of the Mechanical Theory of Heat from the First. 23 



found in its initial condition, another quantity of heat must 

 simultaneously pass from a hotter into a colder body ; and the 

 amount of the latter quantity of heat in proportion to the 

 former depends only on the temperatures of the two bodies 

 between which it passes, and not upon the nature of the body 

 through which the transformation was effected." 



Clearly a proposition so complicated, however accordant 

 with the facts of experience, cannot be accepted as a simple 

 axiom. Hence physicists were obliged to seek an hypothesis 

 that could be more easily expressed, more distinctly repre- 

 sented, than the Second Proposition, and from which the latter 

 could then be strictly deduced mathematically. In fact a 

 series of such axioms for the deduction of the Second Propo- 

 sition have been found. 



Let us consider these in the order in which they have suc- 

 cessively been proposed. For the facility of our survey we 

 will arrange them in two groups. The first Comprises those 

 assumptions which refer to the behaviour of heat as an agent, 

 without entering in detail into the nature of the motion which 

 we name heat ; while the second group comprises those hypo- 

 theses which relate to the nature of the motion. 



To the group of thermic hypotheses belong : — 



(1) Clausius's axiom, proposed by him in his fundamental 

 memoir (read in February 1850 before the Berlin Academy), 

 and afterwards more completely presented * : — "Heat cannot of 

 itself pass out of a colder into a hotter body.'''' 



(2) Thomson's axiom f, which reads thus : — "It is impossible, 

 through the action of dead matter, to obtain mechanical work by 

 cooling any natural substance below the temperature of the coldest 

 of the surrounding objects." 



(3) Clausius's second hypothesis, expressed,^ in his memoir 

 relative to disgregation J, as follows: — "The mechanical work 

 which heat can perform in any change of arrangement of a 

 body is proportional to the absolute temperature at which the 

 change takes place.'''' 



(4) Belpaire's axiom §, viz.: — u If the temperature be infi- 

 nitesimal, the quantity of energy converted into work by an isc- 

 thermal transformation must likewise be infinitesimal." 



These are the thermic hypotheses which, to my knowledge, 

 have been proposed for the derivation of Carnot and ClausmVs 

 principle. The second group comprises the dynamic hypotheses 

 proposed for the same purpose, viz. : — 



(5) The hypothesis of "molecular vortices," set forth in 



* Pogg. Ann, 1850, vol. lxxix. ; PHI. Mag. [IV.] vol. ii. 



t Edinb. Trans. toI. xx., and Phil. Mag. [IV.] vol. iv. 



% Pogg. Ann. 1862, vol. cxvi. § Bull de Belg. 1872. 



