the Weights of Atoms. 191 



little less than this distance : 



A „ = _L4;./(i + i)i T ,. . . . (1) . 



where m?„ w 2 are the masses of the molecules in the two gases 

 in terms o£ that of hydrogen called unity ; F is the square 

 root of the mean of the squares of the velocities of the mole- 

 cules in hydrogen at 0° C. ; and N is the number of 

 molecules in a cubic centimetre of a gas (the same for all 

 gases according to Avogadro's law) at 0° C. and standard 

 atmospheric pressure. I find the following simpler formula 

 more convenient 



J.2= /F i . ^(ri'+Fy) . . . (2), 



2 v b7rA s 12 



where V^, V 2 2 are the mean squares of the molecular 



velocities of the two gases at 0° C, being the values of 3 p/p 



for the two gases, or three times the squares of their Kewtonian 



velocities of sound, at that temperature. For brevity, we 



shall call mean molecular velocity the square root of the mean 



of the squares of the velocities of the molecules. The same 



formula is, of course, applicable to the molecular diffusivity 



of a single gas by taking V l = V 2 =V its mean molecular 



velocity, and s 32 =5 the diameter of its molecules ; so that we 



have 



1 V 

 B=—±^ 1 ^ I (3). 



§ 42. It is impossible by any direct experiment to find the 

 molecular diffusivity of a single gas as we have no means of 

 marking its particles in the manner explained in § 37 above; 

 but Maxwell's theory gives us, in a most interesting manner, 

 the means of calculating the diffusivity of each of three sepa- 

 rate gases from three experiments determining the inter- 

 diffusivities of their pairs. From the inter-diffusivity of each 

 pair determined by experiment we find, by (2) § 41, a value 

 of s, 2 \/ (2 v&irN) for each pair, and we have s 12 = i(si + s 2 )*, 

 whence 



*1 ~ *'l2 + #13 — *23 : S 2 = *12 + S 2 - A — S l3 ', S,, = 8 13 + S 23 — «12 • (1) * 



Calculating thus the three values of s^/ (2\/37rA T ), and 

 using them in (3) § 41, we find the molecular difFusivities of 

 the three separate gases. 



§ 43. In two communications f to the Academy of Science 



* This agrees with Maxwell's equation (4), but shows his equation (6) 

 to be incorrect. 



f " Experiment al-Untersuchungen iiber die Diffusion von Gasen ohne 

 porose Scheidewande," 8Us. d. l\ Akad. d. Wissensch.. March 10 and 

 May 12, 1870. 



