X. The effect produced by an obstacle on a train of electric waves

Abstract

Integrals of the equations of propagation of electric disturbances in terms of the electric and magnetic forces tangential to any surface enclosing the sources of the disturbances have been already obtained. It is proposed in what follows to apply these expressions to obtain the effect of an obstacle on a train of electric waves. The effect of the obstacle can be represented by a distribution of sources throughout the space occupied by the obstacle, and the determination of this distribution or, as appears from the investigation referred to above, the determination of the electric and magnetic forces tangential to the surface of the obstacle due to this distribution of sources, constitutes the solution of the problem. If X', Y', Z', α', β', γ' denote the components of the electric and magnetic forces respectively at the point ξ, η, ζ, on the surface of the obstacle due to the distribution of sources inside it which represents its effect, X' 1 , Y' 1 Z' 1 , α ' 1 , β ' 1 , γ ' 1 denote the values of these quantities when t - r /V is substituted for t , where V is the velocity of propagation of the disturbances, and r = {( x-ξ ) 2 +( y-η ) 2 + ( z-ζ ) 2 } ½ is the distance of any point , x, y, z from the point ξ, η, ζ , and l, m, n are the direction cosines of the normal to the surface at the point ξ, η, ζ , drawn into the space external to the obstacle, the components of the magnetic force at any point outside the obstacle due to the obstacle.