666 Dr. II. D. Kleeman on the Equation of Continuity 

 4>2\ ~ t , ft) is a function whose exact theoretical form is not 



indicated by the investigation except that it has the same 

 value for all substances at corresponding states. It was 

 found that this function does not vary much with the 

 temperature and as a first approximation may be taken 

 as constant. Supposing it constant, its value was deter- 

 mined and found to be of the order of the magnitude of 

 2xl0~ 4t5 (grm.)(cm.)(sec.)~ 2 . The above law of attraction 

 is in this paper made the basis of some equations of con- 

 tinuity of the different states of matter. 



Let us suppose that a molecule in the liquid state has the 

 same amount of kinetic energy or energy of translation 

 as in the gaseous. And let us suppose that the molecules 

 in a liquid are in equilibrium between the gas or Boyle 

 pressure of the molecules acting in one direction and the 

 attraction between the molecules and the external pressure 

 acting in the opposite direction. Then, if P n denotes the 

 negative pressure due to the attraction of the molecules, 

 and p the external pressure and p x the Boyle pressure, we 

 have 



RT 

 P,+* = *i*— > CD 



where m denotes the molecular weight of the substance. 

 This view of the equilibrium of the molecules in the liquid 

 or any other state is now usually adopted by physicists, 

 principally owing to the work of van der Waals. V n has 

 been called the intrinsic pressure of the liquid. 



The law of molecular attraction given at the beginning 

 of the paper enables us to obtain a more definite and 

 fundamental expression for the intrinsic pressure than that 

 obtained from van der Waals' equation of state. It is 

 first of all necessary to make some supposition as to the 

 relative distribution of the molecules in a liquid. Let us 

 suppose, as we did in a previous paper, the liquid cut into 

 equal squares by three sets of imaginary planes, one set 

 of which is parallel to the surface, and that the molecules 

 are situated at the points of intersection of these planes. The 

 attraction of a slab of liquid whose thickness is greater than 

 the radius of the sphere of action of a molecule on a molecule 

 at a distance nx a from the surface is 



where £„ = S\Zm, 



