Density of Water with the Temperature* 115 



(0*000032) in the volumes which exceeds the possible errors 

 of reading (gravimetric or volumetric) . Still up to now our 

 information respecting the variation in the coefficient of ex- 

 pansion of vessels with rise of temperature is not sufficiently 

 clear to allow of its employment as the means of introducing 

 into the existing data respecting the expansion of water cor- 

 rections which would really improve our results. At present 

 we can only say that, in determining the volume of a vessel 

 according to the formula vt=v (l + kt), and finding k for 

 a change of t from 0° to 100°, the greatest errors are intro- 

 duced between 25° and 75° and that they attain some hundred- 

 thousandths of the volume or of the density. 



3. Many observers (Hallstrom, (Stampfer, Hagen, Mat- 

 thiessen) determined the expansion of the solids adopted in 

 the hydrostatic determination of the variation of the density 

 of water, by measuring the linear expansion of the substance 

 from which the body weighed in water was prepared. This 

 method, which does not require a knowledge of the expansion of 

 mercury, involves, firstly, three times the error accompanying 

 the determination of the linear expansion, which error, not- 

 withstanding all the improved methods of determination, is 

 still sufficiently great and will scarcely give a result with an 

 approximation of more than hundredths ; secondly, it is pre- 

 sumed, a priori, that the expansion in a transverse direction 

 is the same as longitudinally, even for drawn-glass tubes, 

 which fact needs demonstration, and in my opinion is very 

 unlikely ; and, thirdly, the above-mentioned method is most 

 often applied to glass tubes from which the body used in 

 hydrostatic weighing is made by blowing or melting ; and it 

 is likely that such deformation involves some change in the 

 coefficient of expansion. In addition to this Hallstrom (1825) 

 found that the cubical expansion of glass is greatly affected 

 by a rise of temperature : 



v t =l+ (5-88 + 0-3150 10- 6 *; 



whereas Hagen (in 1855) found hardly any variation in the 

 coefficient of expansion in the glass he used (through a range 

 of 1*6°-81°), and gave the value : 



^ = 1 + 27-69 tl0- Q . 

 According to the first formula, the volume at 70°= 1*001955, 

 and from the second we obtain 1*001938 — results nearly the 

 same ; but at other temperatures these values vary consider- 

 ably, for instance at 30° the first formula gives V= 1*0001(30, 

 against 1*000831 according to the second. 



Neither of these contradictory results can be considered as 

 correct or depending only on the properties of glass, and 



I 2 



