514 Prof. W. McF. Orr on Clausius’ 
Kirchhof?’?s more general Definition of “ Temperature.” 
Objections to it. 
9. I am not aware that any attempt has been made to give 
a definition of temperature which may be applied to non- 
equilibrium states in any treatise on Thermodynamics, with 
the sole exception of Kirchhoff’s (posthumous) Theorie der 
Wérme, edited by Planck, wherein (p. 114) the temperature 
of a fluid whose parts are in relative motion is defined by 
the statement that the total energy of any indefinitely small 
portion exceeds its kinetic energy by the energy which it 
would possess if it were at rest at the same temperature and 
density. 
This definition appears indeed applicable to a fluid. It 
could not, however, be applied to a solid in general: in a 
solid at rest the stress across a plane is not necessarily normal, 
nor of the same intensity for all planes through a given point ; 
and the state of a solid cannot, like that of a fluid, be specified 
by two coordinates alone, such as, for example, temperature 
and a single pressure: consequently there is in general no 
equation connecting the energy of a solid at rest with its 
temperature and density. This objection may fairly be made, 
I think ; for although the bodies discussed in Thermodynamics 
are chiefly fluids, or solids subjected to such stresses as could 
occur in fluids, they are not so exclusively or of necessity. 
Kirchhoft’s definition appears, however, to be open to the 
more serious objection that it is inappropriate as having no 
reference to any measurements which are usually made or 
which it is practicable to make. When the portion of fluid 
considered is taken small enough, its kinetic energy becomes 
as nearly as we please the same as if it moved without dis- 
tortion, and with the velocity which its mass-centre has, and 
its determination consequently involves only the determina- 
tions of that velocity and of the mass ; to measure its total 
energy, however, it must be isolated from external influences, 
a process which even in the case of a fluid is attended with 
considerable difficulty, and which in the case ofa solid may be 
practically impossible, and after it has come into a state of 
relative equilibrium its temperature must be measured in the 
ordinary way. 
Another Definition suggested. 
10. A better attempt to define in such a case the temperatur e 
at any instant might be stated, I think, somewhat as follows :— 
Suppose that into the centre of the very small portion of the 
body considered there is introduced a much smaller body 
constituting a thermometer of any kind by whose aid the 
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