428 PROCEEDINGS OF THE AMERICAN ACADEMY § I9 



the same, by definition, for all liquids at corresponding- 

 temperatures, the ratio of I' to / must be determined. 

 We have, therefore, for the coefficient of expansion, 

 from (5), 



'- r -^' ' 



4 — -3 



r . . 



where we see that if — - is given, c varies inversely as the 



temperature. 



Therefore e : e' = 7"' : 2"= 7"/ : Z", , or eT", = constant. 



By combining this result with Mendelejeff's formula for 

 expansion, 



I kt 



II. 



Thorpe and Rijcker obtain the following: 



Vt «7; — 273 ' 



whence 



The mean value of a is calculated for 7 liquids, the 

 critical temperature being determined by Sajotschewsky, 

 as 1-995; from 5 other determinations, 1.976; from 10 by 

 Pawlewski, 1.991; and from 12 others, 1.93. Selecting the 

 most probable value, 1.995, ^^^^ critical temperatures of 

 the first 7 liquids are calculated by the formula, 



T — '^^t — 273 TV 



I 7~Tr \ > 



with a remarkable degree of approximation, the average 

 error being very little more than one degree, which is of 



