402 Prof. L. Natanson on the 



and four similar equations ; and from (3) and (6) 



Dt ' Ktyy r) V>t 



F= -jjj'dtf dydz — ^ + (P** ~P) 



4 M 



P(p«-j>) 





whence, by (3), we infer that ~DF/Dt=— 2F/t, as stated 

 above. 



The value of t in air, at the temperature 0° C. and normal 

 pressure, is approximately 2.10 -10 of a second (Maxwell, Phil. 

 Trans. 1867, p. 83). We may also compare the relative 

 values of r in two fluids. In doing so we may assume, in 

 accordance with Prof. Van der Waals' leading idea, that the 

 values of r would bear a constant proportion if they were 

 calculated for a corresponding " states of the fluids *. Hence 

 the coefficients of viscosity will likewise, in corresponding 

 states of two fluids, bear a constant numerical ratio f. 



§ 16. Diffusion. — The signification of the symbols being 

 the same as in § 11, we find the dissipation function of diffu- 

 sion to be 



J?~iffida:dydzAp 1 p2\(v a -Ui) 2 +(v2— Vi) 2 +(w 2 — w i) 2 }* (1) 



The theory of diffusion can be deduced, in the case of two 

 gases, from " kinematical " equations and from the following 

 equations " of coercion," in which D/Dt refers to the total 

 coercive action of both gases : 



TJj? =Ap 2 (w 2 -w 1 ) ; —^ =Ap 1 {u 1 -u s ), . (2) 



and four other equations of similar form. If the dynamical 

 equations of Maxwell and Stefan are true, equations (2) must 

 likewise be fulfilled ; they may be said therefore to agree 

 with experience. Let us now pass to the usual case of slow 

 and quiet diffusion (Maxwell, Phil. Trans. 1867, pp. 73-74). 

 If we write 3 for the temperature, R for the gaseous con- 

 stant, w r e shall find the value of the coefficient of diffusion, 

 or h say, to be ~R^/A(p 1 -\-p 2 ) ; and, if p=p 1 + Vv the charac- 



* See Kamerlingh (Dimes, Algemeene Theorie der Vloeistoffen, Tweede 

 Stuk, p. 8, 1881. 



f See Kamerlingh Onnes, ' Communications from the Laboratory of 

 Physics at the University of Leiden,' no. 12, p. 11, 1894. 



