A Comprehensive Fundamental Electrical Formula

Abstract

IN a letter on “Fundamental Physical Concepts” which appeared in NATURE of August 13, I suggested that it should be possible to dispense with magnetic considerations in fundamental physical theory, and to express the forces acting on elementary electric charges at rest and in uniform or accelerated motion by a single comprehensive formula ; and I was very glad to learn from Mr. Rollo Appleyard's letter in NATURE of September 17 that Sir Horace Lamb had expressed the desirability of dispensing with the duality of electricity and magnetism. Such a formula has now been worked out and may be expressed most conveniently in the form: where f is the force on a charge è moving with vector velocity V', due to a charge e moving with vector velocity V and acceleration &Vdot;' is the vector distance eè of length r; and c is the velocity of electric wave propagation in space. The charges e and è and the electric force E are in C.G.S. electrostatic units; m' is the total mass of è, including its 'electromagnetic mass'; and the square brackets imply vector products.