ON THE MOTIONS OF SIxAIPLE MASSES, 53 



the quantity of motion naust always be measured by the joint ratio of mass to 

 mass, and velocity to velocity ; that is, by the ratio of the products, obtained 

 by multiplying the weight of each body by the number expressing its velo- 

 city ; and these products are called the momenta of the bodies. \Vc appear to 

 have deduced this measure of motion from the most unexceptionable argu- 

 ments , and we shall have occasion to apply the momentum thus estimated as 

 a true measure of force ; at the same time that we allow the practical import- 

 ance of considering, in many cases, the efficacy of forces, according to another 

 criterion, when we multiply the mass by the square of the velocity, in order 

 to determine the energy : yet the true quantity of motion, or momentum, of 

 any body, is always to be understood, as the product of its mass into its velo- 

 city. Thus a body weighing one pound, moving with a velocity of a hundred 

 feet in a second, has the same momentum, and the same (juantity of motion, 

 as a body of ten pounds, moving at the rate of ten feet in a second. 



We may also demonstrate experimentally, by means of !^fr. Atwood's ma- 

 chine, that the same momentum is generated, in a given time, by the same 

 preponderating force, whatever may be the quantity of matter moved. Thus 

 if the preponderating weight be one sixteenth of the whole weight of the 

 boxes, it will fall one foot in a second, instead of 16, and a velocity of two 

 feet will be acquired by the whole mass, instead of a velocity of 32 feet, which 

 the preponderating weight alone would have acquired. And when we com- 

 pare the centrifugal forces of bodies revolving in the same time, at diflerent 

 distances from the centre of motion, we find that a greater quantity of matter 

 compensates for a smaller force ; so that two balls connected by a wire, with 

 liberty to slide either way, will retain each other in their respective situations, 

 when their common centre of inertia coincides with the centre of motion ; the 

 centrifugal force of each particle of the one being as much greater than that 

 of an equal particle of the other, as its weight, or the number of the particles," 

 is smaller. , 



But it is not enough to determine the centre of inertia of two bodies only, 

 considered as single points ; since in general a much greater number of points 

 is concerned : we must therefore define the sense in which the term is in this 

 case to be applied. We proceed by considering the first and second of three or 

 more bodies, as a single body, equal to both of them, and placed in their com- 



