(2) 



330 Dr. R. D. Kleeman on Relations between the 



^i(T) at different temperatures for a number o£ liquids, the 

 latter of the above equations being used for calculating ^(T). 

 The slight deviations of ^i(T) from constancy are regular, 

 there being a slight decrease in its value with the 

 temperature. 



The value of ^i(T) in terms of the critical constants, 

 obtained by substituting for the quantities T, p x , and p 2 in 

 either of the equations their critical values, is 



^(3-log/*). 



The above equations may thus be written: 



PP-§log^=f (3-log Pc ),| 



1/3t> 1/3 r 



^-^^=^(3 -log*).) 



Table II. contains the mean value of ^(T) for each liquid 

 contained in Table III., and the corresponding values of 



^(3-log^), 



The agreement between the two sets of values is fairly good. 



Since the equations (2) are the same in form, for "a given 



temperature each must have at least two real positive roots 



one being equal to the value of Pl and the other to the value 



of j0 2 - J 



An expression for -^ is obtained by differentiating the 

 first, of equations (2), which gives 



dn-T c pY 6 -T P y3' 



It will be seen that at the critical temperature ~ =cc a 

 result that has already been established by thermodynamics. 

 At the absolute zero -Jf™ finite. For intermediate tempe- 

 ratures the equation gives values of -^ which agree roughly 



with the facis, That a good agreement is not obtained is 

 due to ^ (T) being only approximately a constant. A better 

 agreement would be obtained by writing ^(T) =a — Tb when 

 we obtain 



fyi _PiP 1 c !8 l°gPi'-ZTcpJ> 



3T""" %p\ /s -pl /3 T ' 



