of States of Aggregation, 205 



each of the two angular points M and N will describe a line- 

 element that belongs to an edge of the temperature- surface 

 (fig. 4). Analogous edge-formations will appear on the sur- 

 face at those points that correspond to the passage from the 

 liquid into the solid state of aggregation. Hence it follows 

 that the temperature-surface for water in its three states of 

 aggregation cannot be represented, as that of perfect gases, by 

 a single equation of simple form. Such an equation will rather 

 represent in all cases only a portion, more or less limited, of 

 the whole temperature-surface. 



§ 3. Isobars and Isoihermals of the Ice-region, 



If a vertical plane is drawn parallel to the vertical tempe- 

 rature-axis T and to the horizontal volume-axis V, and 

 therefore perpendicular to the horizontal pressure-axis P, its 

 intersection with the temperature-surface is an " isobar " or 

 line of constant pressure. Such an isobar will in general 

 contain two straight horizontal lengths or segments, of which 

 the upper corresponds to the vaporization and the lower to the 

 freezing of water. As horizontal lines on the temperature- 

 surface represent isothermals, each of these horizontal seg- 

 ments is also an isothermal segment. 



Thus, for instance, for the isobar corresponding to the con- 

 stant pressure of one atmosphere the upper horizontal segment 

 coincides with the isothermal for 100° C, and the lower with 

 the isothermal for 0° C. (fig. 5). The length of the upper 

 horizontal segment represents the expansion (about 1650-fold) 

 that attends vaporization ; the length of the lower represents 

 the expansion (about 9 per cent.) that occurs when water 

 freezes. If a vertical line is drawn through a point of the 

 lower horizontal segment, we see that under certain circum- 

 stances three different temperatures can correspond to the 

 same volume under given pressure, since the line of constant 

 pressure is cut three times by the vertical line. 



When the pressure increases, saturated steam experiences a 

 rise in temperature, but melting ice a fall in temperature. 

 Hence in the isobar for a pressure greater than one atmo- 

 sphere the upper horizontal segment will take a higher position, 

 but the under one a loiver position. If, then, the temperature- 

 surface is again represented by a mountain-face, that part of 

 the mountain which represents the passage from the liquid to 

 the solid state of aggregation will appear as a wall of rock that 

 juts out and projects like a cornice (fig. 6). 



Consider a horizontal plane drawn through the lower part of 

 this temperature-mountain ; its line of intersection with the sur- 

 face will be an isothermal of some such form as that in fig. 7; 



