100, Prof. D. Mendeleeff on the Variation in the 



even for ordinary temperatures, exceed hundred-thousandths * 

 while the accuracy of gravimetric and volumetric measure- 

 ments can now be carried to millionths. 



The publication of the present paper previous to my having 

 been able to undertake a series of fresh and properly insti- 

 tuted determinations of the expansion of water, is accounted 

 for by the fact that the collation and elaboration of the exist- 

 ing data referring to this subject has led me to the following 

 somewhat simple expression : — 



fi — i v^~^) ( i \ 



M (A + 0(B-0C K} 



which embraces all that is known for the variation of the 

 density of water (S,) between -10° C and + 200° C f with all 

 the accuracy now attainable. A general expression for the 

 variation of the density of water, while presenting a means for 



tions in detail. I have introduced some of them into the existing data of 

 many observers, but I do not give the results thus obtained in this article, 

 because in the first place I wish to preserve the original results of the 

 experimenters, knowing that the greatest interest is always attached to 

 them, and in the second place because many of these corrections are of 

 doubtful value, unless they are made by the observers themselves. When 

 studying the literature of the subject, it becomes a matter of regret that 

 the majority of observers do not give their original experimental numbers 

 (for example, the apparent volumes or weights of water). If these were 

 known, it would be easier to introduce the necessary corrections and to 

 form an estimate of the magnitude of the errors inherent in the figures 

 thus given. 



* For example, at 25° the volume of water, according to Jollv, is equal 

 to 1-002856 ; according to Matthiessen it is 1-002982. The first number 

 approaches to the values given by Rosetti, Hagen, and others ; the second 

 is nearer to Despretz's determination. 



t In his admirable determinations of the expansion of water from 100° 

 to 200°, Hirn plainly states that at these temperatures the expansion of 

 water is expressed differently and more simply than at lower tempera- 

 tures. Kopp and the majority of investigators give empirical expressions 

 (by interpolation) for the expansion of water for only small variations of 

 temperature, for instance from 75° to 100°, their endeavours to obtain a 

 general expression, comprising the whole range of volumes from 0° to 100°, 

 having been fruitless. Frankenheim (Pogg. Ann. 1852, lxxxvi. p. 463), in 

 undertaking the great labour of making a series of fresh calculations for 

 all the experimental data of Pierre, had in view to seek out a general 

 expression (" Ausdruck des Naturgesetzes ") answering to the " conflict 

 between heat and cohesion which evinces itself in the variation of the 

 density of water,'* but was unsuccessful in finding a general algebraical 

 expression for the dependence which is here concealed. He concludes 

 his memoir with the words "Das Problem ist noch ungelost." From 

 this we see that the great importance of having a simple general alge- 

 braical expression for the expansion of water with a rise of temperature 

 was lonsr since recognized by many scientists. 



