1 62 Prof. R. Clausius on the Second Axiom 



If, however, we wish to make this law the basis of a mathe- 

 matical development, we must give it a more definite form, 

 because the expression effective force of heat may admit of differ- 

 ent interpretations. Hence in that memoir I have, for the pur- 

 pose of thus applying it, expressed the law more fully, as follows: — 



The mechanical work which can be done by heat in any alteration 

 of the arrangement of a body, is proportional to the absolute tem- 

 perature at which the alteration takes place. 



In order to express this law by a mathematical equation, let 

 us imagine the body undergoing an infinitely small alteration of 

 its condition, the change proceeding in a reversible manner, in 

 which the quantity of heat contained in the body as well as its 

 constituents may be altered. Work may either be performed 

 (when the internal and external forces operating on the particles 

 are overcome) or expended (when the particles yield to the forces). 

 This infinitesimal work may be denoted by dh ; work performed 

 is reckoned as positive, and work expended as negative. Then 

 the following equation will stand as the expression of the above 

 law : — 



dh=\dl, (I) 



in which T denotes the absolute temperature, and A a constant, 

 namely the caloric equivalent of the work, and Z represents a 

 magnitude which is perfectly determined by the present condi- 

 tion of the body, without it being necessary to know in what way 

 the body has come into this condition. This magnitude I have 

 named the disgregation of the body. 



If we further assume, as I have done in the above-mentioned 

 memoir, that the absolute temperature of a body is proportional 

 to the quantity of heat present in it, and denote this quantity 

 by H, we can put 



T=CH, 



in which C will be a constant.' The preceding equation is thus 

 transformed into 



A 



TT 



The fraction herein occurring, -r-, represents the quantity of 



heat present in the body, measured, not according to the usual 

 heat-scale, but mechanically ; therefore, in other words, it repre- 

 sents the vis viva of that motion which we name heat. By in- 

 troducing for this magnitude the simple sign h } the equation 

 becomes 



dL = ChdZ (2) 



