146 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
thermal curves and curves of no transmission on a diagram of energy, and are the 
geometrical representation of the application to the particular case of heat and ex- 
pansive power, of two axioms respecting Energy in the abstract, viz. — 
I. The sum of Energy in the Universe is unalterable. 
II. The effect, in causing Transformation of Energy, of the whole quantity of 
Actual Energy present in a substance, is the sum of the effects of all its parts. 
The application of these Axioms to Heat and Expansive Power virtually involves 
the following Definition of Expansive Heat : — 
Expansive Heat is a species of Actual Energy, the presence of which in a substance 
affects, and in general increases, its tendency to expand. 
And this definition, arrived at by induction from experiment and observation, is 
the foundation of the theory of the expansive action of heat. 
u 
Section IV.— OF TEMPERATURE, THE MECHANICAL HYPOTHESIS OF MOLECULAR VOR- 
TICES, AND THE NUMERICAL COMPUTATION OF THE EFFICIENCY OF AIR-ENGINES. 
(32.) In order to apply the propositions of the preceding articles to existing sub- 
stances, besides experimental data sufficient for the determination, direct or indirect, 
of the isothermal curves and curves of no transmission, it is necessary also to know 
the relation, for the substance in question, between the quantity of heat actually pre- 
sent in it under any circumstances, and its Temperature ; a quantity measured by the 
product of the pressure, volume, and specific gravity of a mass of perfect gas, when 
in such a condition that it has no tendency to communicate heat to, or to abstract 
heat from, the substance whose temperature is ascertained. 
The nature of the relation between heat and temperature has been discussed in 
investigations already published, as a consequence deducible from a hypothesis re- 
specting the molecular constitution of matter, with the aid of data supplied by the 
experiments of Messrs. Thomson and Joule and of M. Regnault. Nevertheless it 
seems to me desirable to add here a few words respecting the grounds, independent 
of direct experiment, for adopting the hypothesis of molecular vortices as a probable 
conjecture, the extent to which, by the aid of this hypothesis, the results of expe- 
riment were anticipated, and its use, in conjunction with the results of experiment, 
as a means of arriving at a knowledge of the true law of the relation between tem- 
peratures and total quantities of heat. 
To introduce a hypothesis into the theory of a class of phenomena, is to suppose that 
class of phenomena to be, in some way not obvious to the senses, constituted of 
some other class of phenomena with whose laws we are more familiar. In thus fra- 
ming a hypothesis, we are guided by some analogy between the laws of the two classes 
of phenomena : we conclude, from this analogy of laws, that the phenomena them- 
selves are probably alike. This act of the mind is the converse of the process of 
ordinary physical reasoning; in which, perceiving that phenomena are alike, we 
conclude that their laws are analogous. The results, however, of the latter process 
