Theorem for Irreversible Cycles, 515 
temperature might be measured if the portion considered 
were in an invariable state, the thermometer being moved 
with the body; and assume that if the thermometer is 
sufficiently small, any further diminution of its size makes 
no perceptible difference in its “ reading ”’? when the circum- 
stances are repeated; then the temperature of the portion 
of the body means the temperature indicated at the instant 
by the thermometer. 
This definition has at least the merit of referring to 
measurements which observers actually try to make. 
The difficulty, however, cannot be surmounted simply by 
altering the words in which a definition is expressed. A 
definition is not merely useless but harmful, as leading to 
logical fallacy, unless there is some fact in Nature corre- 
sponding to it. The ordinary definition of temperature is 
based on the experimental fact that the definition is sclf- 
consistent ; 7.¢., that bodies which are in thermal equilibrium 
with the same body are in thermal equilibrium with one another. 
In a similar way the definition suggested above depends 
for its validity on the correctness of the supposition that if, 
on different occasions when the same circumstances recur, 
a number of sufficiently small thermometers are used, they 
would all at the corresponding instants indicate one and the 
same temperature, irrespective of their size (provided it is 
sufficiently small), of the substances of which they are made, 
and of the property which is taken asa basis of measurement : 
that is, they would, when each is placed in contact with 
the portion of the body considered, assume states which 
would be states of thermal equilibrium if in contact with each 
other. There is reason to believe that these suppositions are 
to a considerable extent justified if the body is changing its 
state in respect of density or other property; but it is, I think, 
open to question whether they are legitimate in such an 
extreme case as that of a gas rushing into a vacuum. 
Although further emphasis of the interdependence of fact 
and definition in this matter is probably unnecessary, one 
may draw attention to the mistake which would be committed 
if the definition suggested above were altered so as to permit 
sensible relative motion between the thermometer and the 
parts of the body in contact with it, or if, for example, in the 
case of a stationary atmosphere and a body moved through 
it with a given constant velocity, one were to define equality 
of temperature as the steady state (2. e. in respect of changes 
such as are accompanied by changes in the heat sensations we 
perceive) which would ultimately be attained. it is known 
in fact that the steady state of the moving body is hotter than 
2N2 
