Laics of Molecular Force. 223 



The experimental numbers for oxygen are taken from Amagat's 

 data in the Comptes Rendus, xci. 



The most delicate test we can apply to our form at high 

 volumes is, in the case of air, to compare the calculated with 

 the experimental Thomson and Joule cooling effect. When 

 I did this with the previous equation for air (& = 2*11 aud 

 Z=910), I assumed the difference '7° to exist between the 

 melting-point of ice on the thermodynamic and gas ther- 

 mometers ; but, as already pointed out, Sir W. Thomson 

 having proved this difference not to exist, there must have 

 been a compensation of errors in the application of the 

 previous equation. Thomson's expression for the cooling 

 effect, applied to our equation for air, becomes 



K p dS/dp = 2l/UT-k/2, 



which gives the following calculated values : — 



Cooling effects of air escaping through a porous plug into 

 the atmosphere under a pressure excess of 2*54 metres 

 of mercury. 



Temperature C 7°* 1. 



Experiment . . . '88 

 Calculation . . . '84 



The agreement is the closest to be looked for and proves the 

 accuracy of our equation for air at high volumes. 



At low volumes we can test the form for all the elementary 

 gases and CH 4 by applying it to the calculation of the critical 

 volume, pressure, and temperature in each case. To do this 

 at the present stage we must assume that our form can be 

 trusted to hold not only to the critical volume but also a little 

 past into the liquid region, a legitimate assumption for the 

 elements, where we have seen the internal virial varying 

 inversely as the volume, and so giving a guarantee of con- 

 tinuity, but not legitimate for the compounds where dis- 

 continuity occurs. Then, applying James Thomson's idea 

 of the passage from the gaseous to the liquid state, as pre- 

 cisionized by Maxwell and Clausius, we have the critical point 

 determined by the conditions ~dpfdv = 0, ~d 2 p/^v 2 = 0. 



Along with the characteristic equation these lead to the fol- 

 lowing values: — critical volume Va = ok/2 ; critical temperature 

 T c =lb7/27B&; critical pressure p c = 4,1/ 271c 2 ,— to compare with 

 the experimental values found by Olszewski for 2 and N s 

 (Compt. Bend, c), by Wroblewski fcr air, and by Dewar 

 for CH 4 (Phil. Mag. 1884, xviii.). 



17°. 



39°-5. 



92°-8. 



'86 



•75 



•51 



•80 



•71 



•55 



