Heaviside's Proof of His Expansion Theorem

Heaviside's proof of his celebrated Expansion Theorem, found scattered in his ``Electrical Papers,'' is reconstructed. It is based upon his so-called ``conjugate theorem.'' also discovered independently by Routh, which establishes a relation between any two normal modes of oscillation of a dynamical system. Heaviside's argument applies to systems having finite number of degrees of freedom and no repeated or null roots of the determinantal equation of the system. The relation between Heaviside's, Carson's and Wagner's proofs is also pointed out.