Density of Water with the Temperature. 121 



information respecting the expansion of water from —10° to 

 100° has hardly made any progress since Despretz's determi- 

 nations, as regards their trustworthiness. 



5. Pierre, in 1847, published a series of volumetric-therm o- 

 metric determinations for the expansion of water, hut did not 

 calculate the ultimate figures. A complete calculation of 

 Pierre's results from — 10° to 100° was subsequently made 

 by Frankenheim (Pogg, Ann. 1852, Ixxxvi. p. 463), whose 

 figures are given in the table. 



6. Kopp (Pogg. Ann. lxxii. p. 1), in 1874, like Pierre, 

 measured the expansion of many definite liquids, and amongst 

 them of water, chiefly with a view to compare the expansion 

 of liquids up to their boiling-points. The method adopted 

 was a volumetric-thermometric one. The coefficient of expan- 

 sion of glass was deduced from mercury, taking Dulong and 

 Petit' s number. The calculations for the volumes are given 

 in four separate equations for various ranges of temperature 

 from 0° to 100°. 



7. Plucker and Geissler (Pogg. Ann. 1852, Ixxxvi. p. 238) 

 adopted a method of compensation, and were the first to take 

 Eegnault's figures for the expansion of mercury. Into the 

 thermometrical vessel, whose coefficient of expansion was 

 determined by means of mercury between 0° and 100°, as 

 much mercury was poured as was necessary to compensate 

 the expansion of the vessel, and hence the quantity of water 

 subsequently introduced was considered to expand' in a space 

 whose volume remained unaffected by a rise of temperature. 

 In these determinations too much mercury was taken, so that 

 the apparent expansion of the water contains a certain excess 

 (as Miller observed in 1856) ; secondly, the mean coefficient 

 of expansion of mercury between 0° and 100° was taken to be 

 the same as between —5° and 4-15°, which is evidently 

 inaccurate (the true expansion of mercury between — 5° and 

 + 15° being still unknown, for Regnault's determinations start 

 at higher temperatures) ; and thirdly, the coefficient of expan- 

 sion of the envelope between —5° and +15° is presumed to 

 be equal to the mean coefficient of expansion between 0° and 

 100°, which is also inadmissible. But apart from these points, 

 which are common to the determinations of other observers. 

 the results given by Plucker and Geissler are distinguished 

 for their remarkable accuracy, which shows that the method 

 adopted by them is capable of giving admirable results, were 

 the data of the expansion of mercury and glass fully known. 

 These investigators expressed the results of their determina- 

 tions graphically by a very well-proportioned curve, although 

 for only a small range of temperature not far distant Prom 0°, 



