289 



d-U = rd<t> 

 where d'll is the quantity of energy required, in the form of heat, 

 to produce the varicition d.^. 



In article 65'a, a new form of the thermodynamic function is 

 pointed out, in which the pressure and absolute temperature are 

 taken as independent variables instead of the volume and absolute 

 temperature. It is as follows : — 



*=('' + ^) '■''"• '°«'-/^''''" 



and is useful in solving a particular class of questions. P^ and V^ 

 are respectively the pressure and volume of the given substance at 

 the absolute temperature r^ in the state of perfect gas. 



In article 66, the constants in the formula deduced from the 

 hypothesis of molecular vortices for the elasticity of carbonic acid 

 gas are revised, and adapted to the corrected position of the abso- 

 lute zero ; the result being expressed by the following very simple 

 law : — 



The diminution of the elasticity of carbonic acid gas, produced 

 by the mutual attraction of its particles, varies directly as the square 

 of its density, and inversely as its absolute temperature. 



These constants are determined solely from the experiments of 

 M. Regnault on the increase of pressure between 0° and 100 Centi- 

 grade of carbonic acid gas of constant density, and in the specific 

 gravity and specific heat of the gas. The results of the formula; 

 are then compared, and found to agree most closely with those of the 

 following sets of experiments : — 



1. Those of M. Regnault, on the expansion of carbonic acid gas 

 at constant pressure. 



2. Those of M. Regnault, on the compressibility of carbonic acid 

 gas. 



3. Those of Messrs Joule and Thomson, on the cooling of car- 

 bonic acid gas by free expansion. The results of the last set of ex- 

 periments were anticipated by means of the formula. 



General Formula and Constants for Carbonic Acid Gas. 

 PV _ J7^_ a_ Yo _ 



P V T T ' V 



^0 



P pressure in lb. per square foot, "i at the absolute 

 V volume of one lb. in cubic feet, J temperature t 



