84 LECTURE IX. 



menta are proportional to the weights, but the products obtained by multiply- 

 ing them by the distances from the centre, at which they act, are equal r 

 these products therefore represent the rotatory power of the respective bodies. 

 Hence in a connected system of bodies, revolving round a given point, with 

 equal angvdar velocities, the effect produced by the rotatory motion of each 

 body, as well as the force which is employed in producing it, is expressed by 

 the product of the mass multiphed by the square of the velocity, since the 

 velocity is in tWs case proportional to tli€ distance from the centre ;- and this 

 product is the same that I have denominated the energy of a moving body. 



These propositions are of great use in all inquiries respecting the operations- 

 of machines; and it is of importance to bear in mind, that although the equi- 

 librium of a system of bodies is determined by the equality of the products 

 of their weights, into their effective distances on each side of the centre, 

 yet that the estimation of the mechanical power of each body, when once 

 in motion, requires the mass to be mvdtiplied by the square of the distance,, 

 or of the velocity. For this reason, together with some others, which have 

 been already mentioned, some have considered the square of the velocity as 

 affording the true measure of force; but the properties of motion, concerned 

 in the determination of rotatory power, are in reality no more than necessary 

 consequences of the .simpler laws, oa which the whole theory pf mechanics 

 is founded. _ , 



The effects of rotatory motion may be very conveniently examined, by 

 means of an apparatus, similar to that which was employed for the same pur- 

 pose by Mr. Smeaton. A vertical axis is turned by a thread passing 

 over a pulley, and supporting a scale with weights ; the thread may be applied 

 at different parts of the axis, having different diameters, and the axis supports 

 two arms, 'on which two leaden weights are fixed, at distances which may be 

 varied at pleasure. The same force will then produce, in the same time, but 

 half the velocity, in the same situation of the weights, when the thread is ap- 

 plied to a part of the axis of half the diameter: and if the weights are removed 

 to a double distance from the axis, a quadruple force will be required, in order 

 to produce an equal angular velocity in a given time. (Plate V. Fig. 74.) 



When a number of connected bodies, or a single body of considerable mag- 



