182 Mr. W. Sutherland on the 



coefficient of expansion of air under a pressure of one at- 

 mosphere, and for the density of air, led to the following 

 equation : — 



avT I 



pv = > 



* v — c V 



with the following values for the constants when the unit of 

 pressure is that of a kilogramme weight per square metre and 

 the unit of volume is a cubic metre, v being the volume 

 occupied by a kilogramme of air : — 



a = 29'3, c=-001056, £=12*372. 



This equation was intended for use only within the range 

 of pressures of Thomson and Joule's experiments ; but it 

 happens to give the critical temperature and pressure of air 

 with considerable accuracy. When these are determined as 

 for C0 2 , we get the critical temperature as —154° C, the 

 critical pressure as 40 atmospheres, and the critical volume of 

 a kilogramme of air as '003167 cubic metres. Wroblewski's 

 determinations (Wiedemann's Ann. xxvi. 1885) make the 

 critical temperature about — 140° 0. and the critical pressure 

 about 40 atmospheres. We have seen in the case of C0 2 how 

 a difference of +10° is possible between the true critical tem- 

 perature of a gas and its critical temperature in a capillary 

 tube ; hence the above equation for air, though constructed on 

 limited data, is probably as accurate an equation as is possible 



with our present data. The values of the ratio ^— L given by 



Wo 

 it for 4° C. do not agree exactly with those given by Regnaultfs 

 equation for 4°, 



^=l--0011054f- -lWo0001938(^-lY. 



Wo y-i / \vi / 



Thus, for example, when ^=15 atmospheres, Regnault's 

 equation gives 



•^ = 1-0117; 



Wo 



while the equation above gives 1*0085. The difference is due 

 to the fact that Regnault's determinations at 4° and Amagat's 

 at 16° are not strictly reconcilable with one another. Amagat's 

 were made in capillary tubes ; but as he has pushed his deter- 

 minations to higher pressures than Eegnault, so as to pass the 

 point for which pv is a minimum, and is thus likely to have 

 obtained with more accuracy the general sense of the changes 

 in pv, I adopted his results, seeing that the discrepancy is 



