576 Dr. R. D. Kleeman on Molecular Attraction 



The Values of some Corresponding Quantities. 



The various formulae that we have deduced from the law 

 of attraction between molecules given at the beginning of the 

 paper, contain a number of constants each of which has the 

 same value for all liquids at corresponding temperatures, 

 being functions of the arbitrary function in the law of attrac- 

 tion. Expressions for these constants can be found when 

 the formulae apply to a liquid and its saturated vapour, that 

 is, when the state of the substance is a function of the 

 temperature only. We are enabled to do this owing to the 

 fact that an infinite number of equations can be found con- 

 necting the internal heat of evaporation and surface tension 

 with other quantities. We have already deduced some 

 results along this line * ; we are now able to improve upon 

 and extend them. 



The fundamental equation for the surface tension deter- 

 mined directly from the law of attraction between molecules 

 is 



x=K '"('^r 2 ) 3(2v/ " ri)2 '- • • • • (3) 



where k'" is a constant which is the same for all liquids at 

 corresponding temperatures |. In subsequent transforma- 

 tions we will use the relations p\ = nip c , p 2 = ?i 2 p C} T = n a T c , 

 pz=n i p Cf and p = bp c , the quantities n l5 n 2 , n 3 , n l} and b being 

 of course the same for all liquids at corresponding states. At 

 the absolute zero we then have 



a ^_ «, mb 2 p c ' fK , — x 2 K '"b 2 (pi — p 2 ) 2 /^ , — no 



and therefore 



where p is the same for all liquids at corresponding states. 

 Another value for /n may be obtained from one of the infinite 

 number of subsidiary surface tension relations that can be 

 found. Let us take the modified relation of Eotvos given in 

 this paper. At the absolute zero this becomes 



_ ^/ y/3 w* 0>i-p,)"» T T . 



A °~ /C mm lc ~ { ni -n. 2 fl''\l-un z ) m*l* [c al)) 

 and we therefore deduce 



* Phil. Mag. Oct. 1910, pp. 491-510. 

 t Phil. Mag. May 1910, p. 793. 





