288 



Dr. C. H. Lees on the Thermal 



to their being distributed in layers parallel to the isothermal 

 surfaces, thus : — 



Fiff. 2. 



- — -— - — — — . ■ . ., -— — — - 



It has been recently shown * that the formula 



W = filog*i+^og* ? .... (3 ) 

 fe Pi + p 2 w 



corresponds to a prismatic distribution which, in the case of 

 equal volumes of the constituents being present., is represented 

 in section thus: — 



Fiff. 3. 



As it is not easy to say that one of these three distributions 

 is more likely than another to represent the actual facts, I 

 propose to apply each of the three formulae to the calculation of 

 the conductivities of the mixtures of solids and liquids experi- 

 mented on by Gr. Wiedemann f, Henneberg t, and myself §, 

 and compare the results of the calculations with the values 

 found experimentally. 



It will be noticed that the conductivities determined for 

 successive equal increments of one constituent, correspond 

 for the first formula to the successive terms of an arithmetic, 

 for the second to the terms of a harmonic, and for the 

 third to those of a geometric series, the first and the last 

 terms of the three series being the same. The third formula 

 will therefore give a value for the conductivity of a given 

 mixture between the values given by the first and second 

 formulae. In the tables which follow the values calculated by 

 the three formulae (1), (2), and (3) are referred to as "mean 

 conductivity," "mean resistivity,'"' and "mean logarithmic" 

 respectively. 



* Lees, Phil. Mag. ante, p. 226 (1900). 

 t G. Wiedemann, Vogg.'Ann. cviii. p. 393 (1859). 

 X Henneberg, Wied. Ann. xxxvi. p. 146 (1889). 

 § Lees, Phil. Trans. Royal Soc. cxci. p. 399 (1898). 



