202 Conduction of Electricity through Metals. 



not form definite compounds with each other but did form 

 mixed crystals, we should expect the local force L to be 

 increased by anything analogous to chemical combination. 



We see from the preceding equations that it D were large 

 for these alloys, they would have (1) a small temperature 

 coefficient at normal temperatures and a very small one 

 indeed at temperatures low enough to diminish the specific 

 heats, (2) they would not have a critical temperature and 

 would never pass into the super-conducting state. These are 

 characteristic properties of the resistance of alloys. 



Again, if there are m molecules of the metal (1), n of the 

 other (2) per unit \ volume, we should, from the expressions 

 (7) for the specific resistance of a pure metal, expect that 

 a the specific resistance of the alloy would be given by a 

 formula of the type 



mk x (itf+Dj-^o) ( mk 2 (io + D 2 -w?o')l I f m + n \ 



'""-1 V"-- ' -^1 LV 0/ '""2 



epidi iv epzth 



W 



As this involves the restoring couples D 1 and D 2 it cannot 

 be calculated from the resistances of the pure metals; we see, 

 however, that a t — <r T the, difference between the specific 

 resistances of the alloy at the temperatures t and T, is given 

 by the equation 



<?t 



(tfjMi w ep 2 d 2 w ) J 



the D's have disappeared from this equation, and it is 

 exactly the value we should have calculated on the supposi- 

 tion that the alloy is a mechanical mixture. Tins is the 

 result known as Matthiessen's rule, which states that even 

 when the specific resistance of the alloys cannot, the dif- 

 ference between the resistances at two temperatures can, be 

 calculated from its constituents; another way of stating it 

 is that the difference between the observed and calculated 

 value is independent of the temperature. We have supposed 

 that D is independent of the temperature; if it changes 

 appreciably with it, as it might be expected to do if the 

 nature of the compounds, or mixed crystals formed by the 

 two metals did so, the temperature coefficients would show 

 anomalies such as those found in alloys which have negative 

 temperature coefficients. 



I have shown (' Corpuscular Theory of Matter/ p. 86) 

 that the electric and thermal conductivities will on this 

 theory bear a nearly constant ratio to each other if the 

 electrons which take part in the conduction are in thermal 

 equilibrium with the metal in their neighbourhood. 



