444 SCIENCE PROGRESS 



between the boiling-point and the critical temperature of a liquid 

 is given by 



Boiling-point = "656 x Critical Temperature, 



when temperatures are measured on the absolute scale; so that 

 from the boiling-point one can calculate the critical temperature 

 of a liquid (subject to an error of some 4 or 5 per cent.), 1 and 

 knowing the critical temperature one can compare surface-ten- 

 sions, not only at the boiling-points, but at other corresponding 

 temperatures which are different fractions of the critical tem- 

 perature. Such a process is only approximate, but it is much 

 better than having no guide at all. 



An empirical relation from which critical temperatures can 

 be indirectly obtained has been given by Walden. Over limited 

 ranges of temperature one can write with sufficient accuracy 



T = T (i - aO) and a 2 - a 2 (i - p6) 



for the variation with temperature of the surface-tension and 

 specific cohesion respectively. But these formulae will not bear 

 extrapolation; and in particular if, knowing that the surface- 

 tension vanishes at the critical temperature, we attempt to calcu- 

 late this temperature from either of the relations 



ej = - or e c " = ±, 



a (3 



we obtain results which agree neither with each other nor 

 with the observed value for the critical temperature. But it so 

 happens that in many cases the variation of 9' c in one direction 

 from the true value is compensated by the opposite variation of 

 6' c in the other direction, so that the true value of the critical 



temperature is proportional to — f- -5, and so, as Walden pointed 



out, can be calculated from a knowledge of these temperature- 

 coefficients. 



It would, however, be distinctly advantageous if one pos- 

 sessed a general formula connecting surface-tension and tem- 

 perature which could be extrapolated with confidence up to the 

 critical temperature. Given such a relation, one could then 

 deduce the value of the critical temperature from observations 

 over a limited range of temperature of the surface-tension alone. 



1 This error may be considerably reduced if the effect of constitution on the 

 value of this " constant " be taken into account. 



