Density of Water with the Temperature, 117 



determinations this question will remain doubtful for the 

 future within the limits I indicate ( + 7 for 18210). Matthies- 

 sen (1865) having determined the coefficient of expansion of 

 glass and water, employed them for fresh determinations of 

 the expansion of mercury, but his results are not sufficiently 

 accurate to elucidate the matter *. Besides this, as the mean 

 coefficient of expansion of mercury from 0° to 100° does not 

 give the variation of the coefficient of expansion of glass, 

 which variation must be recognized, therefore we must allow 

 an error, affecting the fifth decimal place, in the data for the 

 volumes of water, which error proceeds entirely from the fact 

 of taking the mean coefficient of mercury as a basis. 



The Determination of Temperatures. — The majority of the 

 determinations of the variation of the density of water with a 

 rise of temperature have been made with the aid of ordinary 

 mercury thermometers, correcting their readings relative to 

 the position of zero and to calibration, although to the exclusion 

 of all that sum of corrections, which the researches of Pernet, 

 Guillaume, and other observers in the Metrical Committee f 

 have recently elucidated. Jolly (1864), however, in his 

 determinations, referred the temperatures to the air thermo- 

 meter directly. In searching, however, for the true law of 

 the expansion of water, it is necessary to express the 

 temperatures by the absolute scale or by the hydrogen 

 thermometer, because in the law of the expansion of liquids 

 we must expect a direct connexion with the law of the 

 expansion of gases, since there is great similarity, although 

 no identity, between the liquid and gaseous states of matter. 

 In order to show how great is the influence of the circum- 

 stance alluded to above, we give the values, from Chappuis' 

 experiments, of the correction At which must be added to the 

 readings of a mercury thermometer of hard glass (whose 

 analysis is 71*5°/ SiO 2 , 14'5%CaO, llo/ Na 2 0, 1'3%A1 3 3 ) to 

 convert them to the scale of the hydrogen thermometer : — 



ds[dt=+ 0-000264 ; AS= -0-000019 



+0-000065 



-0-000148 -0-000013 



-0-0003SO -0000041 



-0-000512 -0-0000 4 6 



-0-000621 -0-000031 



-0-000718 



Along with the corrections At are given the values o( the 

 differential coefficient ds/dt or the variations in the density of 



* Mattliiessen, Pogg. Ann. 1805, exxviii. p. 512. f See note p. 114, 



10°. 



M= 4-0-073; 



0°. 







20°. 



-0-085 



40°. 



-0-107 



60°. 



-0090 



80°. 



-0050 



.00°. 







