PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 57 



The expression for the attraction of any particle, is of the form 



r .. gfl -» 

 6 a* • 



Now whatever be the form of the bounding surface, it is obvious 

 that unless the sphere of sensible action be great, it will suffice to 

 consider it plane and extending to infinity : we shall then have to 

 estimate the aggregate force on a particle resolved perpendicular to 

 the bounding plane. 



Let the atom under consideration be the centre of a spherical sur- 

 face to radius a : take an annulus of this surface such that the radius 

 vector drawn to it makes the angle 9 with the bounding plane: 

 the area of this annulus = 27ra 2 cos 9 dO, 



and the number of particles in it = — — cos 9 d9 ; 



hence the attraction on the particle in question resolved perpendicularly 

 to the bounding plane, 



27ra s sin 9 cos 9 d9 e~ aa 



2 



e 



{Ha — m), 



and the whole force due to the particles in the hemispherical surface, is 



IT Ha _■•' 7T 



S " 2 



6 6 



aa — -. me~ aa 



In order to find the whole attraction on the given particle, we 

 must find the sum of all similar expressions taken through the whole 

 mass : which is 



■n-H , o v irme- a ° 



= -f^ «<r°'(l + 2*— + «r + ")- e *(i- e -'») 



e . \l-e- ae ) e 2 l-e" ae * 

 This is the expression which ought to remain constant, whatever 

 be e, so long as the temperature is so. It is obvious that it varies 

 directly as H, which involves m' — n'q. 

 Vol. VII. Pabt I. H 



