114 Prof. D. Mendeleeff on the Variation in the 



v t = l + (25'3 + 0'0062t)10- 6 t. 



Now the true expansion of mercury through the same range 

 of t is expressed by the formula 



V t = 1 + (179-97 + 0-0208 1) 10~ 6 *. 



Thus the coefficient of cubical expansion of glass is seven 

 times less than that of mercury, while its thermal increment is 

 only three times less. The conclusion arrived at by Benoit * 

 is still more convincing. He found that between 0° and 40° 

 the variation in volume of ordinary glass is expressed by 



v t = 1 + (21-552 + 0-0241 ^lO" 6 1\ 



while, according to Broch, the expansion of mercury through 

 this range of temperature is 



Y t = 1 + (181-652 + 0-004845 f) 10" 6 t. 



Here the increment of the coefficient of expansion of glass is 

 absolutely greater than that of mercury, although at 0° the 

 coefficient itself is more than 1\ times less. From this 

 it is evident that by taking the coefficient of expansion 

 of glass as constant, an error is introduced which affects 

 the result very palpably. Thus, for instance, if the true 

 expansion of glass between 0° and 100° be expressed by the 

 parabola 



^ = 1 + (25 + 0-02*) 10"% 



then the volume at 100° will be 1*0027 and the mean coefficient 

 of expansion will equal 0*000027; whence it may be supposed, 

 for instance, that at 20° the volume of the vessel should be 

 1*000540, whereas in reality it is 1-000508, giving a difference 



* Deductions from the observations of Benoit and Broch, taken from 

 the work by Guillaume, Traite pratique de la thermometrie de precision, 

 1889, p. 336, which forms one of the fruits of the labours of the Inter- 

 national Bureau of "Weights and Measures. As regards the above-cited 

 consequence of Regnault's determinations (Relation des exper. t. i. p. 225), 

 I calculated as follows : — From observation, it appeared that the appa- 

 rent expansion of mercury is expressed by the equation 



W*=l+(154-28+0-00987 t)10-Gt; 



and from determinations of the true expansion of mercury, I had 

 previously calculated (Journal of the Russian Physico-Chemical Soc, 

 Physical Section, 1875, p. 75) that it is expressed, for the same limits of 

 temperature, in the manner given in the text, and hence the expression 

 given above for the volumes of glass. From these data it would have 

 been possible to deduce the variation of the coefficient of expansion of 

 o-lass if experiment had not shown that the amount of this variation is 

 very dissimilar for different kinds of glass. 



