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LXVIII. On the Theory of Freezing Mixtures. By Alfred 

 W. Porter, D.Sc , F.R.S., F. Inst. P., and Reginald E. 

 Gibbs, B.Sc, AJnsLP* 



IN 1874, Professor Guthrie carried out extensive experi- 

 ments on freezing mixtures, and was the first to point 

 out the fallacy of a belief which has persisted till even the 

 present day. Guthrie said : — " In regard to freezing 

 mixtures, I confess to have been here very much misled by 

 the confident but rather erroneous statements of others, to 

 which I attached faith trebly blind, — blind, because no re- 

 corded experiments really support them, blinder still because 

 a little thought in the right direction must have shown their 

 fallacy, and blindest of all because the one experiment of my 

 own in this direction shows that the minimum temperature 

 of an ice-salt cryogen is readied, whether we take the ratios 

 three of salt to one of ice, or one of salt to two of ice, and so 

 points to the wideness of the margin of ratios which may 

 obtain between the weights of ice and the salt" f. 



He showed that the same temperature, viz. the cryohydric, 

 was reached for a wide range of proportions of the constitu- 

 ents, and that the initial temperature of the salt need not be 

 zero ; in fact, in his extreme case the salt was initially at a 

 red heat. 



The present object is to consider an equation representing 

 the heat changes which occur in a freezing mixture, and to 

 illustrate how well it bears out the truth of Guthrie's 

 remarks. 



For the sake of simplicity it is best to concentrate one's 

 attention on a definite mixture, say that of salt and ice, and 

 to suppose that initially the constituents are all at 0° C. and 

 present in the following amounts : ice I gm., water->zero, 

 salt S gm. The vanishingly small quantity of water is 

 introduced only to ensure that there will not be any discon- 

 tinuity under the conditions which accompany the reaction. 

 All possible cases can now be divided into three sections : — 



(1) That in which the masses of ice and salt are such 



that there are both free salt and free ice present 

 at the end of the change of temperature. 



(2) That in which there is no salt remaining. 



(3) That in which there is no ice remaining. 



* Communicated by the Authors. 



t Proc. Phys. Soc. of London, vol. i. Jan. 18, 1875. 



