  It was proved in the first part of this work \cite{0} that Stolarsky's
invariance principle, known previously for point distributions on the Euclidean
spheres \cite{33}, can be extended to the real, complex, and quaternionic
projective spaces and the octonionic projective plane. The geometric features
of these spaces have been used very essentially in the proof. In the present
paper, relying on the theory of spherical functions on such spaces, we give an
alternative analytic proof of Stolarsky's invariance principle.
