186 Prof. Challis on the Hydrodynamwal Theory 



have argued more correctly as follows : — " If we suppose 

 waves of condensation to be propagated from all the atoms 

 contained in a spherical space of radius r, the condensation 

 resulting from the composition of the wares at any distance 

 II from the centre of the sphere very large compared with r, 

 will vary [groom praacime] as the number of atoms — that is, as 

 ?- 3 directly, and as R inversely [the atoms being supposed to 

 be evenly distributed over the spherical space] . If, now, we 

 take another sphere of larger radius, r', and another point 

 whose distance, R', from the centre of the sphere is such 



that ^p = o7 ? then the condensation at the first point is to the 



Xli -LV 



condensation at the other as -p to =- f ; that is, as r 2 to ? /2 , or 



as R 2 to R /2 . Hence, however small maybe the condensation 

 propagated from a single atom, the resulting condensation 

 from an aggregation of atoms in a spherical space may be of 

 sensible magnitude at considerable distances from the centre, 

 if the number of atoms in the given space be very great. 

 The dynamical effect of these compound waves on a particular 

 atom may be investigated in the same manner as the effect of 

 waves propagated from a single atom. ... In this manner it 

 is conceivable that while the individual atoms are repulsive to 

 each other, an aggregation of atoms may give rise to a con- 

 trolling attraction." 



20. The assertion in the last sentence of the above quotation 

 admits of being confirmed as follows by results obtained in 

 the present communication. The waves emanating from a 

 single atom may be considered to be composite waves, as being 

 the result of the reactions at its surface consequent upon the 

 incidence thereon of waves from all surrounding atoms. Now 

 it may well be supposed that the value of kn for these com- 

 posite weaves at a distance from their origin equal to that of 

 one of the nearest atoms, is not of sufficient amount to make 

 the expression in art. 18 for the pressure on this atom a 

 negative quantity. Accordingly adjacent atoms will be 

 mutually repulsive. If we next take a group of atoms evenly 

 distributed in a certain spherical space, it is supposable that 

 the spherical waves resulting from the composition of the 

 waves from all the atoms in the space may still act repulsively 

 on the atoms situated at the boundary, and that thus there 

 will only be repulsive action between the atoms throughout 

 the spherical space. It is certain, however, from what is 

 shown in art. 19, that, on increasing still further the magni- 

 tude of the space, a value of kn will be reached which corre- 

 sponds to attractive action on an atom at the boundary, and 



