Compressibility of Water at different Temperatures. 549 



pressibilities of distilled water at different temperatures {Comptes 

 Rendus, xix.) by an empirical formula^ I was much struck on 

 unexpectedly finding that they followed sensibly this law : — 



The compressibility of water is inversely proportional to the 

 density multiplied by the temperature, as measured from the abso- 

 lute zero of a perfect gas-thermometer, viz. a point 274°'6 below 

 the ordinary zero of the Centigrade scale, and 462°'28 below 

 that of Fahrenheit's scale. 



Hence the compressibility of water varies according to the 

 same law with that of a gas. 



To express the law symbolically, let tl represent the fraction 

 by which unity of volume of water is compressed by a pressure 

 of one atmosphere, D the density of the water, its maximum 

 density being taken as unity, and t the temperature measured 

 from the absolute zero ; then 



3d 11.. D=^. 



K is a constant coefficient, the value of which is — 

 For the Centigrade scale, 72 atmospheres per degree. 

 For Fahrenheit's scale, 40 atmospheres per degree. 



The following table exhibits a comparison between the results 

 of the formula and those of M. Grassi's experiments. It will be 

 observed, that the discrepancies are extremely small, and follow 

 no regular law, being sometimes positive and sometimes negative. 



The value of the single constant in the formula K was deduced 

 from the mean of the first and second experimental results. The 

 values of the density D were computed by means of the empi- 

 rical formula in my paper On the Expansion of Liquids, pub- 

 lished in the Edinburgh New Philosophical Journal for October 

 1849. 



Temperature 

 Centigrade from 



the ordinary 

 I zero. 







10-8 

 13-4 

 15-5 

 25-9 

 34-8 

 430 

 533 



Compressibility of water per 

 atmosphere of pressure. 



0000050584 

 000004 8(579 

 0000048252 

 0000047915 

 O000046a53 

 0000045140 

 000044158 

 0-000042931 



0000050560 

 0000048705 

 0000048378 

 0000047745 

 0000045843 

 0000045573 

 00(K»044414 

 0000044336 



-0-000000024 

 -t-0 000000026 

 +0-000000126 

 -0 000000170 

 -001)0000510 

 -f(»()()(»(MKM;53 

 -fO-(M)(l(l00256 

 + 0000001405 



As it has not yet been ascertained whether this law is appli- 

 cable to other liquids and to water at higher temperatures, I 

 refrain for the present from drawing any theoretical conclusions 

 from it. 



London, March 1851. 



