DYNAMICAL THEORY OF HEAT. 265 
negative). Now, let there be either no molecular change or alteration of tempe- 
rature in any part of the body, or, by a cycle of operations, let the temperature 
and physical condition be restored exactly to what they were at the beginning; 
the second and third of the three parts of the work which it has to produce 
vanish; and we conclude that the heat which it emits or absorbs will be the 
thermal equivalent of the work done upon it by external forces, or done by it 
against external forces; which is the proposition to be proved. 
12. The demonstration of the second proposition is founded on the following 
axiom :— 
It is impossible, by means of inanimate material agency, to derive mechanical 
effect from any portion of matter by cooling it below the temperature of the coldest 
of the surrounding objects.* 
13. To demonstrate the second proposition, let A and B be two thermo-dynamic 
engines, of which B satisfies the conditions expressed in the enunciation ; and let, 
if possible, A derive more work from a given quantity of heat than B, when their 
sources and refrigerators are at the same temperatures, respectively. Then, on 
_ account of the condition of complete reversibility in all its operations which it 
fulfils, B may be worked backwards, and made to restore any quantity of heat to 
its source, by the expenditure of the amount of work which, by its forward ac- 
tion, it would derive from the same quantity of heat. If, therefore, B be worked 
backwards, and made to restore to the source of A (which we may suppose to be 
adjustable to the engine B) as much heat as has been drawn from it during a 
certain period of the working of A, a smaller amount of work will be spent thus 
than was gained by the working of A. Hence, if such a series of operations of A 
forwards and of B backwards be continued, either alternately or simultaneously, 
there will result a continued production of work without any continued abstrac- 
tion of heat from the source; and, by Prop. I., it follows that there must be more 
heat abstracted from the refrigerator by the working of B backwards than is de- 
posited in it by A. Now, it is obvious that A might be made to spend part of its 
work in working B backwards, and the whole might be made self-acting. Also, 
there being no heat either taken from or given to the source on the whole, all the 
_ surrounding bodies and space, except the refrigerator, might, without interfering 

with any of the conditions which have been assumed, be made of the same tem- 
perature as the source, whatever that may be. We should thus have a self-acting 
machine, capable of drawing heat constantly from a body surrounded by others 
at a higher temperature, and converting it into mechanical effect. But this is 
contrary to the axiom, and, therefore, we conclude that the hypothesis that A 
* Tf this axiom be denied for all temperatures, it would have to be admitted that a self-acting 
machine might be set to work and produce mechanical effect by cooling the sea or earth, with no 
limit but the total loss of heat from the earth and sea, or, in reality, from the whole material world. 
VOL. XX. PART Il. 4c 
