472 MR. S. CHAPMAN ON THE KINETIC THEOKY OF A GAS 



The sum of the residuals l>etween columns 3 and 4 is 77 in the first case, 54 in 

 the second* ; more accurate determinations of k would probably reduce these 

 figures, but the agreement is already within the limits of experimental error. It will 

 be seen that the values of k which have been found, viz., 0'69 for argon and helium 

 and 0'65 for oxygen and hydrogen, are intermediate between the values corresponding 

 to the elastic-sphere theory and MAXWELL'S hypothesis, a result which confirms our 

 theory. It is impossible to tell what special molecular structure these numbers 

 indicate until the integrals of Part II. of this paper are worked out for other cases ; 

 it may be that a very slight modification of one of the hypotheses there considered 

 would explain the figures. 



The above tables, and others which might be given, show that our formula agrees 

 well with observation, with a value of k accordant with the theory ; its success 

 is therefore more significant than that of THIESEN'S formula, with its two 

 empirical constants. It may be noticed that THIESEN'S expression can also be put 

 into the form (53), with the speciality, however, that a relation exists between the 

 three independent constants of (53) reducing them to two. Nevertheless, this 

 agreement in functional form is sufficient to explain the success of THIESEN'S 

 expression as an interpolation formula over the limited range (0, l) of p and p'. It 

 may be concluded that, as far as the latter purpose goes, PULUJ'S formula, though 

 not theoretically well founded, is the best (when the values of ^ and ft! at the 

 temperature considered are assigned), because it is very simple in form, quite definite, 

 and sufficiently accurate for most purposes ; while THIESEN'S formula requires the 

 knowledge of two empirical constants, and my own formula is not so well suited for 

 numerical calculation, f 



The study of the variation of the viscosity of mixed gases with tne temperature is 

 best deferred till the analogous question has been discussed for simple gases; the 

 subject will therefore be briefly discussed in 22. 



20. The Coefficient of Viscosity of a Simple Gas. 



The formulae which have already been discussed do not contain any reference to 

 the internal structure of the molecule, so far as this could be avoided, but are 



h The corresponding figures for THIESEX'S formula are 55 and 51, and for PULUJ'S formula 126 and 

 187. Cf. K. SCHMITT, 'Ann. d. Phys.,' 30, p. 393, 1909; pp. 408, 406. 



t The form of the expression (53) is well suited to explain the phenomenon mentioned at the beginning 

 of this section. It shows that /*i 2 is really a weighted mean between p,, p.' and F/F lt the weight depending 

 on the ratios E : F : G and varying with p and p'. For mixtures of C0 2 and H we have F/Fj > p > // ; 

 also as E : G, or 1 + kw[w : 1 + kw'jw is large, on account of the largeness of w/w, /*' is given very little 

 weight in the mean except when p is very small. Therefore, for moderate values of the ratio p/p', the 

 value of pi-, lies between F/Fi and /*, and may exceed the latter considerably. 



The same thing may be noted to a small extent in the above argon-helium table. From the figures 

 already given, we have F/Fj = 2482 x 10" 7 , which Is greater than 2220 x W~", the viscosity of argon at 

 the temperature considered. 



