Abstract
Summarizing the results of the two last parts
we see there are two cases for a BraveIs lattice of
given parameters, (i) the equilibrium conditions cannot be satisfied, (ii) they can be satisfied. In
the latter ease there are again two cases, stability
or instability as determined by the second order terms
of the potential energy. The fulfilment of the
equilibrium conditions depends apparently on a
sufficient number of symmetry elements. The triclinlo cell leads to no equilibrium even if it is
rhombic, apart from those cases which have symmetries
(the three cubic lattices}: or a prism with a
quadratic or rhombic base, leads to no equilibrium
except for a certain ratio of the perpendicular axis
to the plane ones. Moat of the equilibrium con¬
figurations are unstable. According to our result, it
is very probable that the faee-centred lattice is the
only Bravais lattice stable under central forces.
This result seems rather trivial, as central forces
of the type considered are almost equivalent to rigid
sphere^, which arrange themselves of course in the
densest packing. The purpose of this investigation
was more to develop suitable methods which might be
applied to more complicated cases.
