  We investigate the n-body problem on a sphere with a general interaction
potential that depends on the mutual distances. We focus on the equilibrium
configurations, especially on the Dziobek equilibrium configurations, which is
an analogy of Dziobek central configurations of the classical n-body problem.
We obtain a criterion and then reduce it to two sets of equations. Then we
apply these equations to the curved n-body problem in S^3. In the end, we find
the derivative of the Cayley-Menger determinant.
