Do Molecules Attract, Etc. 531 



the centers and directly as the product of the cohesive masses 

 M, then the attraction of two molecules would be M 2 K/V /3 . 

 The pressure per square cm would be M 2 K/7/ /3 . Since the 

 attraction goes but a single molecular diameter we may 

 multiply the numerator and denominator by N 4/3 , where N 

 is the number of molecules in the mass which will make 

 N 4/3 M 2 K/V 4/3 . It is obvious that this expression cannot be 

 true, for the cohesion varies inversely as the square of the 

 volume, and not as the 4/3d power. Assuming, however, 

 that it is correct we would have, as the difference in the 

 cohesive energies in the liquid and vapor, the expres- 

 sion: N 4/3 M 2 K(i/V /3 - i/V^ /3 ). Or changing to density 

 N 4/3 M 2 K(c/; /3 D; /3 )/Wt 1/3 . Hence I, E should equal this 

 expression, and (I, E)/(d' /3 D^ 3 ) - N 4/3 M 2 K/Wt 1/3 = /. 

 This last expression can be tested, since M 2 K can be easily 

 computed from van der Waals "a" by dividing it by N 2 , the 

 square of the number of molecules in the volume V, or Wt; 

 and p.' is given by Mills. The two values are not of the same 

 order of magnitude. For example in pentane, // is no, 

 whereas N 4/3 M 2 K/Wt 1/3 for i gram is 2.214 X io~ 13 calories. 

 A constant very like // is obtained, however, if the foregoing 

 constant is divided by V 2/3 /3N 2/3 . This changes it to the 

 expression 3N 2 M 2 K/V 2/3 Wt' /3 . This would give the value 

 1 02 for pentane. How closely this constant agrees with Mills 

 is shown in Table i. N 2 M 2 K is equal to "a." 



The constant cannot be deduced, therefore, by the 

 assumptions we have made, one of them being that molecules 

 attract each other inversely as the square of the distance, but 

 it is necessary to divide the theoretical constant by 

 Vj /3 /3N 2/3 to get that found. This however, has the effect 

 of changing the equation, near the critical temperature, to 

 the form: Iy E = 3a(i/V 1 i/V v ) which is almost identical 

 with van der Waals. 



This argument will perhaps be still more convincing if 

 it be turned around. Let us suppose Mills' contention is 

 correct and the internal latent heat represents only heat used 

 in overcoming cohesion, then //VJ /8 is the cohesive energy 



