118 



DIRECT PROPERTIES OF MOLECULES 



329 



determined by Boltzmann, as well as one observation by 

 Ayr ton and Perry, with the values of the molecular free 

 paths L calculated from Graham's experiments on trans- 

 piration. The numbers found by him are really much 

 smaller than those obtained by the other modes of calcula- 

 tion, as we see from the following comparison of his numbers 

 with those calculated by the methods of Loschmidt (116) 

 and van der Waals ( 117). 



Values of 10 7 s in cm. 



We might therefore consider it possible that Dorn's 

 numbers represent too small values of the molecular 

 diameters, and that they even form an inferior limit, as 

 Loschmidt's give a superior limit, for the magnitude s-, 

 whose true value lies somewhere between the two. I will 

 not contest the admissibility of this idea, but I must consider 

 it very uncertain, as so many kinds of unproved and even 

 improbable assumptions underlie all these calculations. The 

 hypothesis that the molecules are shaped like spheres, which 

 occurs in the discussion of their dielectric behaviour, seems to 

 me to be especially doubtful ; for the dielectric polarisation 

 will, if the molecules are of a flat shape ( 112), be entirely 

 different from what it will be if they are spheres. 



Franz Exner 1 and Ph. Guye 2 have devoted atten- 

 tion to these relations, in addition to Dorn. The former 

 gives extensive tables of values, among which are some 

 that have been calculated from the indices of refraction 

 observed by Dulong. For the fraction g can be calculated 



1 Wien. Sitzungsber. 1885, xci. Abth. 2, p. 850 ; Exner's Repert. 1885, 

 xxi. p. 446. 



2 Arch. d. Sc. Phys. et Nat. 1890 [3] xxiii. p. 197. 



