112 Prof. D. Mendeleeff on the Variation in the 



the increment of the volume of the vessel, i. e. Jet, is added 

 to the apparent volume W*, whereas V* should be found 

 from the product W^x vf, where v t =l + kt. An example will 

 show how great an error is thus introduced. Supposing 

 V =l, and let us assume the apparent volume of the water 

 at 100° equal to 1*040502, and let the coefficient of expansion 

 of glass =0"00002705. According to the generally adopted 

 method, we should conclude from this that the true volume of 

 water at 100° = l-040502 + 0'002705 = l-043207; whereas in 

 reality it is equal to 1*040502 x 1*002705 = 1*043316: thus the 

 error committed = 0*000109, exceeding that of observations 

 made in the simplest manner. Even with a difference of 

 temperature from 0° not greater than 20°, the error of the 

 above modus operandi is already clearly sensible in the sixth 

 place. This error decreases, but does not disappear, when a 

 similar method is employed in determining the coefficient of 

 expansion of the vessel, viz. the subtraction of the apparent 

 expansion of mercury from the true expansion. 



2. The coefficient of expansion of glass and metals adopted 

 when determining the density of water is usually taken for a 

 range of temperature from 0° to 100°, and the mean value of 

 the coefficient of expansion k of the envelope being found, 

 it is taken as constant throughout the whole of this range. It 

 is, however, beyond doubt, in spite of statements to the con- 

 trary *, that the coefficient of expansion of glass increases 

 considerably (relatively more than mercury) with the tem- 

 perature. Hence the readings of the mercury thermometer, 

 on being reduced to the normal hydrogen thermometer, 

 require a negative correction and not a positive one, as 

 would be necessary if the variations depended upon the 

 unequal expansion of mercury alone f. From Regnault's 



* Hagen (Abhandl. d. K. Akademie zu Berlin, 1855, Math, i.), in a 

 special examination of this question and taking as basis his determi- 

 nations of the linear expansion of glass, states that, between 0° and 100°, 

 the coefficient of cubical expansion of glass is without variation. Yolk- 

 maun (Wiedemann's Ann. 1881, xiv. p. 270), in revising the determi- 

 nations of Rosetti, who found k to increase with t, concludes by- 

 denying this variability, *'. e. he considers k constant from 0° to 100°, as 

 generally admitted by experimenters. I may here remark that in the 

 investigation of other liquids, which have a large coefficient of expansion 

 and offer but slight variations in it, this supposition does not play an 

 essential part. But in water at low temperatures, the coefficient of 

 expansion is small — for instance, between 5° and 10° it is equal to 

 OOOOO0O8, i. e. only twice that of glass ; so that in this case the de- 

 termination of small variations in the coefficient of expansion of glass is 

 of great importance for the accuracy of the final result. 



t Let t be the true temperature (according to the hydrogen thermo- 

 meter), and let us suppose, without greatly departing from the truth in 

 the abstract, that the expansion of mercury from 0° to 100° is 

 expressed by V* = 1 + 0-000180 1 -f 0-00000002 P, 



