FOUNDATIONS OF THE KINETIC THEORY OF GASES. 271 



The numbers in the fourth row are the values of 



and those in the fifth row are from 



It is clear that these formula? give fair approximations to the data, the first for volumes 



down to 0'005 or so, the second for smaller volumes. 



Comparing with formula (C) of § 72, we see that the values of R, Re, and a are 



respectively 



0-00371, 0000021, and 0001 



for the larger volumes, and 



000371, 0000011, and -00012 



for the smaller. The values of y and D can now be determined by the relation in § 72, 

 and a few experimental data. After a number of trials I arrived at 



v =0-0046, 



as most consonant with the data for larger volumes ; and I have provisionally assumed 



the value 



u = 0-004 



for the lower range of volumes, in agreement with what was said in § 69 above as to the 

 probable existence of a short, horizontal, portion of the critical isothermal. The value 

 of y for the first portion of the curve is found to be - 0008 ; and I have assumed it to be 

 -0*0008 for the rest, thus ignoring the condition for the minimax at the commencement 

 of this part of the curve. I consider this course to be fully justified by the arguments 

 given in § 69 above. Thus, taking from the assumption below the value 73 atm. for the 

 critical pressure, we arrive at the following equations for the parts of the critical isothermal 

 which lie on opposite sides of the short, approximately straight, portion : — 



and 



1 \ t{fl + 0-001)(v + 0-0008)y 



v I2(l fr-0-004) 3 \ 



1 \ v(v-0-0012)(v-0-0008)/' 



In a careful plotting of the isothermals of C0 2 from the whole of Amagat's data 

 (including, of course, those given above), I inserted, by means of differences calculated from 

 the preceding formulae for dp/dt, the probable isothermal of 31° C. This is only 0°*1 

 higher than the critical temperature as given by Andrews, which is certainly a little too 

 low in consequence of the small admixture of air. The experimental data in the follow- 



