This paper is about the field of
force in three dimensions due to particles that repel according to the inverse-distance
law, the analog of the field in the complex plane used by C. F. Gauss in studying the
zeros of the derivative of a polynomial. In particular it deals with the analog in three
dimensions of Jensen’s theorem and related theorems in the plane, shows
that the positions of equilibrium in the field of force when the total mass is
zero are invariant under spherical transformation, and gives a geometric
construction to find the force due to an axially symmetric distribution of
matter.
