concourse of circumstances, but, in strictness, it would not be
impossible. The principle would only be a law of probability. Yet this
probability is all the greater the more considerable is the number of
molecules itself. In the phenomena habitually dealt with, this number
is such that, practically, the variation of entropy in a constant
sense takes, so to speak, the character of absolute certainty.

But there may be exceptional cases where the complexity of the system
becomes insufficient for the application of the principle of Carnot;--
as in the case of the curious movements of small particles suspended
in a liquid which are known by the name of Brownian movements and can
be observed under the microscope. The agitation here really seems, as
M. Gouy has remarked, to be produced and continued indefinitely,
regardless of any difference in temperature; and we seem to witness
the incessant motion, in an isothermal medium, of the particles which
constitute matter. Perhaps, however, we find ourselves already in
conditions where the too great simplicity of the distribution of the
molecules deprives the principle of its value.

M. Lippmann has in the same way shown that, on the kinetic hypothesis,
it is possible to construct such mechanisms that we can so take
cognizance of molecular movements that _vis viva_ can be taken from
them. The mechanisms of M. Lippmann are not, like the celebrated
apparatus at one time devised by Maxwell, purely hypothetical. They do
not suppose a partition with a hole impossible to be bored through
matter where the molecular spaces would be larger than the hole
itself. They have finite dimensions. Thus M. Lippmann considers a vase
full of oxygen at a constant temperature. In the interior of this vase
is placed a small copper ring, and the whole is set in a magnetic
field. The oxygen molecules are, as we know, magnetic, and when
passing through the interior of the ring they produce in this ring an
induced current. During this time, it is true, other molecules emerge
from the space enclosed by the circuit; but the two effects do not
counterbalance each other, and the resulting current is maintained.
There is elevation of temperature in the circuit in accordance with
Joule's law; and this phenomenon, under such conditions, is
incompatible with the principle of Carnot.

It is possible--and that, I think, is M. Lippmann's idea--to draw from
his very ingenious criticism an objection to the kinetic th