272 PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



As in tlie formation of steam, if it takes place under the conditions set forth 

 in § 7 the temperature at which the transformation into vapor occurs is a function 

 of the pressiu-e exerted on the piston, so that we might expect that the tempera- 

 ture of the melting ice depends also on the pressure under which it stands ; that 

 the temperature of fusion also varies with the pressure. 



From the analogy between vaporization and fusion, we are authorized to apply to 

 the phenomenon of melting the equations developed in section vii, and therefore 



the second leading equation of the mechanical theory of heat u = . But 



* ^ ^ A.T.«A 



while, in the formation of steam, the magnitude ^ was given through the experi- 

 ment, it is here wholly unknown ; on the other hand, we know the quantities 

 r, A, T, and «, and hence have 



(Ill) 



A-T ' u 



As we have above seen, r =79.035. The absolute temperature at which, under 

 the pressure of the atmosphere, the melting of ice takes place, is T=273°. "We 



know, moreover, that A=-— — . For the computation of ^ there is wanting, 



therefore, only the value oi u. In the melting of ice, we know a diminution of 

 volume takes place. The volume of one kilogram of water at 0° is y^O.OOl 

 cubic metre. The volume of one kilogram of ice at 0°, taking the mean of 

 different computations, is it'=:0. 00109 j hence 



u=v— IV = — 0.00009, 



and therefore negative. If we place now for r, A, T, and u, in equation, (111,) 

 the numerical values cited, the result is 



.__ 79.035 • 424 

 ~ 273 • 0.00009* 



Should the difference of pressure ^, which corresponds to a lowering of tempera- 

 ture of 1°, be expressed, not in kilograms, but in atmospheres, we shall have to 

 divide by 10333, and we then obtain 



^=— '- -=132 atmospheres: 



10333 • 0.00009 -273 ^ 



that is to say, an augmentation of pressure from 1 to 132 atmospheres would cor- 

 respond to a lowering of the melting point by 1° 0. ; an augmentation of the 

 pressure by one atmosphere will therefore be followed by a lowering of the 

 melting temperature of ice equal to jig-, or 0.0075° C. 



That the temperature at which ice melts varies with the pressm'e, and that 

 thus an elevation of the pressure corresponds to a hivering of the freezing point, 

 was first theoreticall}^ demonstrated by James Thomson, (Proceedings of the 

 Royal Society of Edinburgh,) and then by Clausius, (Pogg. Aunal., Lxxxi,) and 

 was experimentally verified by William Thomson, (Pogg. xVnnal., LXXXi.) The 

 latter availed himself, for this experiment, of a thermometer in which ether was 

 employed instead of quicksilver as the thermometric fluid. The reser\-oir of 

 this thermometer was three and a half inches long and three-eighths inch wide. 

 On the tube, six and a half inches long, was a scale of five and a half inches 

 length, divided into 220 equal parts. The extent of this scale corresponded to 

 a difference of temperature of about 3° F., so that a division represented on an 

 average Jj of a degree of P. The thermometer was so regulated that it showed 

 the temperature between 31° and 34° F. In order that the reservoir might not 

 be compressed when submitted to a strong pressure, it was hermetically inclosed 



