436 



DR. C. H. LEES ON THE THERMAL CONDUCTIVITIES OF SOLIDS 



006 

 007 

 006 



005 



k. 



004 

 003 

 002 

 001 



O 10 O 4O SO 60 7O 80 90 100 



PercenCage by volume. 



These results, taken in conjunction with those found for liquids and solutions, 

 show conclusively that the thermal conductivity of a mixture is not a linear function 

 of its composition. The observed conductivity is always less than that calculated 

 from the linear law, and, on the other hand, greater than that calculated on the 

 assumption that the resistivity is a linear function of the composition. The 

 second assumption is, however, a closer approximation to the observed facts than 

 the former. 



Since neither of these simple assumptions seems capable of representing the facts, 

 which, by their uniformity, appear, notwithstanding, to point to some general law of 

 mixtures, it seemed advisable to calculate the conductivity of a model of a mixture 

 built up in some simple way so as to lend itself readily to the process. 



Suppose a cubic centimetre of some substance, having a conductivity p , to be 

 divided by equidistant planes parallel to its faces, into 1000 small cubes of 1 millim. 

 edge ; and let n small cubes of the same size but of a material of conductivity p be 

 substituted for n of the cubes of the cubic centimetre chosen at random. The large 

 cube is then a mixture of two materials, and its conductivity may be readily 

 calculated if the lines of flow are assumed to be parallel to one edge of the cube. 



If p is the thermal resistivity of the original, p that of substituted small cubes, 

 the probability that, when n are substituted, p of them will be found in any column 

 chosen at random, 



-! (1000-?i)! / 1000! 



~ pi (np)\ (10 p)l (1000 - n - lQ~-Jj)l / 10! 990! 



!(1000-n)! 10! 990! 



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



and the heat conducted through such a column, when its ends differ in temperature 1 C., 



