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 Industrielle, he has 
revived the term vis inertise (vis inertiae, 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 inertise of its moving elements, and obser- 
ving that one-half of their aggregate vis viva is equal to the aggregate work of their 
vires inertise, it follows by the principle of virtual velocities, that 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 inertise 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 inertise, 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 whi^ji .may be opposed to its motion, and bring j 
establish the truth of this interpretation 
/ 
v 
it to rest. A very simple investigation 
y 
of the analytical formula represented by the term vis viva. Let a body whose weighte/__ 
m 
/ A 
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-j-; or it is 
equivalent to a number of units of work represented by W II, or (since V 2 = 2 g H) 
I W 
by~2 y • ^ 2 > 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, Mecanique Industrielle, troisieme partie. 
f 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 w r eight, 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. 
