Conductivities of Mixtures and of their Constituents. 287 



k = 

 1 



P1+P2 



1 1 



P1T+P217 



(0 



(2) 



i?i+B 



where k l and £ 2 are the conductivities of the constituents, and 

 p 1 and p 2 either the masses or the volumes of each present. 

 Paalhorn, Winkelmann, and Schott, in their paper on the 

 conductivities of glasses "*, used the first form with the jo's the 

 masses of the constituents present ; but Winkelmann has 

 recently recalculated the results f, using the second form, 

 with the ^>'s the volumes of the constituents present, and 

 found a better agreement than formerly. 



Focke % uses the first formula, with the p's the masses, to 

 represent his own results on the conductivities of various kinds 

 of glass. Both theory and experiment §, however, point to the 

 fact that it is the proportion by volume which ought to be 

 used in such calculations ; and I shall confine myself in what 

 follows to the consideration of the proportions by volume, 

 calculated on the assumption that the mixture is simply a 

 physical mixture, and is formed without contraction. Under 

 these conditions the formula 



JL __ Pl^l + P2K2 

 Pi +P2 



corresponds to the constituents being distributed in the space 

 between the two parallel isothermal surfaces, through which 

 the heat enters and leaves the medium, in the form of right 

 prisms with their axes perpendicular to these surfaces, thus : — 



Fig. 1. 





and the formula 



P ^ + ^k 2 

 P1+P2 



* Wied. Ann. \l p. 738 (1894) 

 t Ibid, lxvii. p. 160 (1899). 

 J Ibid, lxvii. p. 155 (1899). 



§ Lees, Phil. Trans. Royal Society, exd. p. 433 (1898) j Phil. Mn< 

 ante, p. 224. 



