106 Prof. D. Mendeleeff on the Variation in the 



affected * by the existence of errors in the fundamental quan- 

 tities, it appears useless at present to expect values of any 

 accuracy for the constants A, B, and C in formula No. 1. 

 According to the numbers of formula No. 5, we find that 



A = 94- 10, B = 703'51, C = 1'90. ... (6) 



These figures satisfy the conditions A>10 and B>370, and 

 also that they should be all positive and greater than unity, 

 so that F (t ) > and < 1 ; but the true values of A, B, and C 

 can only be found after fresh and more accurate determina- 

 tions. As a first approximation, especially for ordinary tem- 

 peratures f , the above values will suffice, justified as they are 

 by a comparison of the calculated results with the aggregate 

 of already known data (see Tables I., II., III.). 



Previous to revising the extant information concerning the 

 expansion of water, it will be well to examine the corrections 

 and errors relating to the data of the subject. On this head 

 special attention must be paid to the influence of pressure, 

 the coefficients of expansion of solid bodies, and the methods 

 employed for determining the temperatures. 



Influence of Pressure. — Taking the aggregate of results 

 from previous sources (Regnault, Wertheim, Grassi, Amaury, 

 and others) of information about the compressibility of water, 

 it appears that the magnitude jjl (the coefficient of compressi- 

 bility corresponding to a rise of pressure equal to one atmo- 

 sphere) decreases when the temperature rises from 0°, whereas 

 for all other liquids fx increases with the temperature. The 

 researches of Pagliani and Vicentini J, however, show that 



* In Prof. Markoff's researches (Proceedings of the Imp. Acad, of 

 Sciences, St. Petersburg, 1889), the possible variations of a, b, & c in the 

 expression y—a-\-bx-\-cx l for a given limit of the variable x and a de- 

 terminate error of the variable y are considered in an exhaustive manner. 

 This question is stated and solved for a particular case in the work 

 " Investigation of Aqueous Solutions according to their Specific Gravitv," 

 1887, p. 289, by the present Author. 



t If we had to deal with a small range of temperature, for instance 

 from 0°-40°, then the rectilinear expression of (j)(t) would amply suffice 

 within the limits of possible errors (see Tables II. and III.). In that case 



A like expression, with the difference that in the numerator (£—4) has an 

 index of more than 2 and less than 3, appears sufficient for the entire 

 range of expansion, but then great difficulty is experienced in the calcu- 

 lations and in reality three constants are introduced, the same as in 

 formula No. 1. But an expression of the form 



g, =1 (*-4)% 

 proves unsatisfactory. A-\-Bt ' 



X Pagliani and Vicentini. Unfortunately I have not read their memoir 

 in the original, but only know it from an account published in Wiede- 

 mann's Beibliitter, 1884. 



