On the Identity of Energy. 483 
they are more than definitions, are really three very important 
aspects of one law*. They may be regarded as (1) a defi- 
nition of time, (2) a definition of force, (3) a statement of a 
law of Nature. 
The law of Nature they embody is capable of various modes 
of expression, such as these (in brief):— 
Change of Momentum= Impulse. 
Resultant force = 
Action + Reaction=0. 
Force is always one component of a stress. 
The last form is perhaps as convenient as any for our 
present purpose, and is our first lemma. 
To deny action at a distance is easy; we have only to say, 
“Tf a stress exist between two bodies they must be in con- 
tact.”” This constitutes a second lemma. 
We then only further require the definition of work and 
energy; for instance, these:—A body does work when it exerts 
force through a distance; the measure of work being { Fads. 
Hnergy is that which a body loses when it does work; and it 
is to be measured as numerically equal to the work done. 
[The repetition with mere change of sign, about gain of 
energy when negative work is done by a body, or positive 
work done upon it, may be understood. | 
Now at once follows, simply and rigorously, the law of 
the conservation of energy ; and not only conservation, but 
conservation in the new form, viz. the identification of energy; 
thus: If A does work on B it exerts force on it through a 
certain distance; but (Newton’s law) B exerts an equal 
opposite force, and (being in contact) through exactly the same 
distance ; hence B does an equal opposite amount of work, 
or gains the energy which A loses. The stress between A 
and B is the means of transferring energy from A to B, 
directly motion takes place in the sense AB. And the 
energy cannot jump from A to B, it is tranferred across their 
point of contact, and by hypothesis their “ contact” is abso- 
lute: there is no intervening gap, microscopic, molecular, or 
otherwise. The energy may be watched at every instant. 
Its existence is continuous; it possesses identity. 
It is no use objecting that two pieces of ‘‘matter’’ are 
never in contact—nobody said they were. If they are not, 
and it seems quite certain that they are not, then evidently one 
* For argument in support of this view, see ‘The Engineer,’ 1885, 
March 20, April 24, May 15. 
