264 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
with it if the mean translatorj energy of the molecules is the same for each. This 
principle of temperature-equilibrium shows that, for all states of mattei, the 
equilibrium of energy between bodies in contact in a steady state in\olv'es that a 
definite molecular relation of the one body shall equilibrate a definite molecular 
relation of the other; and its universality requires that this relation, whatever it 
may prove to be, shall be a very fundamental one. 
51. It would seem that we can make at any rate an advance towards a complete 
view by realizing that, even if our sensations of heat had not compelled us to assign 
a fundamental place to temperature in the physical scheme, the principle of negation 
of perpetual motions must have led to the formulation of that conception, just as it 
lias in fact led to the conception of potentials. If thermal equilibrium between two 
homon'eneous bodies A and B in contact were not conditioned merely by some 
o 
phvesical property of A alone being equal to some property of B alone, then if we had 
A in contact with B, and B with C, each in a state of equilibrium, and, removdng B by 
mechanical means, moved A into direct contact with C but with such ideal constraint 
applied to the matter in bulk that chemical action is prevented, the physical state of 
each of these latter bodies would become changed, involving the pei'formance of 
mechanical work; and a self-acting cycle could be designed by vv^hich we might thus 
obtain an unlimited quantity of work, that is, so long as there remained any diffused 
molecular energy to be converted. Hence in equilibrium there must be a property, 
namely the temperature, of each indivddual body in the field that has the same value 
for all of them ; although of course this does not prevent us from imagining a 
partition or constraint, nearly adiathermanous, across which such equilibrium would 
be established as slowly as we please. It follows also that equilibrium of tempera¬ 
ture must be the same whether it is brought about by conduction or by radiation. 
Temperature, as thus introduced, has nothing to do directly with the field of force in 
which the body is situated : for the relations of bodies to fields of force, in which 
they are moved about, are treated independently in the consideration of energy 
relations, and must not be introduced twice over,—or, in other words, the perpetual 
motion principle can be directly applied. 
The single fundamental principle, on vvdiich all thermodynamic and thermochemical 
theory rests, would thus be the axiom of the negation of perpetual motions : and this 
stands rather in the relation of a principle that could hardly be conceived to be other¬ 
wise on any feasible physical scheme, than of one of vvdiich vv^e can expect to offer any 
formal demonstration. Various essays have been made to deduce Carnots principle 
and a dynamical specification of temperature from special liypotheses as to molecular 
action : it may be held that, in so far as these are useful it is by way of illustration. 
It is evmn possible to conceive, l)ut onl}^ in a highly abstract sense, that thermo¬ 
dynamics might have been developed in Carnot’s manner out of the perpetual 
motion axiom alone, without the aid of Joule’s demonstration of the nature and 
measure of heat; tliere would then have been merely no knowledge of what had 
