Magnetic Properties of Pure Iron. 363 



opposed to any theory involving any large solubility of that 

 element. 



The mathematical expression here given for the relationship 

 between the electrical resistance of a metal and the size or! 

 the component crystals is very similar to that given by 

 Yon Weimarn *. Regarding the question as being ana- 

 logous with the electrical resistances of colloidal solutions, it 

 was argued that the observed resistance of a metal is the 

 sum of two values, the first of which is proportional to the 

 volume of the sample, the second being dependent on the 

 surface energy of the intercrystalline amorphous films. 

 This latter value is obviously a function of the number of 

 crystals per unit volume, while the first is a constant for each 

 metal. The relationship, therefore, is almost identical with 

 the author's, though it has been arrived at from a totally 

 different point of view. Its validity is dependent on certain 

 assumptions from which equation (1) is free, and no attempt 

 was made to supply experimental evidence in support of the 

 expression. 



The speculation of Lord Rayleigh j concerning the in- 

 fluence of the Peltier effect on the electrical resistance of 

 binary alloys offers a still more interesting subject for 

 comparison. This was shown to result — in the case of 

 immiscible components — in a back electromotive force (which 

 simulates an added resistance) arising from the couples 

 set up at the surfaces of contact of the two constituents. 

 In a pure metal a similar result should flow from the 

 presence of the amorphous films between the crystals. In 

 the case of an alloy of fixed composition the increased 

 resistance was shown to be independent of the number of 

 the couples, i. e. of the number of crystals of each present. 

 In the case under consideration, however, the conditions are 

 somewhat different, since, as is probably the case, the films 

 are of the same thickness with both big and little crystals. 

 The quantity of the cement present in the latter case is thus 

 increased, and considering the mass to be composed of disks 

 of crystalline and amorphous material alternately, the amount 

 of metal present in the latter state is n times the thickness 

 of each film where n is the number of films, i. e. crystals 

 per unit of length. 



If e is the thermo-electric power of the couple formed by 

 the components of the alloy, h and h' the thermal conductivity 



* Von Weimarn. 'International Journal of Metallurgy/ iii. p. 65. 

 f Rayleigh, ' Nature/ liv. p. 154 (1896). 



