Electromagnetic waves in a perfectly conducting tube

The problem of waves in conducting tubes has already been treated by various authors. Nevertheless, the solutions here proposed, offering certain peculiarities with respect to the velocity of the corresponding waves, and partly also with respect to the shape, and distribution of the lines of force, seemed worthy of notice. Let z be measured along the axis of an infinite right cylindrical tube of circular section. The material of the tube is assumed to be a perfect conductor, its interior being empty or filled with air. The electromagnetic waves will be assumed throughout to be axially symmetrical and of permanent type, i. e. to conserve all their features while proceeding along the tube.