Density of Water with the Temperature. 119 



digressions of the interpolation -formulae from the observed 

 figures in various regions of temperature. But on comparing 

 the results thus obtained, I have come to the conclusion that — 

 1, the introduction of all the possible corrections does not 

 make the results of separate observers agree with one another ; 

 and 2, the greatest quadratic deviations do not appear in the 

 results of those observers whose results are apparently the 

 least trustworthy, but in those cases where the methods 

 adopted are described in the greatest detail and most circum- 

 stantially. For this reason, I give in Table I. the original 

 figures of the observers without introducing any corrections 

 whatever ; and it is only to aid their comparison that I 

 express the results in volumes, taking the volume at 4° equal 

 to 10 6 . Further, in Table II. figures are given which have 

 been determined at different times by various investigators, 

 deduced from an aggregate of data corrected in all respects 

 and considered as most trustworthy. Finally, in Tables II. 

 and III., besides the densities and volumes of water found 

 from formula No. 1, the magnitude of the errors, which may 

 now be looked for in the best determinations, are given. 

 These possible errors, inherent in contemporary data, may 

 evidently also occur in the results given by formula No. 1, 

 for its constants and very form could only be founded upon 

 previous determinations. 



Table I. contains the figures for the volumetric variations 

 of water found by the following investigators : — 



1. Hallstrom, in Abo (Pogg. Ann. i. p. 168). He made 

 his determinations (in 1823) by weighing in water a glass 

 sphere (vol. about 162 c. c.) blown out of the same material 

 as a tube, whose linear expansion he determined in a direct 

 manner. Hallstrom interpolated the specific gravities, taking 

 that at 0° as unity, according to the formula 



S^ = l+^— bt 2 + ct 3 ; 



the constants, multiplied by 10 6 , a = 52*939, 6 = 6*5322, and 

 c = 0*01445, were found by the method of least squares for 

 t from 0° to 30°. The determinations made by Hallstrom 

 must be taken as exemplary. Subsequently Hagen and 

 Matthiessen adopted the same method. The chief cause 

 why the results obtained by Hallstrom are all below the 

 truth, lies in the fact that his results for the linear expansion 

 of glass, at temperatures between 0° and 30°, were below the 

 actual figures. Taking & = 0*000026, we obtain results from 

 Hallstrom's figures which very nearly approach the date oi' 

 the best and latest determinations. 



2. Muncke (Memoires pt-es. a VAcadimie des Sciences d 



