176 



Mr. W. Sutherland on th 



values of the same ratio, as calculated from the equation, are 

 furnished for comparison : — 



Values of ^r-v 



p'v 





50°. 



100 c . 



200°. 



300°. 



Amagat 



Equation 



1-0145 

 1-0144 



] -0087 

 1-0086 



1-0040 

 1-0028 



1-0020 

 1-0001 





The agreement is satisfactory at the high temperatures, if 

 it is remembered that the values of the ratio given by experi- 

 ment cannot be considered to be free from an error of at least 

 1 in 1000. But it must also be borne in mind how limited the 

 range of temperature is which I was restricted to using in 

 determining the form of Dr. Walter's function /3, on account 

 of the unknown amount of distortion which the isothermal for 

 35 0, 5 experiences through capillary action both in Amagat's 

 and Andrews^s experiments, a distortion which is most serious 

 at the most important part of the curve. I have shown that, 

 as regards C0 2 , the experimental evidence is in such a state 

 that no form can with finality be proved to be the one fit and 

 proper form. The equation which I have given possesses the 

 merit of representing the compressibility of C0 2 at 100° and 

 at 70° up to a pressure of 400 atmospheres, of having revealed 

 the important effect of capillary action on the circumstance of 

 the critical state, and of giving the saturation pressures of C0 2 

 almost exactly as they have been experimentally determined. 



The discussion, to which I proceed, of our equation in the 

 light of the thermal effects studied by Thomson and Joule 

 when gases are allowed to escape from under pressure through 

 porous plugs, and of Regnault's experiments on the expansion 

 of gases, is now of the utmost importance, as in these experi- 

 ments we have to do with changes in the molecular potential 

 energy. 



According to the law of the inverse fourth power, without 

 further hypothesis, we saw that the potential energy of a 

 number of molecules is § of the virial of their mutual attrac- 



tions. 



Now, in the characteristic equation 



# . — is the virial 



> 2 



of the molecular attraction, and § l(— 1 is the change 



of the virial on the expansion of the gas from volume v x to 

 volume v 2 . Hence the change of molecular potential energy 



