( 425 ) 



tials ft of llie tin as solid siil^stance and ft^ of the tin in the liquid 

 amalgam, namely that 



(i z=z e — c 7' / 



fi, =., -0, 2' + iry/o./(i-.r) \ (^) 



In this it has been assumed, firstly tiiat the tin, crystallised from the 

 amalgam, does not consist of mixed crystals, hnt of pure tin — a suppo- 

 sition, which has heen proved by experiment to be nearly correct — 

 and secondly, that the energy -quantity *' is no function of .r. Tiater 

 on we will cb-0|) this last sinqditied supjiosilion. and demonstrate, that 

 a more accurate cah-ulation of the fuiu'tion (t^ alFects the coiii-se of 

 the meltingpoint-lines (/i/anfifftfireh/, but not </ualitativeli/. Then it is 

 our object to demonstrate at once, that tiie entire qualitative course, 

 as represented in the iigui-e, follows from the equations (1) in con- 

 nection with tlie course of the lo<jarUlirnic function of 1 — ./'. By 

 putting the two potentials equal to each other, we obtain: 



(,,^ _ ,) _ {c, - c) T := - RT lor, (l-.r), 



or calling e^ — e =z q (the heat of fusion of the solid tin, wIhmi passing 

 into the amalgam), and the quantity c^ — c = y -. 



q — yT =: — RT log (1 — .c), 

 from wliich follows : 



T — ^ (2) 



This is then the most simple form of the meltingpoint-line. 

 On introducing the temperature of fusion of pure tin 7'^,, ./■ becomes 

 Ü, and we obtain : 



7' - "^^ 



y 



so that we may also write: 



7' 7' 

 T = -^ = " (3) 



1 ?/o,,(l-.r) -^^ ^ 



9 



Rl\ 



it we abbreviate to f). 



7 



We notice at once, that on the development of the logarithuiic 



function, the formula, for very small values of ./', passes into 



7' 



r:j\ 



7 



