TEMPERATURE AND TIME—MACGREGOR. 23 
volume of the mercury in the thermometer, which are the same 
fraction of its apparent volume at the temperature, say, of melt- 
ing ice, are due to equal changes of temperature. 
It is found that if we employ thermometers containing 
different liquids, and compare the changes of volume, pressure, 
&e., of bodies due to change of temperature, with the co-thermal 
changes in the apparent volumes of these liquids, the laws of 
the variation of volume, pressure, &c., thus obtained have 
different forms, but that if gases, far removed from their 
temperatures of condensation, be employed instead of liquids 
the laws obtained have the same form. Hence it is manifestly 
advantageous that laws of the variation of quantities with temper- 
ature should be expressed in terms of the co-thermal changes in 
the apparent volume of a gas enclosed in a glass vessel. 
Sir William Thomson has shown that if the variations of 
the volume, pressure, &c., of bodies, due to a change from one 
temperature to another, be compared, not with the co-thermal 
change in the apparent volume of a liquid or a gas enclosed in a 
glass vessel, but with the work done by a reversible heat engine, 
working with its source at the one temperature and its refrigerator 
at the other, and taking in at the source an amount of heat 
sufficient to raise the entropy of the working substance by a 
fixed amount, the laws of the variation of the volume, pressure, 
&e., of bodies, expressed in terms of the work thus done, will be 
the same, whatever the working substance of the heat engine — 
may be. Hence it is manifestly still more advantageous that 
laws of variation with temperature should be expressed in this 
way. But laws of the variation of volume, pressure, &c., expressed 
in this way, are no ore truly laws of the variation of these 
quantities with respect to temperature, than those expressed by 
the aid of the Mercury Thermometer. 
In fine, neither time nor temperature can be measured, 
And when we seem to claim to measure them by expressing 
laws of the variation of quantities with time or temperature, in 
terms of time or temperature respectively, we are simply ex- 
pressing these laws of variation in terms of the contemporaneous 
or co-thermal changes respectively, of some body chosen as a 
standard. 
