THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
265 
become of energy that had ceased to be mechanically available. It is thus the 
principle of the limited conservation of available energy, rather than the complete 
conservation of total energy, that reigns in general noii-molecular physics. 
There is still however the complication that the available energy of a system 
is not a function of its state alone, but involves comparison with some standard state 
into which it is possible for the system to be transformed. To find the extent of 
this undetermined element, let us simplify the relations in the ordinary manner, 
by adopting the scale of temperature that is given by the expansion of an ideal 
perfect gas, and find out how much energy is dissipated or lost to available 
mechanical effect, when a quantity of heat Hj is abstracted at the temperature 
and of it H is returned at the temj^erature T. If all possible mechanical effect were 
produced, only • T/T^ would be thus returned instead of H : hence the dissipation 
is H — Hj. T/T^ or T (H/T — Hj/T^). Thus an operation of this kind which does 
not involve dissipation does not alter H/T ; and by accumulation of such changes it 
follows that any two states of the system which are convertible without dissipation 
have SH/T the same for both. The entropy function of Clausius thus necessarily 
enters into the analytical formulation of the principle of mechanical availability. 
Between a standard state at temperature Tq and another state at T the dissipation 
rs T {(fi - 4) ; thus the available energy A in the latter state is E — T> + T()^o> 
where E is the total energy which involves an undetermined constant part, and cf)Q is 
another undetermined constant which represents the entropy of the system in the 
standard state. I he temperature of the starrdard state to which the system is 
referred could not of course be the ideal, practically infinitely remote, temperature 
winch IS called absolute zem that worrld imply that the energy is all mechanically 
available as in ordinary statics. 
The presence of this undetermined multiple of T does not really restrict the 
application of the theorem of minimum availability : it merely implies that when 
once mechanical and constitutional equilibrium has been determined at any assigned 
temperature by making A a minimun with respect to the other independent variables, 
still further degradation will occur if opportunity is allowed for fall of temperature 
by escape of energy from the system. All that it is necessary to ascertain iir any 
problem is the equilibrium as regards physical state and chemical constitution at 
each temperature, and the capacity of the system for heat, which specifies the 
thermal change that occurs when the temperature is altered. There is no restriction 
involved in taking the temperature the same throughout the system, for that is 
a necessary condition of equilibrium : when it is convenient to imagine partitions 
impervious to heat, the parts of the system thus separated can be treated as 
independent systems. The available energy, here arrived at directly from the 
* This seems to be substantially tbe position whicb Rankine took up in 1853 (“ Scientific Papers,” 
p. 311): cf. also the weighty introduction to “Outlines of the Science of Energeties,” 18.58, he. cit, 
pp. 209-220. It is in fact the standpoint of Carxot’s “ Reflexions.” 
VOL. CXC.—A. 2 M 
