The bending of electric waves round a conducting obstacle

1. The mathematical theory of the formation of a shadow when waves impinge on an obstacle rests on an application of Huygens’ principle, which may be stated in the form that, if a closed surface S be drawn, enclosing all the sources of the waves, the circumstances that obtain at any point outside this surface at a definite time can be expressed in terms of the state of affairs at the surface S at previous times. For waves of sound, the usual analytical expression involves a knowledge of both the velocity potential of the motion and the velocity normal to the surface S at each point of it for all time; for electric waves, which may be taken to include waves of light, it requires a knowledge of both the electric and magnetic forces tangential to the surface S for all time.