272 PROFESSOR TAIT ON THE KINETIC THEORY OF GASES. 



incr tabic were taken directlv from the curve so drawn. They are, of course, only 

 approximate : — especially for the smaller volumes, for there the curves are so steep that it 

 is exceedingly difficult to obtain exact values of the ordinates for any assigned volume. 

 It is also in this region that the effects of the slight trace of air are most prominent. 



Approximate Isothermal of 31° C. 

 The third line is calculated from the first of the above formula?, the fourth line from the second. 



v 1 -024 02 -015 -0125 '01 -0075 006 005 0045 -004 -0035 -003 -0025 002 



p(exp.) 112 371 424 516 572 634 69*6 724 729 73 73 732 768 114 392 



J113 37-2 425 51-4 570 633 69'6 723 7295 73 7316 744 796 964 149 



2H calc -)| 73-0 732 791 117-6 377 



For volumes down to 0*0035 the agreement is practically perfect. The remainder of the 

 data, even with the second formula, are not very well represented. The value of p for 

 volume 0*003 has given much trouble, and constitutes a real difficulty which I do not 

 at present see how to meet. It is quite possible that, in addition to the defects men 

 tioned above, I may have myself introduced a more serious one by assuming too high a 

 value for the lower critical volume, or by taking too low a temperature for the critical 

 isothermal. Had I selected the data for the isothermal of 31°*3 or so, it is certain that 

 (with a slight change in v) the agreement with the formula would have been as good as 

 at present for the larger volumes, and it might have been much better for the smaller. 

 But I have not leisure to undertake such tedious tentative work. As it is, the formula? 

 given above represent Amagat's results from 31° to 100° C. for volumes from 1 to 0*0035, 

 with a maximum error of considerably less than 1 atmosphere even at the smallest of these 

 volumes. And, even with the least of the experimental volumes, the approximations to 

 the corresponding (very large) pressures are nowhere in error by more than some 4 or 5 

 per cent. This is at least as much as could be expected even from a purely empirical 

 formula, but I hope that the relations given above (though still extremely imperfect) may 

 be found to have higher claims to reception. 



[Since the above was put in type it has occurred to me that this remarkable agree- 

 ment, between the results of experiment on a compound gas. and those of a formula 

 deduced from the behaviour of hard, spherical, particles, may be traced to the fact that 

 the virial method is applicable, not only to the whole group of particles but (at every 

 instant) to the free particles, doublets, triplets, &c, in so far as the internal relations 

 of each are concerned. Hence the terms due to vibrations, rotations, and stresses, in 

 free particles, doublets, &c, will on the average cancel one another in the complete 

 virial equation. How far this statement can be extended to particles which are not 

 quite free will be discussed in the next instalment. 5/6/91.] 



