Then 



h /jj G^ 

 ~M VH. 



p: 



This formula was successfully applied in a previous paper, to the 

 representation of M. Regnault's experiments on the expansion of 

 gases, the co-efficients being determined empirically. 



If the substance is in the state of perfect gas, 



^ X M V 



Let Vg be the volume of unity of weight of any substance in the 

 state of perfect gas, under unity of pressure, at some fixed absolute 

 temperature r^. Then 



The foregoing are the principal conclusions arrived at in the first 

 section of the paper, which treats of the relations between heat and 

 expansive pressure. 



The second section treats of the relations between heat and ex- 

 pansive power. 



Let the indefinitely small quantity of heat which must be com- 

 municated to unity of weight of a substance, topi'oduce the variation 

 of temperature d r, simultaneously with the variation of volume d V, 

 be denoted by 



d .Q=dQ + dQ,' 



d Q, being the portion which remains in the body as sensible heat, 

 being directly employed in increasing the velocity of the molecular 

 revolutions, and 8 Q', the variation of latent heat, being that which 

 is transformed into expansive power and molecular action, in alter- 

 ing the form and sizes of the orbits of the revolving particles. Then 



