326 DIRECT PROPERTIES OF MOLECULES 117 



On combining with these the values of the free paths given 

 in 78 and 79, as obtained from Graham's experiments 

 on transpiration, we obtain for the molecular diameters the 

 values : 



Air . . . s = 0-80 x 10~ 7 cm. 



Carbonic acid . O63 



Hydrogen . . 0*40 ,, 



These numbers are markedly smaller than those given 

 before, but they are of the same order of magnitude, and 

 therefore we may see in them a confirmation of the correct- 

 ness of the theoretical views from which we have started. 



We should obtain a better agreement if we replaced the 

 numerical factor of the formula, 3/\/2 = 212, by a greater 

 value. Our determination of this factor really rests on a not 

 entirely safe footing, and it has not always, therefore, come 

 out the same. 1 We might object that the correction, which 

 the value of the free path needs on account of the space 

 occupied by the spheres of action, must not be applied 

 quite in the same way as that which we have to make to 

 Boyle's law for the same reason. The two corrections, 

 therefore, b and 4* ^irsPN, need not be equal to each other, but 

 may still differ by a numerical factor ; and this factor is 

 obtained by Clausius 2 and G. Jager 3 from the considera- 

 tion that molecules which are near each other cannot be 

 struck by another colliding particle at every point of their 

 surface if they really occupy space ; there is therefore a 

 diminution of their surface to be taken into account in the 

 calculation, and this consideration leads to the formula 



1 In the first edition of this book another smaller value, 1-5, was taken ; 

 this results from assuming as strictly valid the calculation first developed in 

 34* of the Mathematical Appendices. There are grounds of probability in 

 its favour which depend on the phenomena described in 118 (Heilborn, 

 Exner's Bepert. 1891, xxvii. p. 369; Sydney Young, 1898, Chem. News, 

 Ixxviii. p. 200), but the larger value seems to me to be theoretically better 

 established. 



2 Mech. Warmetheorie, 1889-91, iii. pp. 57, 213 ; Wied. Ann. 1880, x, 

 p. 102. 



3 Wien. Sitzungsber. 1896, cv. Abth. 2, p. 97. 



