Variation in Density of Water with Temperature. 125 



acquainted with Muncke's and Starapfer's results. But his 

 results were but little known, since Despretz's figures (see 

 Table I.) were published shortly after and attracted general 

 attention. The same remark applies to Kopp and Pierre's 

 figures, published ten years later. 



Miller (Phil. Trans. 1856, p. 146), when establishing the 

 relation of the English pound to other units of weight, 

 examined the existing data for the density of water, and 

 having corrected them for the expansion of mercury, he 

 compiled them into a very simple formula, according to which 

 the logarithm to seven places of the volume (reckoning unity 

 at 3°'945), equals 



32-72(£-3-945) 2 -0-215(£-3-945) 3 , 



and his tables (from 0° to 25°) were long used by many 

 investigators. He took Despretz's, Pierre's, and Kopp's data 

 as a basis for his calculations. 



Rosetti, taking Despretz's, Kopp's, Hagen's, and Matthies- 

 sen's, in addition to his own determinations, calculated the 

 mean regulated values, which are frequently made use of at 

 the present time. 



Volkmann (Wied. Annalen, 1881, xiv. p. 277), adopting 

 Levy's determination (1881) for the expansion of mercury 

 (viz. 0=018207 from 0° to 100°), recalculated the determina- 

 tions made by Kopp, Pierre, and Jolly, embracing Hagen's 

 and Matthiessen's data, and rejecting those figures which he 

 regarded as being very incorrect, and took an average of all, 

 without, however, subjecting them to any regularization and 

 preferring to remain as near as possible to the empirical 

 results. 



Mendeleeff (' Messenger of Commerce,' 1884, and separate 

 work, ''The Investigation of Aqueous Solutions according to 

 their Specific Gravity/ 1887, p. 42), in studying (1880-84) 

 the existing data concerning solutions, made a calculation 

 similar to Volkmann's, taking as a basis the expansion of 

 mercury from 0° to 100° as equal to 0'00018210 + 0'0000007, 

 which he deduced in 1875 from Regnault's determinations ; 

 and, taking into consideration all the figures given by Des- 

 pretz, Kopp, Plucker and Geissler, Hagen, Jolly, Henrici, 

 Weidner, Matthiessen, Him and Rosetti, he calculated the 

 averages, which are given in the table. The figures are, 

 however, only given to hundred-thousandths of the density, 

 without being referred to the hydrogen thermometer, and in 

 the calculation for 20° a mistake occurred, so that this 

 number is not included. 



During the current year, Admiral Makaroff (Journal of 



