Chemical Attraction between Atoms from Physical Data. 91 



of certain quantities. Further, the known part of the 

 law may contain quantities which were excluded from the 

 arbitrary function. Now the law of attraction between two 

 molecules of the same kind deduced by the writer * is 



*lh e) 



where z is the distance between the molecules, 2 ^ m i * s ^ ne 

 sum of the square roots of the atomic weights of the atoms 



of a molecule, and <£ 2 ( — , ^ \ is a quantity which is the same 



for all molecules at corresponding temperatures. The 



quantity (£>J — , =^\ must therefore be a function of the 



ratio of the distance between the molecules to the distance of 

 separation in the liquid. state at the critical temperature, and 

 the ratio of the temperature of the molecules to the critical 

 temperature. The function is arbitrary as its form cannot 

 be determined from the data from which the expression for 

 the law was obtained. We see that it does not contain 

 2 s/ M 1<t and we therefore have the important result that the 

 " chemical " attraction at a given distance from an atom is 

 proportional to the square root of its atomic weight. 



The problem to solve next is to determine the exact form 

 of this function. We have seen f that if we assume it a 

 function of the temperature only, a value for the intrinsic 

 pressure is obtained which agrees very well with that ob- 

 tained by supposing the matter evenly distributed in space, 

 in which case the intrinsic pressure can be shown to be equal 

 to Lipi. Further, the coefficient of diffusion of one gas into 

 another calculated on this supposition agrees well with the 



facts. The law of attraction may then be written — 5 - , where 



K is a function of the temperature. It was also shown that 

 the power of z cannot be less than the fifth but must be 

 rather greater, for otherwise the " chemical " attraction be- 

 comes comparable with the gravitational for distances greater 

 than one cm. But we would expect that the function 

 depends strictly both on the distance between the molecules 

 and their temperature, and this can be proved to be the 

 case. 



We have seen at the beginning of the paper that if it can 



* Phil. Mag. May 1910, pp. 783-809. 

 t Phil. Mag. Oct. 1910, pp. 665-670. 



