130 Prof. D. Mendeleeff on the Variation in the 



0° and 40° to be very probable. We have already seen the 

 remarkable concurrence of the formula with Hirn's data for 

 temperatures above 100°; so that from both sides — for the 

 lowest and the highest temperatures — the applicability of the 

 formula to the reality is quite likely, and the results given by 

 it are not less trustworthy than the averages deduced from 

 experiments. 



With respect to temperatures between 40° and 100°, the 

 evidence of investigators is more conflicting than could be 

 desired, and than is called for by the value of the possible 

 errors given in Table II. For instance, at 70° the difference 

 of the volumes observed by Jolly and Matthiessen amounts to 

 204 millionths, and the volumes observed by Kopp and Pierre 

 differ by 687 millionths, whereas the possible error at 70° 

 given in Table II. only amounts to +85 millionths. But the 

 volume at 70° given by the formula (1022549) differs from 

 the general average (1022513) by only 36 millionths, and 

 from Rosetti's experimental result (1022529) by only 30 

 millionths, and occupies a position among the results given by 

 Jolly, Matthiessen, Kopp, Pierre, Hagen, and Despretz ; it is, 

 therefore, more probable than the figures of any one of these 

 observers, and even more likeiy to be true than the average 

 result, for the very reason that the formula satisfies alike the 

 data for 70° and for higher and lower temperatures. In 

 other words the figure shown by the formula for, say 70°, is 

 confirmed not only by experiments made at 70°, but also by 

 determinations at 0° or at 200°. 



Besides the specific gravity, calculated by the formula and 



given in the second column, and the measure of the errors, 



which probably will not be exceeded in more accurate fresh 



determinations, Table III. contains the following quantities: — 



ds 

 (a) The differential coefficient j 1 found from the formula. 



The values of this differential coefficient are not only useful 

 practically in calculating results for intermediate temperatures, 

 they not only demonstrate the mode of variation of the density 

 of water, but they also present, in my opinion, a great theo- 

 retical interest, because natural phenomena, in their differential 

 expression, always become simplified and easier to study. It 

 appears to me to be highly instructive that the differential 



ds 

 coefficient 7- for lower temperatures gives a line of considerable 



curvature, but for higher temperatures asymptotically ap- 

 proaches a straight line, which circumstance I propose to take 

 advantage of hereafter, for certain deductions relative to the 

 expansion of aqueous solutions and of various other liquids. 



(b) The differential coefficient^-, or the variation of the 



