286 PROFESSOR MOSELEY ON THE THEORY OF MACHINES. 



machines, than in the application which he has so successfully made to it of this 

 principle of vis viva*. In the elementary discussion, however, of this principle, which 

 is given by M. Poncelet in the Introduction to his Mdcanique Inditstrielle, he has 

 revived the term vis inertise (vis inertise, vis insita (Newton)), and associating with 

 it the definitive idea of a force of resistance opposed to the acceleration or the retard- 

 ation of a body's motion, he has shown (Arts. 66. and 122.) the work expended 

 in overcoming this resistance through any space, to be measured by one-half the vis viva 

 accumulated through the space ; so that throwing into the consideration of the forces 

 under which a machine works, the vires inertiae of its moving elements, and obser- 

 ving that one-half of their aggregate vis viva is equal to the aggregate work of their 

 vires inertiae, it follows by the principle of virtual velocities, tliat the difference 

 between the aggregate work of those forces impressed upon a machine which tend to 

 accelerate its motion, and the aggregate work of those which tend to retard the 

 motion, is equal to the aggregate work of the vires inertiae of the moving parts of 

 the machine : under which form the principle of vis viva resolves itself into the prin- 

 ciple of virtual velocities. So many difficulties, however, oppose themselves to the 

 introduction of the term vis inertiae, associated with the definitive idea of an oppo- 

 sing force, into the discussion of questions of mechanics, and especially of practical 

 and elementary mechanics, that it has appeared to the author of this paper desirable 

 to avoid it. It is with this view, that in the researches which form the subject of the 

 paper now submitted to the Society, a new interpretation is given to that function of 

 the velocity of a moving body which is known as its vis viva ; one-half that function 

 being interpreted to represent the number of units of work accumulated in the body 

 so long as its motion is continued, and which number of units of work it is capable 

 of reproducing upon any resistance which may be opposed to its motion, and bring 

 it to rest. A very simple investigation will establish the truth of this interpretation 

 of the analytical formula represented by the term vis viva. Let a body whose weight 

 is W be conceived to descend freely by gravity through a height H, and to acquire 

 a velocity V. It will have become capable, by reason of its motion, of overcoming a 

 certain pressure through a certain space, that is, of yielding a certain amount of 

 work, which amount of work may be conceived to be accumulated in it. The amount 

 of the work which it has become capable of yielding, is manifestly that which would 

 raise another body of the same weight W, to the same vertical height H-f-; or it is 

 equivalent to a number of units of work represented by W H, or (since V^ = 2 ^ H) 



] W 

 by -^ — . V^, that is, by one-half the vis viva. Thus the work accumulated in a body 



moving with the velocity V, is represented by half the vis viva, when that velocity is 

 acquired by the action of gravity. Now the work accumulated in a body moving 



* See Poncelet, M^canique Industrielle, troisieme partie, 



t If a mechanical contrivance could be so interposed as to receive the whole of the work of the descending 

 weight, and communicate it to an equal ascending weight, this last would manifestly be projected upwards 

 with the same velocity with which the first reached the ground, and would therefore ascend to the same height. 



