256 Mr. J. F. Buchanan [May 8, 



critical temperature r, at which the apparent coefficient of cubic 

 expansion of the ice is equal to 0. 



A block of 100 c.c. of ice, which contains 1*5105 gram of NaCl 

 diffused through it, furnishes on being melted 91*67 c.c. of water, 

 which contain 0*9167 gram of chlorine, dissolved in it as chloride 

 of sodium. This water contains chlorine in the proportion 1 gram 

 to 100 grams of water, and represents a concentration about one-half 

 that of average sea-water. When the volume of ice, Vq, is 1 cubic 

 metre, the water produced by its melting contains chlorine in the 

 proportion of one part to one million parts of water by weight. 



Waters which contain dissolved matter equivalent to no more 

 than 1 gram of chlorine in 10,000 grams of water are in the category 

 of ordinary fresh waters, and we see that the critical temperature 

 of ice which furnishes such water lies as low as -2°*o. When the 

 dissolved matter is equivalent only to 1 gram of chlorine in 100,000 

 grams of water, the critical temperature is -0°*725. The other 

 waters are in the category of distilled waters, and it is doubtful if, 

 by any chemical means whatever, we could determine as little 

 dissolved matter as 1 gram chlorine in one ton of water ; yet the 

 critical temperature of such ice lies nearly a quarter of a degree below 

 the melting temperature of pure ice. The critical temperature of 

 expansion of ice affords a means of detecting impurity equivalent 

 to quantities of chlorine as small as one gram in ten tons, and even 

 one gram in one hundred tons of water. 



In his work on The Properties of AYater and Ice, Pettersson gives 

 in Plate XXI. the curves of the change of volume with tempera- 

 ture, of three samples of ice frozen from samples of melted sea ice. 

 They are numbered in descending order of concentration, YI., Y. 

 and IV. For the details, which are interesting, the reader must 

 consult the original work. The nature of these samples is roughly 

 indicated by their specific gravity at 0° C, referred to that of dis- 

 tilled water at 4° C, and by the percentage of chlorine in them. 



I calculated by the method which I have above developed, the 

 volume of ice at 0°, containing 1*5105 gram chloride of sodium, 

 which would show the same volumetric behaviour as these samples. 

 The results are given in Table lY. 



Pettersson's volumes (P) for certain whole degrees of temperature 

 {t) are taken. The water which agreed with the volumetric behaviour 

 of each of Pettersson's samples was found empirically, and the volume 

 of the ice at each temperature, t, for each sample calculated as , in 



