LIQUIDS AND ALLIED EXPERIMENTS. 33 



If we differentiate the equation 



m = A — ( ) 



t \p w p a / 



logarithmically, with respect to p g the result is 



Pu 



Pg(j>g—Pv>) 



and since k = m/a(dp/dl), the same relative error will occur in m, m, v, v, k, 

 and k. Since p w = 1 (nearly) and the assumed value of p g = 2.868 and 8p g = 

 — 0.402, this correction is 



—0.402 

 2.868(1.868) = _a ° 75 



Unfortunately the error 8p g is too large to admit of differentiation. The 

 correction for m may, however, also be given directly by multiplying by 



i/p w -i/p 



where the numerator contains the correct values. In this way, for the 

 mean temperature of observation, the fraction is 



^74=i-o.o87i 

 0.6544 



or the correction is —8.7 per cent. It will therefore be necessary to reduce 

 all the values specified by this amount. It is needless to apply the cor- 

 rection to the above tables, since their chief purpose was to show the 

 character of the variation of m in the lapse of time, and all temperature 

 corrections, etc., have there been made. But in table 9 of the next section, 

 which is a summary of essential results, the correction has been introduced 

 in full. The final data are therefore smaller than the above. 



25. Summary. Relatively Slow Diffusion of Mixed Gases. — The data 

 of the preceding tables have been brought together in all their essential 

 features in table 9, values in parenthesis being nominal, due to the variable 

 gas constant, R, involved. In case of mixed gases the initial diffusion is 

 simply tabulated for comparison and the gradient selected (water heads h") 

 merely furnished a means of obtaining a datum (k or k in parenthesis), inde- 

 pendent of the dimensions, etc., of the apparatus. In these cases (k) or 

 (k) have no immediate meaning, because the diffusion is differential under 

 conditions which have not been disentangled. The data, like m, which is 

 not free from the constants of the apparatus, merely indicate the enor- 

 mously rapid diffusion at the outset, while the potential energy of separated 

 gases is being expended. In case of mixed gases m also is nominal, the true 

 datum being v, the number of cubic centimeters diffusing per second as 

 explained above. 



