432 Messrs. Thorpe and IMcker on the Relations between 



simple expression given by Mendelejeff for the expansion of 

 liquids, we should like to state exactly the position which we 

 ourselves think ought to be assigned to it, and the use which 

 may legitimately be made of it. 



Prof. Mendelejeff has shown* that the expansion of liquids 

 under constant pressure between 0° C. and their boiling- 

 points may be expressed by means of the very simple formula 



where V* is the volume at t° (that at 0° C. being unity), and 

 k is a quantity which differs for different substances, but 

 which may for any one substance be considered invariable 

 between 0° 0. and the neighbourhood of the boiling-point. 



The great merit of Mendelejeff 's law is that it is proved by 

 him to express the law of expansion to within the limits of 

 the differences between the results of different observers ex- 

 perimenting on the same liquid. Thus, if the results of any 

 one observer alone are considered, they may no doubt be most 

 accurately expressed by a formula of the type 



Y t = l + a't + Vt 2 + ct\ 



Another equally reliable observer will, however, obtain for the 

 same liquid a formula 



Y t = l + a"t + b"t 2 + c"t*, 



where a f , b f , c r differ appreciably from a ,f , b ,f , c" . These 

 slight differences depend on the unavoidable errors of experi- 

 ment, which may perhaps in the future be diminished, but 

 which at present affect the work of the best observers using 

 the best known methods. Hence formulas such as those given 

 above can only be considered as approximations to the true 

 law of the expansion of the liquid to which they refer. That 

 law will be most nearly given by combining the results of 

 several physicists whose methods and observations are equally 

 good, rather than of relying upon those of any one. 



Now Mendelejeff has shown that the volumes calculated at 

 different temperatures by means of the formula 



differ less from the results of good observers than they do 

 from one another. It might in any given case be possible to 

 obtain another more complex formula which would express 

 the mean result more accurately, but it would remain very 

 doubtful whether the greater mathematical accuracy obtained 

 * Journ. Chem. Soc. April 1884. 



