126 Prof. D. Mencleleeff on the Variation in the 



the Eussian Physico-Chemical Society, 1891, Physical Section, 

 p. 30), in elaborating the vast material collected by him during 

 his voyages round the globe, relative to determinations of the 

 density of sea-water, deduced a formula which expresses the 

 expansion of water between —5° and +35°, employing the 

 compilations of his predecessors, and amongst others of Herr, 

 made for the International Metrical Commission. 



To these compilatory data I subjoin (a) the arithmetical 



mean of all the data of Table I. ; (b) the value of -7 , i. e. the 

 increment of the volume corresponding to an increment of 

 temperature of one degree ; (c) the value of — , or the incre- 

 ment of volume corresponding to an increment of pressure 

 of one atm. (this =/^Y £ ); and lastly (d) the value of the 

 possible error in contemporary determinations of the volumes 

 of water. The numbers in this line were deduced on the 

 basis of the following considerations : — 



(1) Since it is conditionally received that the volume at 4° 

 equals unity (or 10 6 , according to the notation adopted in this 

 table) , it follows that at 4° the error will be zero, and we may 

 grant that all the errors are proportional to the difference 



(2) Since the existing data are, for the most part, referred 

 to readings of the mercury thermometer, they must contain 

 that error which these readings include if we suppose them 

 corrected in every other respect. The minimum of this error 

 for the best thermometers of hard glass is given above, but I 

 do not think it necessary to add this error to the sum of 

 possible errors, because, in the first place, it can now be to a 

 great extent corrected, and, in the second place, with different 

 thermometers the amount of this error must present a certain 

 unavoidable variability, whose value cannot possibly be now 

 determined. 



(3) In the determination of temperatures, the observers 

 have up till now been satisfied with hundredths of a degree, 

 and frequently even tenths, so that, generally speaking, the 

 error for temperatures may be taken as +0 o, 05. However, 

 for temperatures below zero, where there are fewer observa- 

 tions and these more difficult, the amount of this error must 



E * Although perhaps the maximum density is not exactly at 4°, still it 

 undoubtedly lies between 3° -5 and 4°'5 ; and within this range the 

 volumes of water vary so little, that practically, within the limit of 

 existing errors, this density may be presumed to be situated at 4°, all the 

 more so, as all later investigators give it a temperature very near 4°, for 

 instance Hagen 3 G '98, Rosetti 4°-07, Kopp 4°-08, &c. 



