Theorem for Irreversible Cycles. 513 
might well be devoted. Any definition which can be regarded 
as at all satisfactory refers, in the first instance at least, to 
a body whose-parts are without relative motion and which 
has attained an invariable state ; the matter is more difficult 
when such motions exist, or when its state is otherwise varying. 
The definition, or rather the test, of equality of temperature, 
which apparently finds most favour is that two bodies have, 
in general, the same temperature if, when placed in contact, 
there occurs in either no change of volume. ‘This test is, 
however, unduly restricted, as it refers to one particular 
method alone of measurement ; if for “no change of volume” 
we substitute “‘no change whatever such as is, within the 
limited range of hotness in which we can apply a test, 
associated with changes in the heat sensations caused by that 
body,” we obtain a definition which allows temperature to be 
tested by other means, as, for instance, by the electric resist- 
ance of platinum or by the electromotive force of a metallic 
circuit, methods which are actually in use. Two bodies in 
which, when placed in contact, no such change occurs are 
said to be in thermal equilibrium with one another. 
_ Any such definition becomes obviously self-contradictory 
if applied to a body whose density and volume are changing 
sensibly. Many, indeed, if not all definitions of terms as 
measurable quantities, are only provisional ; definitions and 
laws are necessarily interwoven, and the statements of each 
require to be continually amended as knowledge increases. 
Probably the most striking instance of this in the whole 
domain of physical science is furnished by the fundamental 
laws and definitions of dynamics. The proper understanding 
of fundamental terms employed in any science is of the 
utmost importance: this is, however, only half a truth; it is 
an aim of science to formulate a system of definitions and 
laws based on each other by the aid of which natural events 
may be described as simply as possible. To prohibit the use 
of terms whose meaning cannot always be stated with pre- 
cision, or of statements which it is impossible to put directly 
to the test, would bar almost all scientific progress ; every 
increase in exactness in such matters requires, constitutes, and 
causes an addition to knowledge. Itis necessary, however, that 
definitions and laws should not contradict themselves and each 
other. And the-recognition of difficulties in such matters con- 
stitutes a step towards their removal; this fact will, I hope, 
justify the remarks in the present paper. 
_ Phil. Mag. 8. 6. Vol. 8 No. 46. Oct. 1904. 2N 
