of States of Aggregation. 209 



£ = 0-00744) and repeating the above calculation with these 

 values ; we then find for the angle <p the more exact equation 



tan = 4-483, or = 77° 25 / (3) 



Equation (1) can also be used for the passage from the solid 

 into the liquid state of aggregation, if for u the increment 

 (negative) of volume that occurs on melting and for r the 

 latent heat of water are substituted. The latent heat of water 

 has the value * 



' Z=80 (4) 



for the pressure of one atmosphere and the melting-point 

 (0° C.) corresponding to this pressure. In melting, the mass 

 diminishes in volume by 



u = 0-00109 -0-001 = 0-00009 cubic metre. . (5) 



Hence, on substituting —a for +u and I for r in equation (1), 

 we obtain the differential equation 



^ = __i_ (6) 



dT AttT w 



as the relation between the pressure and melting-point, I and 

 U being functions of T. To the temperature T = 273 corre- 

 spond the values given in (4) and (5); and on substituting these 

 we obtain for the value of the differential coefficient 



dp 424x80 _ 1QQ0545 ( 7 \ 



dT~~ 0-00009x273" ioe>UOiO. . . {(} 



To a pressure-increment therefore of 1380545 kilograms 

 weight per square metre (or 133*6 atmospheres) corresponds 

 a lowering of the melting-point by one degree C, if the dif- 

 ferential coefficient does not alter in value for this change of 

 temperature t» It follows that near the principal edge the 

 band of the surface which lies between the frost- and melting- 

 edges, and represents the mixture of ice and water (fig. 9 J, 

 makes a very small angle with the horizontal plane, since an 

 extremely small lowering of the isothermal for the melting- 

 point corresponds to a very considerable increment of pressure. 

 The angle marked y\r in fig. 10 differs therefore only very little 

 from a right angle. 



To a diminution of the pressure by the weight of 1 kilogram 

 per square metre would, by equation (7), correspond a rise 

 of the melting-point by tswq oTs degree. When, therefore, the 

 pressure diminishes from 10333 to 62*58 kilograms weight 



* Wiillner, Experimentalphysik, 2nd ed. iii. p. 548. 

 t Clausius, Mechanische Wdrmetheorie, 2nd ed. i. p. 173. [This result 

 was first shown by Professor J. Thomson. — Tb,.] a 



Phil. Mag. S. 5. Vol. 5. No. 30. March 1878. P 



