ABSTRACT
The classical theory of systems of one point charge can be generalized in various ways. Systems of an arbitrary but finite number of point charges will be studied and their fundamental equations will be derived from an action principle. This generalization of the one-particle system will permit us to deduce what a test charge would measure, since such a charge is a limiting case of a physical charged particle. General variations of the field and the particle variables yield conservation laws, provided the Euler-Lagrange equations of Noether's theorem are satisfied. Additional conservation laws are obtained for the free fields. The interest in the action-at-a-distance theory as stated by J. A. Wheeler and R. P. Feynman was threefold: the complete elimination of the field, the avoidance of self-energy difficulties, and the explicit symmetry in past and future, evident from.
