122 Mr. W. Sutherland on the 



absolute temperature of the gas, were led to the form 



where is temperature on Thomson's absolute thermo- 

 dynamic scale, given within ordinary experimental limits by 

 the equation „ ^_ _ 



If, in the small second term, we consider that p ex — , the 



v 



equation takes Rankine's form — 



If T represents temperature, measured from the absolute zero 

 of an air-thermometer, on which the temperature of melting 

 ice is supposed to be 273°, then within ordinary ranges of 

 temperature we can put = T + A, the value of A being *7, 

 as determined by Thomson and Joule (" Thermal Effects of 

 Fluids in Motion," part iv., Phil. Trans. 1862). With 6 ex- 

 pressed in terms of T, Thomson and Joule's equation becomes 



■p 

 j9v=AT + AA— 7p-> 



where the occurrence of the small constant term AA is of 

 great importance in thermodynamic and molecular theory. 



Hira*, by his thermodynamic ideas, was led to the con- 

 clusion that the equation of a body in any state could be 

 obtained by generalizing the equation to a perfect gas ; thus, 



(p + R)(«-^)=AT. 



R is a term resulting from the molecular attractions, and is 

 called by Hirn the internal pressure. He determines it for 

 different substances as a function of the volume, involving 

 two constants and i|r, which he calls the atomic volume, and 

 takes as representing the actual spatial extension of the mole- 

 cules whose united domains form the volume v. 



Athanase Dupre was the first writer, to my knowledge, 

 who endeavoured to show the bearings of Laplace's ideas of 

 molecular forces on the form of characteristic equations and 

 to apply them. Let $(v, t) be the potential energy (travail 

 mecanique interne) of the molecules of a body whose volume 

 is v at temperature t. Then it follows from Laplace's theory, 

 with the assumptions involved in it, that (j>(v,t) varies 



* " Theorie Mecanique de la Chaleur," Ann. de Ch. et cle Ph t 4 serie, xi. 



