116. This does not mean, of course, that (A) is constant in itself, or
any other of the left-hand members of this equation, for, in truth,
they are always changing about into each other--now, some visible
energy being changed into heat or electricity; and, anon, some heat or
electricity being changed back again into visible energy--but it only
means that the sum of all the energies taken together is constant. We
have, in fact, in the left hand, eight variable quantities, and we
only assert that their sum is constant, not by any means that they are
constant themselves.
117. Now, what evidence have we for this assertion? It may be replied
that we have the strongest possible evidence which the nature of the
case admits of. The assertion is, in truth, a peculiar one--peculiar
in its magnitude, in its universality, in the subtle nature of the
agents with which it deals. If true, its truth certainly cannot be
proved after the manner in which we prove a proposition in Euclid.
Nor does it even admit of a proof so rigid as that of the somewhat
analogous principle of the conservation of matter, for in chemistry we
may confine the products of our chemical combination so completely
as to prove, beyond a doubt, that no heavy matter passes out of
existence that--when coal, for instance, burns in oxygen gas--what we
have is merely a change of condition. But we cannot so easily prove
that no energy is destroyed in this combination, and that the only
result is a change from the energy of chemical separation into that of
absorbed heat, for during the process it is impossible to isolate the
energy--do what we may, some of it will escape into the room in which
we perform the experiment; some of it will, no doubt, escape through
the window, while a little will leave the earth altogether, and go
out into space. All that we can do in such a case is to estimate, as
completely as possible, how much energy has gone away, since we cannot
possibly prevent its going. But this is an operation involving great
acquaintance with the laws of energy, and very great exactness of
observation: in fine, our readers will at once perceive that it is much
more difficult to prove the truth of the conservation of energy than
that of the conservation of matter.
118. But if it be difficult to prove our principle in the most rigorous
manner, we are yet able to give the strongest possible indirect
evidence of its truth.
Public-domain text, read in full here on John Shaqi.
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