292 On the Thermal Conductivities of Mixtures. 



also in a plane perpedicular to that of the drawing, i. e. con- 

 sisting of cubes of the two media, will be greater than that of 

 the prisms of fig. 3, and will therefore deviate more from the 

 value of the conductivity found experimentally than does that 

 given by the logarithmic formula. Hence it seems unne- 

 cessary to attempt an accurate calculation of the conductivity 

 of the mixture of cubes. Also, since the deviations from the 

 calculated values found in the cases considered in the above 

 tables, appear to differ in character from one mixture to 

 another, they indicate that the thermal conductivity of a 

 mixture is not completely determined by the conductivities 

 of its constituents, and by the volume of each constituent 

 present. 



The attempts which have hitherto been made to represent 

 the thermal conductivity of glass as a function of its compo- 

 sition and of the unknown conductivities of its constituents, 

 must therefore be considered as not justified by our know- 

 ledge of the behaviour of mixtures of substances the con- 

 ductivities of which are known. 



The formula expressing the conductivity of a mixture in 

 terms of its composition and the conductivities of its con- 

 stituents, must then contain at least one quantity dependent 

 on the characters of the two constituents, and the calculated 

 values of the conductivity may be made to coincide with the 

 observed values at three points. There are many empirical 

 formulas which under these conditions give values that agree 

 fairly well with the intermediate observations ; and although 

 I have found the formula 



t^ M'+ftt,- (4) 



Pl+P-2 



where n is an arbitrary constant, on the whole satisfactory, 

 the material at our disposal for testing the relative values of 

 the various empirical formulae which might be suggested, is 

 not yet sufficient to warrant the selection of any one of them 

 as the best representation of the thermal conductivity of a 

 mixture. 



The result of this examination may then be summed up as 

 follows : — 



Of the three values for the conductivity of a mixture 

 calculated from the mean conductivity, mean resistivity, or 

 mean logarithmic formula, that from the mean conductivity 

 is most unsatisfactory, and that from the mean logarithmic 

 formula least unsatisfactory. The logarithmic formula gives 



