§ l8 OF ARTS AND SCIENCES. 425 



In the case of the 47 liquids examined by Thorpe, it must 

 be frankly admitted that although the observed values lie, 

 in every case but one, between those calculated by the 

 two formulae, the average is twice as near the indication 

 of Mendelejeff as to that of the Theory. More significance 

 would, however, be attached to this fact, were there a 

 sufficient number of observations, made independently, 

 with which the results of Thorpe might be compared. 

 The curvature of the line representing the expansion Is 

 subject to a constant error due to the standards of com- 

 parison ; and the fact that nearly every other observer has 

 found a greater curvature, not only for liquids in general, 

 but also for those few examined in common with Thorpe, 

 should not be left out of accorait. 



For the purpose of comparison. Table IX. was con- 

 structed, showing the differences between the volumes 

 according to Mendelejeff's formula and those from the 

 mean results of Kopp and Pierre, for the eleven liquids 

 already examined. 



It will be noticed that the volumes for ether do not 

 agree with those calculated by Mendelejeff, owing prob- 

 ably to the use of other data by the same observers, 

 which I have not been able to discover. The fig^ures 

 taken from Sharpies' Tables are not so favorable as those 

 quoted in the paper. The sums of the squares of the 

 differences are represented in the table below. 



If, for various reasons, butyric acid be omitted from 

 the list, the sums of the squares of the errors will be 

 2,432,832 for Kopp and Pierre, 2,289,662 for Mendelejeff, 

 and 414,460, for the Theory; or, throwing out fusel-oil, 

 which is most unfavorable to Mendelejeff, the sums will 

 become 1,551,256, 736,953, and 243,518, respectively. 



The statement of Mendelejeff, that the empirical for- 

 mula represents the expansion within the limit of error of 

 observation, is therefore completely borne out in tlw3 case 



