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Proceedings of the Boyal Society 
expressing that the change of vis viva is measured by the amount 
of work done hy the force. What is expended in work is therefore 
stored up as vis viva. (This is given generally for a single 
particle by Newton ; Princiyia^ Section YIII., Prop. XL.) ^ 
A simple case is that of a weight raised, or falling, in a vertical 
line. Here the work expended in raising it is so many foot 
pounds, each being the work employed to raise one pound a foot 
high. And in fact, by the ordinary formula for projectiles, 
v‘^^2gs, 
mv^ TTr 
or =zmg.s= IL.s, 
or the vis viva acquired by falling through a space s, is equal to 
the work lost in falling, or required to restore the body to its 
original position. Now, the raised weight, in virtue of its position^ 
has a power of doing work which it does not possess when lying 
on the ground; this is an example of what is called Potential 
Energy. As it loses this in falling, it gains an exact equivalent in 
vis viva, which is what is called Kinetic Energy. In this example 
we see that the sum of the potential and kinetic energies is constant ; 
and the same is true in other common cases, such as the potential 
energy of a drawn bow and the kinetic energy of the arrow, the 
potential energy of compressed air in the reservoir of an air-gun 
and the kinetic energy of the bullet, and so on. It is true even 
in such a case as the potential energy of a distorted tuning-fork 
and the kinetic energy of the sound it produces, if we include in 
the latter the vis viva of the vibrations communicated to surround- 
ing bodies. 
It is easy to give a general proof, that if the particles of any 
system act each on another with forces which are in the direction 
of the line joining them, and dependent on the mutual distance 
only, in such a system the sum of the potential and kinetic energies 
cannot he altered except hy external forces; and therefore, if the intro ' 
ductory statem'ents about matter he true, and physical phenomena such 
as heat, electricity, &c., he referred to motion of matter, there can he no 
alteration in the sum of the energies of the universe. This is the 
general statement of the Conservation of Energy. 
From this we at once deduce a proof of the impossibility of pro- 
