686 Dr. R. D. Kleeman on the Equation of Continuity 



along the straight line. This well known condition is 

 expressed by the equation 



I 



p . dv=p(v l — i\>). 



Substituting for p on the left-hand side of the equation 

 from equation (10) and integrating, we obtain an equation 

 which may be written 



where h is a positive quantity much smaller in magnitude 

 than the term which precedes it, and 



87066 



= \2/3 7/3(2\/»<i) 2 . 



p: 



Now P(p2_pp j g t j le i n temal heat of evaporation per gram 

 of substance and p(u 2 — «i) the external work done during 

 evaporation, and the latter quantity is therefore much 

 smaller than the former. The quantity (p(v 2 — Vl ) —h) is 

 therefore probably very small in comparison with the first 

 term in the equation, and the first two terms therefore of 

 the same magnitude. We may therefore suppose 



?P 



in the equation, where ,v is a very small fraction which is 

 taken as constant, and we therefore have 



E(pl-pl) =Tlog£\ (11) 



where E is a constant. This equation was tested in the 

 case of a number of substances over considerable ranges of 

 temperature. The result is given in the sixth and thirteenth 

 columns of Table II., which contain the values of E calcu- 

 lated by means of this equation. It will be seen that E is 

 remarkably constant for each substance. This equation thus 

 gives very accurately the relation between p l5 p 2 , and T, 

 for different temperatures of a liquid. 



p m 

 The value of E is proportional to -p-, and therefore pro- 



(2 An ) 2 

 portional to v y »' . The fifth column of Table III. 

 m • p c 



