118 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
For this purpose, let us take the ascertained fact of the production of heat by the 
expenditure of mechanical power in friction, according to the numerical proportion 
determined by Mr. Joule ; and let E denote the quantity of mechanical power which 
must be expended in friction, in order to raise the temperature of unity of weight of 
a given substance from that of absolute privation of heat to a given temperature r. 
During this operation, let the several elements of the external surface of the mass 
undergo changes of relative position expressed by the variations of quantities denoted 
generally by p, and let the increase of each such quantity as p be resisted by an ex- 
ternally-applied force such as P. 
Then during the elevation of temperature from absolute cold to r, the energy con- 
verted to the potential form in overcoming the external pressures P will be 
Also let the internal particles of the mass undergo changes of relative position ex- 
pressed by the variations of quantities denoted generally by r, and let the increase of 
each such quantity as r be resisted by an internal molecular force such as R. 
Then the energy converted to the potential form in overcoming internal molecular 
forces will be 
S.jlWr. 
Subtracting these quantities of energy converted to the potential form by means 
of external pressures and internal forces, from the whole power converted into heat 
by friction in order to raise the temperature of the mass from that of absolute priva- 
tion of heat to the given temperature r, we find the following result : — 
Q=E-2.(p£fj»-2.fRrfr; 
and this remainder is the quantity of energy which retains the form of heat, in unity 
of weight of the given substance at the given temperature ; that is to say, the Total 
Actual Heat. 
It is obvious that Total Actual Heat cannot be ascertained directly ; first, because 
the temperature of total privation of heat is unattainable ; and secondly, because the 
molecular forces R are unknown. 
It can, however, be determined indirectly from the latent heat of expansion of the 
substance. For the heat which disappears during the expansion of unity of weight 
of an elastic substance at constant actual heat from the volume V A to the volume V B , 
under the constant or variable pressure P, is expressed (as will be shown in the 
sequel) by 
so that from a sufficient number of experiments on the amount of heat transformed 
