424 PROCEEDINGS OF THE AMERICAN ACADEMY § 18 



have been remarkably free from sources of accidental 

 error. 



MendelejefF points out that the law of expansion may be 

 represented, within the limit of error of observation, by the 

 extremely simple empirical formula, 



kt ' 



where k is a constant very nearly equal to the coefficient 

 of expansion. 



By calculating k for the next to the highest temperature 

 in the table, I find an average error of only five ten-thou- 

 sandths in the use of this formula for the 47 liquids exam- 

 ined by Thorpe. The formula claims, therefore, a careful 

 investigation. 



Differentiating and dividing by the volume, we have 



dV k J 



II. 

 III. 



dt" 



The first derivative is therefore onl}' about one-third as 

 great as the Theory would indicate, and the other deriva- 

 tives are also much smaller, so that the isobaric curves 

 will be straighter; but from Table VII. it will be suffi- 

 ciently evident that the whole difference in question is less 

 than the mean difference between two observers such as 

 Kopp and Pierre. 



From a purely empirical point of view, it is not easy to 

 decide between the relative values of the formula of Men- 

 delejeff and that of the Theor}'. 



