CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 467 



on the variation of the coefficient of diffusion (of the gases concerned) with 

 temperature. 



The formula for the coefficient of conduction in a mixed gas (equations 40 and 41) 

 seems very complicated, but the calculations from it in any particular case are quite 

 simple. Fortunately we have experimental data for testing the law. WACHSMUTH,* 

 at Halle, has recently determined the conductivity of mixtures of argon and helium 

 in various proportions ; the gases being monatomic, our formulae are properly 

 applicable. WACHSMUTH himself undertook the research, at Prof. DORN'S suggestion, 

 in order to determine f in the formula ^ = fnQ,, taking the value of n from 

 TANZLER'S experiments (which will l>e discussed in the next section) on the viscosity 

 of mixtxires of argon and helium. He found that f so determined for the mixture 

 was greater than , approaching a maximum (about 4) when there was 60 per cent, 

 of helium in the gas, and falling to $, as SCHWABZE showed, when either gas was 

 eliminated. This fact is interesting, but, in the absence of any explanatory theory, 

 does not lead to anything further. 



WACHSMUTH also found that the observations could be represented to within 2 per 

 cent, or 3 per cent, by the formula 



s jy 



^' 3 = l+Ap'/p + l + Bp/p' 



(modelled on a similar formula for the viscosity of gases which we shall consider 

 presently). As there were only four observations and two empirical constants the 

 fact is not very remarkable ; when p = of course S 13 = W, and when p' = we have 

 >,.) = S-. A much better agreement was obtained by allowing the empirical constants 

 A and B (obtained by the method of least squares) to be imaginary. In this case the 

 expression reduces to the quotient of a cubic by a quartic homogeneous expression in 

 the variables p, p' ; as WACHSMUTH remarks, the relation is good as an interpolation 

 formula, but that is all. 



We proceed to determine the value of ia from our formula. Taking oxygen as 

 the standard gas (for which p a = 0'001429 at C. and normal pressure) we have w 

 (for argon) equal to 1'224, and w' = 0'125. The values of MO (*', M at C.) 

 determined by SCHULTZE (loc. cit. on p. 463), viz., 0'0002104 and 0'0001891 respec- 

 tively, will be used ; also the previously given values of C v . The coefficient of 

 diffusion D^ for argon and helium has been determined by SCHMIDT and LONIUS 

 (references given in 21) ; reduced to C. and normal pressure, in C.G.S. units it is 

 0'650.t We now have all the necessary data for the calculation of & 12 in the case of 

 rigid spherical molecules and of Maxwellian molecules. For the case of attracting 

 spherical molecules we need also the coefficient C 12 ; this has not been determined, to 



* 'Halle Disa.,' 1907; ' Phys. Zeitschrift,' 7, p. 235, 1908. The method was that due to SCIILKIER- 

 MACHKR, and the appiratus was that previously used by SCHWARZE and GUNTIJER, alre ady quoted, 

 t As explained in 21, this value is uncertain to within 2 per cent, or 3 per cent. 



3 o 2 



