36 



THE DIFFUSION OF GASES THROUGH 



and consequently the gas a, with the diminution of p b +p c + ' ' • will also 

 escape slowly. As a whole the results contain a remarkably striking com- 

 mentary on the meaning and potency of the pressure gradient. To develop 

 an equation, however, which embodies all these facts, in such a way as to 

 predict the observations quantitatively, has not been accomplished in the 

 above paper. In fact, if we write 



i+fmdt 



m = pv-\-vp = pv-\- p 



where w is the initial charge of pure gas, m and v are given in terms of p by 

 equations (31) and (35). Hence the equation may be expressed in terms 

 of p and becomes eventually 



— (pv — m) — 2pv- 

 P 



(pv — m) =0 



Table 10. — Values of p (density) in the final diffusions of mixed gases. B — 7r = 74cm.; 

 n = 987, 000 +p' dynes; k a = 1.09X io~ ls ; &/,= 1.92X 10- 14 ; Rh/R a = 14.44. 



l(R h /Rg-i) 



~ R a \a ka l) U(k a -i 





From 

 table 7. 



From 

 table 5. 



mVXio 10 



PoXio G 



a 



0.40 



82 



11. 5 



20. 5 



11. 5 



1 1 ,260 



998,500 



14 27 



0.987 (air) 



5 9 



1,200 



6.4 



20.0 



10.0 



9.790 

 997,100 

 . 0864 

 0.981 (hydr.) 



/ 



h" 



p' 



n 



P/Po 



X 





Here v and m involve p, while wand m are proportional to p. Moreover, the 

 phenomenon expressed in terms of p, the density of the imprisoned gas, 

 should be integrable, but the equation does not seem to reduce down suffi- 

 ciently to make the attempt at integration worth while. 



With regard to equations (31) or (35) it should be pointed out that when 

 m or v is known, p may be computed in terms of the coefficients, k a and k h , 

 of the two gases diffusing into each other. As in the final phases of the 

 phenonemon m is nearly constant, the density and hence the composition 

 of the gas undergoing diffusion in one direction may be found with some 

 precision. Thus in table 9 the air-hydrogen and hydrogen-air diffusions, 

 when m has become constant, correspond to mixed gases of the density and 

 composition indicated in table 10. 



The marked irregularities of the graphs in case of air and oxygen, when 

 there are temperature variations, has been referred to the effect of solution, 

 which absorbs a soluble gas at falling temperatures and rejects it at rising 

 temperatures, contemporaneously with the occurrence of diffusion. It is 



