomet- 

 rically the direction of the projectile, although in practice it may 

 easily be ascertained. 



If the ball be discharged from the point A, with one revolution 

 in a second, its velocity in the circle would be 12.57 feet per sec- 



ond, and its centrifugal velocity would be = .^ = — j — = 39.44 

 feet per second, and the initial projectile velocity would be = 

 a/12.57- +39.442=41.40 feet per second, disregarding for the 

 present atmospheric resistance. And if, in the way of illustration, 

 AF be considered as the direction of the force in the circle AD, 

 the sides Kk and Km, of the parallelogram Amvk, being made 

 proportionate to the two velocities 12.57 and 39.50 respectively, 

 the diagonal Av of the parallelogram will represent in direction 

 and proportional amount the velocity 41.45 or initial projectile 

 velocity. If a billiard-ball, moving upon a table with a velocity 

 equal to 12^ feet per second in the direction EF, were to re- 

 ceive at A an impulse in the direction of en, which alone would 

 cause it to move with a velocity equal to 39^ feet per second, no 

 other direction and velocity could be assigned to it than that de- 

 signated by the diagonal Av of the parallelogram. The revolving 

 ball is supposed to move in the direction Ak with the velocity of 

 12.57 feet per second, represented by that side of the parallelogram, 

 and at the same time to be acted upon by a force which would 

 cause it to move with a velocity equal to 39J feet per second, in 



