1896.] A new Method of determinhig Freezing Points. 251 



flow set up below the surface. With a solid sphere that is rough or 

 wet, the phenomena are quite different from the earliest moments of 

 contact, and very similar to those produced by a liquid sphere. 



Although a few theoretical or conjectural points are touched on, 

 the authors prefer to abstain at present from even general explana- 

 tions, and to put forward the photographs simply as a record of facts 

 of fluid motion, hoping tltat the puzzling nature of some of the 

 phenomena may evoke attention and interest among those most 

 competent to explain them. 



II. "A New Method of Determining Freezing Points." By 

 Meyer Wildermann, Ph.D. Communicated by Lord 

 Kelvin, F.R.S. Received January 13, 1896. 



(Abstract.) 



The subject of" this paper is the best means of determining 

 freezing points in dilute as well as in concentrated solutions. Two 

 things have to be considered : the proper arrangement of equi- 

 librium in the heterogeneous system, and the proper treatment of 

 the instrument used for measuring temperature. 



A. Arrangement of Equilibrium. — I begin with the statement that 

 the equilibrium between the solid and liquid solvents in the hetero- 

 geneous system (ice and water) is a "perfect" one, and this is 

 characterised by the fact that, at the slightest change of the temper- 

 ature of equilibrium, one of the two 'parts of the* heterogeneous 

 system disappears, above freezing temperature, the solid, below it, 

 the liquid. In carrying out an experiment the heterogeneous system 

 is simultaneously cooled down or warmed by the arrangements of 

 the experiment (air bath, &c), and the velocity with, which the 

 given liquid is cooled down must also come into consideration. This, 

 isolated process must be expressed by Newton's equation, dtjdz — 

 c(t g — t), in which c is inversely proportional to the quantity of liquid 

 and to the heat capacity, and directly proportional to the surface of 

 the whole volume of the liquid, and t g is the convergence tem- 

 perature of the liquid if no ice be present, and can be above or below 

 the freezing temperature. If the convergence temperature be above 

 the freezing temperature, the liquid it>, at the freezing temperature, 

 continuously warmed by the experimental arrangements to a higher 

 than the freezing temperature t , and the process of ice melting takes 

 place. If the convergence temperature be below the freezing temper- 

 ature, the liquid is, at the freezing temperature, continuously cooled 

 to a lower temperature, and the process of ice separation takes place. 

 The velocity of ice melting has been found to be expressed by the 



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