205 



the water, after liaving been frozen, might be again melted, and so 

 reduced to its original state, without the expenditure of work, accord- 

 ing to tlie principles of Carnot already referred to. By the con- 

 tinued repetition, with the same mass of water, of the processes thus 

 indicated, an unlimited quantity of work might be developed out of 

 nothing, which is impossible. It, therefore, appears that if the water 

 be made to perform work while freezing, either work or some equi- 

 valent agency must have been expended in freezing it. Now, the 

 only way of accounting for this expenditure is by the assumption of 

 the second proposition. 



The fact of the lowering of the freezing-point by pressure being 

 demonstrated by the method of which an outline has just been given, 

 it becomes desirable, in the next place, to find what is the Ireezing- 

 point of water for any given pressure. The most obvious way to 

 determine this would be by direct experiment with freezing water. 

 This experinunt has, however, not as yet been made ; and it would 

 be difficult to make it with the precision which would be desirable, 

 since the variation to be appreciated is extremely small ; so small, 

 indeed, as to afford sufficient reason for its existence never having 

 been observed by any experimenter. The exact amount of the va- 

 riation may, however, be deduced in a different way from experi- 

 mental data, of which we are already in possession. These data are 

 (1.), The known expansion of water in freezing ; and (2.), The quan- 

 tity of work given out by a unit of heat in descending through a de- 

 gree near the freezing-point, which has been deduced from the experi- 

 ments of Regnault on steam, and has been already laid before the 

 Royal Society, in a paper by Professor William Thomson. The de- 

 sired result is expressed in the formula, 

 « = -0072P, 

 in which P is the pressure above the first atmosphere, expressed in 

 atmospheres as units, to which the water is subjected, and t the low- 

 ering of the freezing-point, expressed in degrees centigrade, produced 

 by the addition of that pressure. This formula may be applied for 

 any pressure from nothing up to many atmospheres. 



VOL. II. 



