12 Prof. Thomson on the Dynamical Tlteory of Heat. 



Prop. II. (Camot and Clausius). — If an engine be such that, 

 when it is worked backwards, the physical and mechanical agen- 

 cies in every part of its motions are all reversed, it produces as 

 much mechanical effect as can be produced by any thermo- 

 dynamic engine, with the same temperatm-es of source and refri- 

 gerator, from a given quantity of heat. 



10. The former proposition is shown to be included in the 

 general " principle of mechanical eflPect," and is so established 

 beyond all doubt by the following demonstration. 



11. By whatever direct effect the heat gained or lost by a 

 body in any conceivable circumstances is tested, the measure- 

 ment of its quantity may always be founded on a determination 

 of the quantity of some standard substance, which it or any equal 

 quantity of heat could raise from one standard temperature to 

 another ; the test of equality between two quantities of heat being 

 their cajiability of raising equal quantities of any substance from 

 any temperature to the same higher temperature. Now, according 

 to thedjTiamical theory of heat, the temperature of a substance can 

 only be raised by working upon it in some way so as to produce 

 increased thermal motions Avithinit, besides effecting any modifi- 

 cations in the mutual distances or arrangements of its particles 

 which may accompany a change of temperatui'c. The work neces- 

 saiy to produce this total mechanical effect is of course propor- 

 tional to the quantity of the substance raised from one standard 

 temperatm-e to another ; and therefore w'hen a body, or a group 

 of bodies, or a machine, parts with or receives heat, there is in 

 reality mechanical effect produced fi'om it, or taken into it, to an 

 extent precisely proportional to the quantity of heat which it 

 emits or absorbs. But the work which any external forces do 

 upon it, the work done by its own molecular forces, and the 

 amount by which the half vis viva of the thermal motions of all 

 its parts is diminished, must together be equal to the mechanical 

 effect produced from it ; and consequently, to the mechanical 

 equivalent of the heat which it emits (which will be positive or 

 negative, according as the sum of those terms is positive or ne- 

 gative). Now let there be either no molecular change or alte- 

 ration of temperature 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 l)e the thermal equivalent of the work done upon it by ex- 

 ternal forces, or done by it against external forces; which is the 

 proposition to be ])roved. 



12. The demonstration of the second proposition is founded 

 on the following axiom : — 



