434 Critical Temperatures and Thermal Expansions. 



Having thus defined as accurately as we can the position 

 which we think that Mendelejeff's law holds, we need hardly 

 say that we do not claim any higher status for our own formula 

 connecting the law of expansion and the critical temperature. 

 We were most careful to express in our paper our appreciation 

 of the iact that our expression was based upon Mendelejeff's, 

 and therefore it ranked only as a theoretical deduction from 

 an extremely close approximation to the truth, and is to be 

 employed only under the conditions for which that approxi- 

 mation was valid. 



Thus we have shown that the critical temperature of a 

 liquid (T c ) is given very approximately by the formula 



TV,-273 

 lc ~ a(V«-l) ' 



where Y t is the volume at t° C, T=273 + £, and a is a con- 

 stant which we proved is nearly = 2. 



We should, however, never have thought of applying this 

 formula to determine the critical temperature of water from 

 the expansion up to 200° 0. We have not applied it to water 

 at all, on account of the well-known peculiarities of the ex- 

 pansion of that substance ; but had we done so, we should 

 have regarded it as holding only between 0° C. and the boil- 

 ing-point. We have distinctly laid it down that it is under 

 these conditions k is to be determined*. In proving, there- 

 fore, that the values of the critical temperature, calculated 

 from the expansions at temperatures above the boiling-point, 

 vary very widely from those obtained under the conditions 

 adopted by Mendelejeff and ourselves, MM. Bartoli and Strac- 

 ciati have only shown that the formula does not hold good 

 under circumstances to which its authors never intended it to 

 be applied. 



We are, however, gratified to find that these gentlemen, 

 notwithstanding their criticisms, show a reliance upon our 

 formula even greater than that which we feel ourselves. The 

 values of the constant a given in our paper prove that its true 

 value is uncertain, at all events to 1 per cent, or more. 

 MM. Bartoli and Stracciati, however, give in their second 

 paper a number of critical temperatures calculated by the 

 formula to tenths of a degree. If the tenth of a degree is to 

 be determined with accuracy, the constant a must be known 

 to O025 per cent. We beg, therefore, those who may do us 

 the honour to use our formula, neither to outrage it under 

 conditions to which it does not apply, nor to use it as though 

 it were more accurate than it pretends to be. 

 * Journ. Chem. Soc. loc. cit. p. 139. 



