EXPERIMENTAL KNOWLEDGE OF THE PROPERTIES OF MATTER. 505 



abstracts published ia the ' Fortscbr. der Physik ' since 1845 will be 

 found attempts in this direction. 



Mendelejeff's Relation letween V and t /o?- Liquids. 



Mendelejeff' proposes the formula V= 1/1 — kt, similar to Gay- 

 Lussac's formula for gases, but in which k is a specific constant for each 

 liquid; and substantiates this as an approximate formula by applying it 

 to the volumes given by Thorpe for liquids at various temperatures, 10°, 

 30°, 60°, and in some cases 150°. Arranging 47 liquids studied by Thorpe 

 in order of their rates of expansion with rise of temperature, from the 

 least to the most expansible, an inspection of the figures is sufiBcient 

 to suggest at once the idea that all expand in a similar manner, and that 

 the difierence between their expansions is one of scale only. This is 

 shown by Mendelejefi' by taking the expansion for mercury as calculated by 

 him from Regnault's results in the form V=l +10"^ ISOIT + 10"' . •2T2, 

 in which T is any temperature of the luercury. Comparing the expan- 

 sion of mercury with that of PBrj, one of the least expansible of the 

 liquids given in the table, and with nitric peroxide N2O4, the most rapidly 

 expanding liquid of those given, Mendelejeff shows that 46'8°, 93*7°, 

 140-9°, 189-1° are temperatures T at which the volumes of the mercury 

 (vol. at 0°=1) are the same as are the volumes of PBrj at temperatures 

 t such that Tjt is 4-68, 4-68, 4-69, 4-72. So for comparison of the 

 volumes of mercury and nitrogen peroxide at temperatures T and t re- 

 spectively, he finds for mercury at temperatures 43-6°, 86-5°, 129'7°, 174-6° 

 the same volumes as nitrogen peroxide has at temperatures 5°, 10°, 15°, 

 20° respectively, so that in this case T/f has the values 8-72, 8-65, 8-65, 

 8-70, showing that phosphorus tribromide expands 4-7 times more strongly 

 than mercury, and nitrogen peroxide 8-7 times more strongly than 

 mercury, but in qualitative respect the expansion of these as well as 

 other liquids is on a uniform plan. 



As the density of a mass is inversely as its volume, if we take the 

 density of a liquid at 0° as 1, the density D=l — 7r;^ at the temperature t; 

 hence dDjdt = —k (or if density is Dq at 0°, D=D° (l—kt), and 

 dD/dt = —kDo). This result is remarkably confirmed by some specific 

 gravity determinations, by Miss E. K. Gutkowska in Mendelejeff's 

 laboratory in 1881, of some American kerosene (petroleum). At 0°, 16°, 

 32°, 48° the specific gravities found were -8056, "7940, "7824, 7708, 

 whence an equal difierence "0116 for equal temperature-intervals; here 



dD^ '2111= _ -000725. Similar results were obtained for Baku 

 dt lb 



petroleum.^ 



Mendelejeff remarks that he found in 1860 ^ that the coefficient of 

 change of density of liquids varied more simply than the coefficient of 

 change of volume ; and that this, combined with his investigations from 

 1880 to 1883 (loc. cit.) of the products of distillation of Baku petroleum 

 in which he was obliged to find the change of density with changing 

 temperature, induced him to consider all liquids in reference to changes 

 of density rather than volume in the first place, and that he thus arrived 

 at the law of expansion V = 1 / 1 — A;i. 



' C. S. J. 1884, p. 126. = Russ. Phyg. Chem. Soc. Journ. 1883, p. 189. 



' L. Ann. 114, 165. 



