688 Scientific Proceedings, Royal Dublin Society. 
possible, and, as it were, to shake the particles into new situa- 
tions, and in this way facilitate their taking up relative mean 
positions which give stable equilibrium.’ The linking premised in 
No. 6 will, however, where it is present, limit or prevent this effect. 
8. In some cases these disturbances ‘are increased so as to pro- 
duce a retrograde condition and disturb existing equilibrium. 
Tt is evident that in all cases whatever, in which stable equil- 
librium is attainable, the arrangement of particles whose nature 
has been thus premised will, if we neglect the small disturbances, 
ultimately come to be such that the pressures subsisting between 
them, together with the external force of compression, form a 
system in stable equilibrium.” And as, according to one of the 
data just given, the mutual repulsions fall off rapidly when the 
distance separating two particles passes a certain limit, this statical 
equilibrium may be regarded as that of the stronger repulsions, 
i.e., of those between particles whose distances apart are within 
these limits, the weaker repulsions, if any, subsisting between the 
particles whose distance apart exceeds these limits being negli- 
gible. 
Thus all repulsions between the particles, except those between each 
particle and the particles closely surrounding it, are to be taken as 
negligible. 
Fundamental Law of Closest-packing. 
Whether the particles are all of one kind, or of two or more 
different kinds, the effect of the mutual repulsions, under the con- 
ditions stated, exclusive of No. 8 above, will be to continually 
1 The small movements of the particles may be oscillatory ; indeed the interaction 
of the repulsions will, if the particles have inertia, cause them to be so, but it is not 
necessary for our present purpose to attribute any persistence or regular periodicity to 
any of the oscillations, although the existence of some kind of regularity is not pre- 
cluded. 
The origin of the disturbances is immaterial; one thing is however clear: the inter- 
action of the hypothetic particles will, if they have inertia, cause a disturbance occurring 
at any point to be communicated to other points around by wave-movements of some 
kind. 
2 Tf the attainment or persistence of complete equilibrium is prevented by the passing 
disturbances referred to, the given conditions will nevertheless be found continually 
removing the traces of every slight retrogression thus caused and striving after the 
equilibrium arrangement. (Compare p. 674). 
