
MECHANICAL ACTION OF HEAT. 571 

aQ+d.8= (1455) aQ +h aV= (1+0f' Paved’. (@) aQ 
+(a% Zo ) dv. 
This expression is a complete differential, and may be written thus :— 
d(Q+8)=4 { Q+9(@ + (@ avj-1) fray } ae 4(80n 
(Q being treated as a constant in performing the integration / Pd V). 
Its integral, Q+S, the sum of the heat of the body, and of the potential of its 
molecular actions, is the same quantity which I have denoted by the symbol ¥ 
in the 10th article of a paper on the Centrifugal Theory of Elasticity, and whose 
differences are there stated to represent the total amount of power which must 
be exercised on a body, whether in the form of expansive or compressive power, 
or in that of heat, to make it pass from one volume and temperature to another. 
This integral corresponds also to the function treated of by Professor WILLIAM 
Tomson in the fifth part of his paper on the Dynamical Theory of Heat, under 
the name of “ Total Mechanical Energy.” 
(52.) We have now obtained a system of formule, expressing all the relations 
between heat and expansive power, analogous to those deduced from a considera- 
tion of the properties of temperature, by Messrs CLausius and Tomson, and from 
the Hypothesis of Molecular Vortices in the previous sections of this paper; but, 
in the present section, both the theorems and the investigations are distinguished 
from former researches by this circumstance;—that they are independent, not only 
of any hypothesis respecting the constitution of matter, but of the properties, 
and even of the existence, of such a function as Temperature; being, in fact, 
simply the necessary consequences of the following 
DEFINITION OF EXPANSIVE HEAT. 
Let the term ExpanstvE Heat be used to denote a kind of Physical Energy con- 
vertible with, and measurable by, equivalent quantities of Mechanical Power, and 
augmenting the Expansive Elasticity of matter, in which it is present. 
(52 A.) It is further to be remarked, that the theorems and formule in the pre- 
ceding articles of this section are applicable, not only to heat and expansive power, 
but to any two directly convertible forms of physical energy, one of which is 
actual, and the other potential. They are, in fact, the principles of the conversion 
of energy in the abstract, when pee according to the following definitions 
of the symbols. 
‘ Let Q denote the quantity of a form of actual physical energy present in a 
given body ; 
