420 Professor Sir James Dewar [Jan. 16, 



the temperature of the laboratory, about 17° C. From the two sets 

 of observations the value of the mean coefficient of cubical expansion 

 between 17° C. and the temperature of liquid air, was calculated, and 

 whenever the expression coefficient of expansion is used, the volume 

 coefficient is meant. 



loE AT Low Temperatures. 



The actual density at the temperature of liquid air of pieces of ice 

 cut from large blocks, gave the value 0-92999. The density at 

 0° being 0*91599, this gives for the mean cubical coefficient 

 0-00008099. 



We may take 0-0001551 as the mean coefficient of expansion of 

 ice between 0^ and — 20° C. Thus the mean coefficient of expansion 

 between 0° and —188° C. is about half of that between 0° and 

 — 20° C. The mean coefficient of expansion of water in passing 

 from 4° to -10° C. is -0-000362, and from 4° to 40° C. it is 

 0-0002155. Hence the mean coefficient of expansion of ice between 

 0° and —188° C, is about one-fourth of that of water between 0° 

 and 10° C, and half of that between 4° and 100° C. 



If the densities of ice at still lower temperatures could be deter- 

 mined, the values of the coefficient of expansion thence deduced would, 

 we have every reason to believe, be less than the value given above. 

 AVe shall therefore not be overstraining the case if we use the 

 value just found to determine an upper limit to the density of ice at 

 the absolute zero. The result is 0-9368, corresponding to a si^ecific 

 volume 1-0675. Now the density of water at the boiling-point, is 

 0-9586 (corresponding to the specific volume 1-0432), so that ice can 

 never be cooled low enough to reduce its volume to that of the liquid 

 taken at any temperature under one atmosi)here pressure. In other 

 words, ice molecules can never be so closely packed by thermal con- 

 traction as the water molecules are in the ordinary liquid condition, 

 or the volume of ice at or near the absolute zero is not the minimum 

 volume of the water molecules. It has been observed by Professor 

 Poynting * that if we suppose water could be cooled without freezing, 

 then taking Brunner's coefficient for ice, and Hallstrom's formula for 

 the volume of water at temperatures below 4° C, it follows that ice 

 and water would have the same specific volume at some temperature 

 between -120° and -130° C. Applying then the ordinary thcjrmo- 

 dynamic relation, no change of state between ice and water could be 

 brought about below this temperature. Clausius has shown that the 

 latent heat of fusion of ice must be lowered with the temperature of 

 fusion some 0-603 of a unit per degree. If such a decrement is 

 assumed to be constant, then about - 130° C. the latent heat of fluidity 

 would vanish. Thus under a pressure of about 16,000 atmospheres 



♦ "Change of State, Solid, Liquid," Phil. Mag., 1881. 



