of the Liquid and Gaseous States of Matter. 



6' 



According to Descartes's Rule of Signs the maximum 

 number of positive roots that a- in equation (7) can have is 

 three, and the maximum number v in the original equation 

 can have is therefore also equal to three. Since the conditions 

 of equilibrium of the molecules in matter are independent of 

 its state of aggregation, there should be continuity as we 

 pass from the liquid to the gaseous state. The isothermal 

 for a given temperature would therefore in certain cases be a 

 curve of the well-known form a, b, c, d, e, shown in the figure ; 

 the points b, c, d correspond to the three values of v at a given 

 pressure. The points d and b correspond to the saturated 

 vapour and liquid respectively at the same temperature. The 

 p^rt of the curve between b and d is, however, not realizable 

 in practice. Whv this is the case will be discussed later. 



At the critical point, denoted by E in the figure, the three 

 values of v become equal to one another. The equations 

 giving the value of a when it has three equal positive roots 

 in equation (7) are, according to the Theory of Equations, 



(a) 



f = a w + aya 1 + a 2 o* + a 3 = 0, . 



^ = 10o- 9 + 7a,<7 6 + 3a 2 <r 2 =0, . 



da ' 



-da- ' z 



Phil Mag. S. (>. Vol. 20. No. 118. Oct. 1910. 



(P) 



2Y 



