98 On a Fundamental Theorem in the Mechanical Theory of Heat, 

 thereby is expressed by ^ dv. Hence we have the equation 



and by substituting this value of -, in the equation (13), the 



latter becomes 



d^ dp 



dt dt /T tf\ 



T=7 ^ ^ 



But, according to Mariotte and Gay-Lussac's law, 



a-\-t 

 p= . const., 



^ V 



where a is the inverse value of the coefficient of expansion of the 

 permanent gas, and nearly =273, if the temperature be given 

 in degrees C. above the freezing-point. Eliminating p from (15) 

 by means of this equation, we have 



dT dt ., ^. 



Y=7+t' ^^^^ 



whence, by integration, 



T= (« + /). const. ..... (17) 



It is of no importance what value we give to this constant, be- 

 cause by changing it we change all equivalence-values propor- 

 tionally, so that the equivalences before existing will not be 

 disturbed thereby. Let us take the simplest value, therefore, 

 which is unity, and we obtain 



T=a + t (18) 



According to this, T is nothing more than the temperature 

 counted from «°, or about —273° C. below the freezing-point, 

 and, considering the point thus determined as the absolute zero 

 of temperature, T is simply the absolute temperature. For this 

 reason I introduced, at the commencement, the symbol T for the 

 reciprocal value of the function /(/). By this means all changes 

 which would otherwise have had to be introduced in the form of 

 equations, after the determination of the function, are rendered 

 unnecessary ; and now, according as we feel disposed to grant 

 the sufficient probability of the foregoing assumption or not, we 

 may consider T as the absolute temperature, or as a yet unde- 

 termined function of the temperature. I am inclined to believe, 

 however, that the first may be done with hesitation. \ 



ii A$^6i ,}^h, ,\^ .oVi ,^i .laV 4* .c^ .\^¥x .^r 



