6$± Dr. R. D. Kleeman on the .Equation of Continuity 

 expressing the conditions for equal roots we have 



87066 / Pc \ 7 % ,— N9 , „ RT P C 

 ^=-T-(W (V "^ and ^^* 



These two equations, we see, are o£ the required form but 

 the numerical constants have not the proper value. We will 

 therefore, as before, assume b = (n — n 2 p). From the equa- 

 tions of condition for equal roots we then have that if we 

 put 



n x = — , and n 2 = -s, 

 Pc Pc 



wo obtain two equations of the above form connecting the 

 critical constants; and if we further putz/ 1 = , 06 and v 2 = '60'2 

 the numerical constants in the equations will have the 

 proper value. The above equation of state and the one 

 given previously will be further discussed later in this 

 paper and in subsequent papers. It may be noticed here 

 that 



1 ('002- p - -06 V 

 P,\ Pc I 



the expression obtained for 6, is of the same form as the 

 value obtained previously, viz. : 



V-734- ^ -176). 

 PS Pc ' 



The reason that the part bed of the curve in the figure is 

 not realized in practice does not seem to have yet been 

 made quite clear. It is intimately connected with the 

 property of a liquid and vapour to be able to exist in equi- 

 librium side by side ; in fact, it appears that in all cases 

 where two portions of matter of different densities can be in 

 equilibrium in contact with one another, the states corre- 

 sponding to the intermediate densities cannot be realized 

 in practice. According to the equation of condition of a 

 molecule in the liquid or gaseous state, it follows that if 

 each molecule is in the same condition, two portions of matter 

 of different densities cannot exist in equilibrium in contact 

 with one another. The matter of less density would con- 

 dense upon that of the greater density. Therefore, since a 

 vapour can exist in contact with the liquid, the molecules 

 must differ from one another in some way. The explana- 

 tion is that the molecules differ from one another in their 



