OF THE MOTIONS OF A SOLID BODY. 237 



nected with the arms of an inflexible line, and move with 

 equal velocities in the same direction, they will obviously 

 be totally stopped by the application of a fulcrum at the 

 centre of gravity ; for the propositions respecting equi- 

 librium are as well deducible from the composition of mo- 

 tion as from that of force, and the motion of A is here 

 equivalent to the motion of B, which now moves with 

 equal velocity at half the distance from the fulcrum, being 

 still twice as large as A : but it was before shown to be 

 equal to the motion of B, when it moved with half the ve- 

 locity at a distance equal to its own : consequently these 

 two motions of B are equivalent, with respect to effect in 

 producing rotatory motion : and the same may be shown 

 when the bodies and their motions are in any other pro- 

 portions. It is also obvious, that since the velocity is as 

 the distance from the centre of rotation, the power, with 

 respect to that centre, will be as the square of that dis- 

 tance, or as the square of the velocity. 



Scholium. It is therefore of importance to bear in 

 mind, that although the equilibrium of a system of bodies 

 is determined by the equality of the product of their 

 weight into their effective distances on each side of the cen- 

 tre, yet the estimation of the mechanical power of each body, 

 when once in motion, requires the mass to be multiplied 

 by the square of the distance, or of the velocity. For this 

 reason, and for some others, the square of the velocity has 

 been considered by many persons as affording the true 

 measure offeree; but the properties of motion, concerned 

 in the determination of rotatory power, are in reality no 

 more than necessary consequences of the simpler laws, on 

 which the whole theory of mechanics is founded. It is 

 only within about half a century, that the mechanical philo- 

 sophers of Great Britain have begun to entertain correct 



