456 Drs. Ramsay and Young on 



would be proportional to c in the equation p-=ct, where c varies 

 inversely as the volume. But our equation, p — bt—a, intro- 

 duces another term, a, which is negative. These values of a 

 are represented on the diagram by the extremities of the 

 isochoric lines, where they cut the vertical line representing 

 absolute zero of temperature. The tangents of the angles 

 made by these lines with a horizontal line are proportional to 

 the values of b in our equation. 



On referring to Plate IX. it will be noticed that, beginning 

 at the largest volume, two adjacent isochors cut each other at 

 a point, as regards pressure and temperature, not far above 

 zero. With decreasing volumes the points of intersection of 

 adjacent isochors occur at higher and rapidly increasing tem- 

 peratures and slowly increasing pressures ; and this proceeds 

 until the critical volume is reached. With still smaller volumes, 

 however, the points of intersection of adjacent isochors occur 

 at lower and decreasing temperatures and pressures ; the 

 former decrease slowly, but the latter with great rapidity, and 

 soon extend into the region of negative pressures. 



It is evident from the diagram that each isochor between 

 the largest and the critical volume is the tangent of a curve, 

 representing the relations of pressure to temperature ; while 

 the isochors below the critical volume are tangents to another 

 curve, also exhibiting the like relations. Neither of these 

 curves is identical with the vapour-pressure curve, which falls 

 in the area between them. 



It will be noticed that, in the area included between the 

 line of zero pressure and these two curves, each isochoric line 

 is cut by two others at every point along its whole length ; 

 but outside this surface, and above the line of zero pressure, 

 no two lines cut each other, and below the line of zero pressure 

 each isochor is cut at each point by one other. The physical 

 meaning of the fact that within the first-mentioned region 

 three isochors intersect each other at one point is, that a gram 

 of the substance may occupy three different volumes at the 

 same temperature and pressure. Now, on referring to the 

 diagram on Plate VII., representing the experimentally un- 

 realizable portions of the isothermal curves, it is evident that 

 on each isothermal line, at pressures limited by the superior 

 or inferior apices of the isothermal, there are, corresponding 

 to each pressure, three volumes. At any pressure above or 

 below these pressures the isothermal line is cut only once, by a 

 horizontal line of equal pressure ; so that, for each pressure, 

 there is only one corresponding volume. At each apex a 

 horizontal line of equal pressure cuts the isothermal line 



