The analysis of electromagnetic wave propagation in a bent pipe of rectangular cross section, (x = R, x = R+a, y = 0, y = b), is based on the Maxwell field equations, expressed in cylindrical coordinates (r, 6, y) (Fig. 1). As in the case of the straight pipe,1 the time variation is given by the exponential ewhere co is the angular frequency. The angular variation is given by e~xe, where 2 is the propagation constant for the bent portion. The equations may be written In (1) He, Hr, Hy, Ee, Er and Ey are the components of magnetic and electric field, « is the electric inductive capacity, and p. the magnetic inductive capacity. The electrical conductivity, c, and charge density, p, are assumed to be zero.The field components Hr, Hv, Er and Ey may be expressed in terms of He and Ee by various combinations of the equations (1). These giveHy(Gr2) = -S rdHe/dy + rjcotEe + r2jwtdEe/dr,Er(Gr2) = -2 rdEe/dr -2 Ee + r2jundHe/dy, drLGr dr J dy2 2 dy dr * Received June 29, 1943. The paper constitutes part of a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University, May, 1943. The author wishes to thank Professor L. Brillouin of Brown University for his many helpful suggestions.