THERMAL EFFECTS OF FLUIDS IN MOTION. 
351 
was pointed out that any system of thermometry, founded either on equal additions 
of heat, or equal expansions, or equal augmentations of pressure, must depend on the 
particular thermometric substance chosen, since the specific heats, the expansions, 
and the elasticities of substances vary, and, so far as we know, not proportionally 
with absolute rigour for any two substances. Even the air-thermometer does not 
afford a perfect standard, unless the precise constitution and physical state of the 
gas used (the density, for a pressure-thermometer, or the pressure, for an expansion- 
thermometer) be prescribed ; but the very close agreement which Regnault found 
between different air- and gas-thermometers removes, for all practical purposes, the 
inconvenient narrowness of the restriction to atmospheric air kept permanently at 
its standard density, imposed on the thermometric substance in laying down a rigorous 
definition of temperature. It appears then that the standard of practical thermo- 
metry consists essentially in the reference to a certain numerically expressible quality 
of a particular substance. In the communication alluded to, the question, “ Is 
there any principle on which an absolute thermometric scale can be founded?” was 
answered by showing that Carnot’s function (derivable from the properties of any 
substance whatever, but the same for all bodies at the same temperature), or any 
arbitrary function of Carnot’s function, may be defined as temperature, and is there- 
fore the foundation of an absolute system of thermometry. We may now adopt this 
suggestion with great advantage, since we have found that Carnot’s function varies 
very nearly in the inverse ratio of what has been called “ temperature from the zero 
of the air-thermometer,” that is, Centigrade temperature by the air-thermometer 
increased by the reciprocal of the coefficient of expansion ; and we may define tem- 
perature simply as the reciprocal of Carnot’s function. When we take into account 
what has been proved regarding the mechanical action of heat*, and consider what 
is meant by Carnot’s function, we see that the following explicit definition may be 
substituted : — 
If any substance whatever, subjected to a perfectly reversible cycle of operations, takes 
in heat only in a locality kept at a uniform temperature, and emits heat only in another 
locality kept at a unifor'm temperature, the temperatures of these localities are propor- 
tional to the quantities of heat taken in or emitted at them in a complete cycle of the 
operations. 
To fix on a unit or degree for the numerical measurement of temperature, we may 
either call some definite temperature, such as that of melting ice, unity, or any number 
we please ; or we may choose two definite temperatures, such as that of melting ice 
and that of saturated vapour of water under the pressure 29'9218 inches of mercury 
in the latitude 45°, and call the difference of these temperatures any number we 
please, 100 for instance. The latter assumption is the only one that can be made 
conveniently in the present state of science, on account of the necessity of retaining 
a connexion with practical thermometry as hitherto practised ; but the former is far 
* Dynamical Theory of Heat, §§ 42, 43. 
