128 Prof. D. Mendeleeff on the Variation in the 



in a much less degree, as is seen from the comparison of the 

 volumes thus obtained (last line of Table II.) . 



In Table III. are cited the results given by formula No. 1, 

 which is here given in the form in which I employed it for 

 calculation : 



(t-±y 



^~ l 10000(0, 



10000(0 = 1-90(94-10 + 1) (703-51-0, 



where 



and 



# = 128-78 + 1-158 £-0-0019 t 2 . 



These figures refer to the density of water S^ which is 



inversely proportional to the volumes, ?'. e. $ f V t = 1. The 



density at 4° is taken equal to unity. 



In calculating this formula, averages were taken of the 



determinations of many investigators (Despretz, Kopp, Jolly, 



Rosetti, Hagen, and Matthiessen), and those of some of them 



(of the first four observers) were corrected for the expansion 



of mercury, adopting the value 0*01821 as its variation in 



volume between 0° and 100°; but no correction was made for 



the variation of the coefficient of expansion (mercury and 



solids) with a variation of temperature, nor for the readings 



of the mercury thermometer as referred to the hydrogen-scale 



(since such corrections cannot be considered as uniform or 



sufficiently investigated at present). The figures, therefore, 



obtained by the formula may contain the same errors as 



commonly occur in the existing determinations, and for this 



reason I have indicated the possible errors in the density in 



this table. For temperatures below 100°, they are found 



from the errors in the volumes given in Table II., on the 



dV 

 ground that c/S = ^ ; for higher temperatures than 100° 



they are derived from the considerations set forth in examin- 

 ing the influence of pressure (see ante). But although the 

 figures given by the formula may contain errors to the amount 

 indicated, still it is unlikely that they attain, for ordinary 

 temperatures (0° to 40°), ^ or \ of the value given, since the 

 difference between the results given by experiments and the 

 formula is much less, between 0° and 40°, than the amount 

 of the possible errors. Thus, for instance, for 15° we obtain 

 a density 0*999152 or a volume 100849, which differs from 

 the mean results of Yolkmann, Rosetti (Table II.) , Jolly, and 

 Hagen by less than J- of the error, which is admissible in the 

 existing data on the grounds stated above. Such being the 

 case we may take the results given by the formula between 



