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Prof. J. Dewar. Coefficients of the Cubical [Apr. 16, 



Vincent refers to " only one " estimate for natural ice, namely, 

 0*0001125, adding that "the mean of three available results for arti- 

 ficial ice is 0*000160 finally, he gives the mean of four determina- 

 tions of his own, namely, 0*000152. Apparently then, we may take 

 0*0001551 as the mean coefficient of expansion of ice between 0° and 

 (say) - 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 9 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 we had the densities of ice at still lower temperatures, the values 

 of the coefficient of expansion thence determined would, we have every 

 reason to believe, be less than what we have found. We shall there- 

 fore not be overstraining the argument 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 specific volume 1*0675. Now 

 the lowest density of water, namely, at the boiling-point, is 0*9586 

 (corresponding to 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 atmosphere pressure. In other words, ice mole- 

 cules can never be so closely packed by. thermal contraction as the 

 water molecules are in the liquid condition, or the volume of ice at 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° ; applying the 

 ordinary thermodynamic relation, then no change of state between ice 

 and water could be brought about below this temperature. On the 

 other hand, Clausiusf 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° the latent heat of fluidity would vanish. J Baynes dis- 

 cusses the same subject,§ and arrives at the conclusion that at a tem- 

 perature of - 122°*8 C. and under a pressure of 16,632 atmospheres 



* " Change of State, Solid, Liquid," 'Phil. Mag.,' 1881. 

 t ' Mechanical Theory of Heat,' p. 172 (1879). 



% In my paper " On the Lowering of the Freezing-point of Water by Pressure," 

 1 Roy. Soc. Proc.,' 1880, it was proved that up to 700 atmospheres the rate of fall 

 was constant and equal to the theoretical value within the range of pressure if 

 the difference between the specific volumes of ice and water remain constant j 

 thence the latent heat of fusion must diminish just as Clausius had predicted. 



§ ' Lessons on Thermodynamics,' p. 169 (1878). • 



