Some Applications of the Method of Images—I.

Solution of Some Electrostatic Problems by the Method of Images. (a) Charged Wire between Two Parallel Plates.—In Part I. of this paper the authors obtain expressions for the potentials at any point between an infinitely long charged wire and two conducting infinite planes parallel to it, for the surface density of the induced charge at any point on the plates, and for the capacity per unit length of such a condenser. These expressions contain only circular and hyperbolic functions. (b) Charged Wire Inside an Infinite Rectangular Tube.—In Part II., the potential at any point inside of the tube is obtained by a single infinite summation of the potentials due to each of a singly infinite set of images as given by the expression in Part I. Thus, although the problem is essentially one of doubly periodic functions, the solution appears in circular and hyperbolic functions. Comparing a square tube with a circular tube of the same capacity, each with a small wire of a given size through its center, the square tube has the larger perimeter. Tables are given showing the variation of the capacity of a certain rectangular tube with the size of the wire at its center and with the position of a certain sized wire. (c) Two or Four Charged Wires Inside a Rectangular Tube.—In the case of certain symmetrical positions this problem can be solved immediately from the preceding results.