Critical Temperatures and Thermal Expansions. 433 



represented the physical facts more closely. Mendelejeff (as 

 we think rightly) considers that the simplicity of the formula 

 which he has suggested gives it a special claim upon our 

 attention ; and he proves that it expresses, at all events as a 

 first but very close approximation, all that we certainly know 

 about the expansion of liquids. 



It is therefore no argument against Mendelejeff 's formula 

 to remark, as MM. Bartoli and Stracciati have done, that 



Y t = — !— -=l + kt + k 2 t 2 +kH 3 + &C; 

 1 — kt 



and that in the formulae given by Pierre, Kopp, Hirn, Thorpe, 

 &c, the constants a, b, and c do not differ by a constant ratio, 

 as the expression would require. This criticism would only 

 hold good if all these observers had obtained the same, or 

 closely identical, values of a, b, and c ; whereas, as a matter 

 of fact, the values of b and c given by different observers may 

 differ very widely. The very merit of MendelejefFs remark 

 is that, although the results of no one physicist are expressed 

 h J Y t =l + kt + Jc 2 t 2 + JcH d , 



yet that this formula in its simpler form, 



y <= I=B> 



expresses the results of all as accurately as those results will 

 allow ; and that since it is thus sufficiently accurate and ex- 

 traordinarily simple, it may claim to be the best general 

 formula hitherto proposed for expressing the laws of liquid 

 expansion. 



These remarks are subject to the conditions w T hich Mende- 

 lejeff made clear, that the formula was only applied to the 

 range of temperature between 0° and the neighbourhood of 

 the boiling-point, and that the constant k increases slightly as 

 the temperature rises. This latter fact indicates that the law, 

 though very accurately expressing the known facts, is only 

 an approximation to the truth. 



MendelejefPs formula, then, appears to us to stand in some- 

 what the same position as Boyle's or Charles's laws. It is a 

 first approximation, which expresses the facts, under given 

 conditions of temperature and pressure, with great accuracy. 

 The difference between the cases is that, whereas the devia- 

 tion of each of the principal gases from Boyle's law has been 

 studied, Mendelejeff has shown that the most careful researches 

 do not enable us to state with certainty what is the magnitude 

 of the error caused by applying his formula to any particular 

 liquid. They show only that k increases very slightly as the 

 temperature rises. 



Phil. Mag. S. 5. Vol. 21. No. 132. May 1886. 2 H 



