of the Mechanical Theory of Heat from the First. 31 



same state. In another state, i and C have other values, which 

 again are constant as long as the new state is unchanged. 



If the infinitesimal quantity of energy dQ, be conveyed to 

 the body, the variables C=T and i change also infinitesimally ; 

 consequently 



€=T-(T + ^T) + T; 



and recollecting that in this case T also can only be infinitesi- 

 mally different from T, we obtain, for an infinitesimal change 

 of state, 



C=T, 



wherein, for each element of energy clQ received, that vis viva 

 C=T must be employed which the body has directly on the 

 reception of that element. 



If now we integrate equation (9) between the limits corre- 

 sponding to the initial and final states, we have 



X 



C g («)0 



reSj 



J"' 



Extending the integral to a complete circular process gives 



' d S=o, • • (10) 



This equation corresponds perfectly with the following, 



'^=0 (11) 



which expresses the Second Proposition for reversible circular 

 processes. In equation (10) % denotes the total vis viva which 

 the body possesses directly on the reception of the element of 

 energy dQ ; in equation (11), T denotes the absolute tempera- 

 ture which the body possesses directly it receives the heat-ele- 

 ment dQ. If it be assumed (as it usually is) that the absolute 

 temperature is a quantity proportional to the total vis viva } 

 equation (10) immediately changes into equation (11). 



In the preceding considerations we have endeavoured to keep 

 aloof from every hypothesis, basing our deductions solely upon 

 the principle of the Conservation of Energy. We believe we 

 have thereby proved that the Second Proposition can be de- 

 duced from the First without any further hypothesis. 



Budapest, June 15, 1875. 



