as a Standard of Electromotive Force. 211 



Cd, takes place by steps o£ d9, and that no diffusion takes 

 place from the solid formed in one step to that formed in the 

 next. Also that the solid formed in any step is of uniform 

 composition and in complete equilibrium with the liquid 

 which remains. Under such conditions, it can be estimated 

 that (in some of the amalgams) about one third of the material 

 might still be fluid at 6 2 although, according to fig. 1, the 

 whole should be solid *. 



§ 5. The effect of sudden cooling. — From the above sketch 

 of the process of crystallization we see that the surface of 

 a u slowly " cooled amalgam will generally contain a lower 

 percentage of cadmium than the material as a whole, and 

 may even be fluid, although the temperature and percentage 

 composition of the material are such that it should (in true 

 equilibrium) be a uniform solid. 



We see also that the relation between the curves ABCD 

 and ABEF of fig. 2 is immediately explicable if, for any 

 reason, the amalgams of the branch CD are of more uniform 

 composition than those of EF. 



The former amalgams were cooled suddenly from the fluid 

 state to a temperature much below that at which they would 

 have become completely solid if the rate of cooling had been 

 infinitely slow. Each alloy would therefore pass rapidly 

 through the range of temperature in which equilibrium 

 between two phases is possible, and although, in each element 

 of the material, there might be incipient crystallization with 

 accompanying redistribution of the Cd, as the temperature 

 fell, this process being slow could not proceed very far. 



The greater part of the solidification would thus take 



* Thus at the end of the first step the temperature is 9 l -b9, the 

 liquid phase contains (a— la) per cent. Cd and the solid phase (b—lb) 

 per cent. And, of m grams of a per cent, alloy, the quantity 



(b-a)-d(b-a) 



will have frozen. It happens that for a considerable range of tempera- 

 tures and concentrations in the present case, the liquidus and solidus 

 curves of fig. 1 are sufficiently nearly parallel straight lines to permit 

 the assumption, l(b— a) =0, between Q x and & 2 . From this also, if we 

 assume that there are n equal steps of 86 in the cooling process, we get 

 n^a=b — a, and hence Im^—m/n. The quantity of liquid remaining at 



the end of the first step is thus ml\ — -). Continuing the process it 



will be found that the quantity of liquid remaining at the end of the nth. 



step is mil — -j which, if we assume nto be very large, has the value 



m/2'72 verv nearly. 



P2 



