86 KEPORT 1891. 



Hence if 



V=6^ (3) 



as 



we have 



dQ=r,ds (4) 



BO that 7j as well as 6 is the reciprocal of an integrating factor of clQ, or, 

 as we may call it, an ' integrating divisor ' of clQ,. Since dS/ds may be 

 regarded as a function of S, we see that the product of the temperature 

 into any arbitrary function of the entropy of a body is an integrating 

 divisor of (?Q, and therefore possesses properties analogous to 6 in equa- 

 tion (2). 



Hence the absolute temperature $ is not fully defined by equation (2), 

 and the Second Law of Thermodynamics is not, therefore, completely 

 proved by the establishment of an equation of this form. 



3. It is, therefore, necessary to take into account the other property by 

 which temperature is characterised, namely, that heat always tends to pass 

 from a body of higher to one of lower tem-perature, and in particular that 

 if two bodies in contact have the same temperature there ivill be no transfer- 

 ence of heat between them. 



The Second Law of Thermodynamics consists in the fact that among 

 the integrating factors of dQ there is one whose reciprocal, 6, possesses 

 the properties of temperature just mentioned. 



4. But, nevertheless, without considering the properties of thermal 

 equilibrium between difierent bodies we derive one very important infer- 

 ence from equation (2) — namely, that the thermal condition of a system 

 whose parts are in thermal equilibrium can be completely defined by a 

 single coordinate, or, in other words, that the consideration of thermal 

 phenomena only adds one to the total number of coordinates otherwise 

 required to fix the state of a dynamical system. 



5. Impossibility of a Perfectly General Mechanical Proof. — To reduce 

 the First Law of Thermodynamics to the principle of Conservation of 

 Energy it is only necessary to assume that heat is some form of energy ; 

 no hypothesis is required as to what particular form this energy takes. 

 It was natural, therefore, that physicists should at a very early date 

 endeavour to reduce the Second Law in like manner to a purely dynami- 

 cal principle, and the jirinciple of Least Action naturally suggested itself 

 as the pi'obable analogue of Carnot's principle. But here a limitation at 

 once arises f.om the necessity of giving a dynamical meaning to dQ, the 

 energy communicated to the system in the form of heat, and of separating 

 dQ, fi'om — dW, the energy communicated in the form of mechanical 

 work. 



6. This limitation requires that some special assumption shall be made 

 regarding the nature of heat, and the natural and almost inevitable 

 assumption is that every finite portion of matter is built up of a very 

 large number of elementary portions, called molecules, and that the form 

 of energy known as Heat is due to the relative motion of the molecules 

 among themselves. 



But, fui'ther, these molecules must be characterised by some peculiar 

 property, such as their (practically) infinitely large number whereby 

 their dynamical properties differ in some manner from those of a finite 

 number of particles or rigid bodies. For without such a distinction it 

 would be impossible to deduce any dynamical equations involving dQ, 



