276 Remarks on the Central Forces of Bodies 



that through which the centripetal force alone, acting uniformly, 

 would cause the body to fall in the fiftieth part of a second ; the 

 tangent, therefore, represents the line from which the body 

 would be deflected in an instant of time, and not that in the di- 

 rection of which it would move ivith all its projectile force. 



Again, if the segment of a fly-wheel disintegrated by centrifu- 

 gal force would be projected " in a straight line, whose direction 

 is that of the tangent," the pressure which produces the fracture 

 must act upon each particle of iron in the direction of a tangent 

 to the circle in which the particle is revolved, for the direction of 

 a moving body is always that in which a single force, or the re- 

 sultant of two or more forces, acts to cause the motion. And it 

 is self-evident that no amount of force, applied in that direction 

 upon the particles in the revolving rim, could overcome the at- 

 traction of cohesion. And it is equally evident that such cannot 

 be the direction in which the pressure acts, for whilst it is stated 

 that the tangent is the direction in which the dissevered fragment 

 is projected, we are informed that the force which causes the 

 fracture acts at right angles to the tangent. 



By the theory given above, however, which is founded upon 

 observation and experiment, all the circumstances that attend this 

 phenomenon are easily explained. And when we consider the 

 immense increase of centrifugal force as the velocity of the rim 

 is increased, and the direction in which the resultant of the two 

 forces acts, we ought not to be surprised to find that such masses 

 of iron can be broken and projected with so much destructive ef- 

 fect by this powerful agent. The operation of the sling may 

 also, in this way, be explained in a few words. For a man, with 

 a thong three and a half, feet long, has only to give to a stone at 

 the final effort a velocity, in a very small segment of a circle, 

 equal to 133 feet per second, which would be at the rate of 360 

 revolutions in a minute, and he will project it with a force equal 

 to that given to a ball of the same weight by an ordinary charge 

 of gunpowder, after deducting one third of its initial velocity for 

 atmospheric resistance. But to " accumulate" an equal force in 

 the circle by the strength of his arm, he would have to revolve 

 the stone at the rate of 6850 revolutions in a minute, which is 

 impossible. 



Without intending to enter into any particulars as to the proba- 

 ble results of a practical appUcation of this principle, I will close 



