104 Prof. D. Mendeleeff on the Variation in the 



Then Thorpe and Riicker * concluded, on the bases of Van der 

 Waals's theory, that the modulus of expansion of liquids k 

 stands in intimate dependence on the temperature of their 

 absolute boiling-points T 2 , namely that 



i=2T 2 -273 . (4) 



As in formula No. 2, F (t) is essentially analogous in its 

 signification to k in formula No. 3, I tried to calculate the 



value of =,-? r or <j>(t) instead of F(£), hoping thus to include 



the conception of the absolute boiling-point of water, and this 

 led to the form of formula No. 1. 



2. It was necessary for the complete expression of the ex- 

 pansion of water as a liquid that F(£) should remain a positive 

 fraction less than unity at all values of t, starting from a 

 certain "critical" low temperature (below —10°), T 1? at 

 which water solidifies under any condition (of pressure, elec- 

 trical state, &c), up to the higher " critical " temperature 

 or absolute boiling-point T 2 , at which water passes into vapour 

 under any condition ; because it is only between these two 

 limits T 2 and Tj that the specific gravity of liquid water can 

 be observed. Outside these limits F (t) may acquire an 

 imaginary value, or become greater than unity, or negative 

 in sign. The form of formula No. 1 answers to these require- 

 ments for F (t) , because according to it 



F(0 = 



(A+*)(B-*)C 4>(t)' 



3. It is known that if certain conditions be observed water 

 may be cooled to — 10°, and even much lower, without being 

 converted into ice, and therefore A must be greater than 10. 

 On the other hand, Dewar f showed that the absolute boiling- 

 point of water does not lie below + 370°, therefore B must be 

 greater than 370 ; and as 2T 2 enters into formula No. 4, we 

 may suppose that B will express a quantity greater than 2T 2 , 

 and that the value of it will be greater than 2T X . 



4. These considerations of a theoretical character led me 

 to conclude that the value of <£(£) should be found for various 

 temperatures, and if these considerations were correct, that 

 {t— 4) 2 /(l — S*) or <j)(t) should be expressible by the parabola 



4>(t)=sa + bt + ct 9 , 



* Thorpe and Eiicker, Journal of the Ohem. Son., April 1884, 

 xlv. p. 135. 

 t Dewar, Phil. Mag. 1884, (5) xviii. p. 210. 



