AND LIQUIDS AND THEIR VARIATION WITH TEMPERATURE. 437 



n\ (1000 -n)! 101990! 10 



= p\ (n - p)\ (\fT- p)\ (990 -n+p)\ 1000! ' (10 - p) p n + pp ' 



Hence the conductivity of the mixture on the assumption that cross-transmission 

 from column to column may be neglected, 



i'= 10 



M!(1000 -n)\ 10! 990! 



! (990- n + p)\ 1000! (10 - p) p u 



The values of the factorial expressions have been calculated for n = 200, 400, GOO, 

 and 800 with the aid of DE MORGAN'S tables of n !* and are as follows : 



The results of calculations of the conductivities of mixtures for which pn = 1, and 

 p = gij- and yg- respectively, are given in the following curves, along with the 

 observed curves for mixtures of water and alcohol, and of vaseline and marble, 

 and the curves for conductivity and resistivity following the linear law, for com- 

 parison. The calculation gives conductivities always below the observed values, 

 a result which is due in part, and it may be entirety, to the neglect of the trans- 

 verse transmission of heat from column to column of the model. The agreement 

 is, however, sufficiently near to justify the statements that the thermal conductivity 

 of a substance is not greatly modified when it enters as one constituent in a physical 

 mixture, and that the thermal conductivity of a mixture depends directly on the 

 amounts and conductivities of its constituents. 



* ' Encyclopedia Metropolitana,' vol. 2, p. 486. 



