156 BELL SYSTEM TECHNICAL JOURNAL 



R„ = /.153 - (.061 + 1.077) 



= -.061 + /.076 



which is in better agreement with the earlier values of Rh . 



No similar computations have been made to test the corresponding 

 approximation for Re obtained when the correction term (6-5) is added to 

 the leading term in (6-1). However, it appears that for a = 1/6 and the 

 representative value k = .38, (6-5) is only about one sixth as large as ia/(2k) 

 and hence is relatively unimportant. 



References 



1. S. 0. Rice, Reflection from Corners in Rectangular Wave Guides — Conformal Trans- 



formation, this issue of the B. S. T. J. 



2. S. A. Schelkunoff, Solution of Linear and Slightly Non-linear Differential Equations, 



Quart. Jl. Appl. Math., 3, 348-360 (1946). 



3. P. S. Epstein, Reflection of Waves in an Inhomogeneous Absorbing Medium, Proc. 



Nat'l. Acad. Set., 16, 627-637 (1930). 



4. K. Rawer, Electrische Wellen in einem geschichteten Medium, Ann. der Physik, 35, 



385-416 (1939). 



5. L. R. WaUicr and N. Wax, Non-Uniform Transmission Lines and Reflection Coeffi- 



cients, //. Appl. Phys., 17, 1043-1045 (1946). 



6. R. E. Langer, The Asymptotic Solutions of Ordinary Linear Differential Equations 



of the Second Order, with Special Reference to the Stokes Phenomenon, Bull. 

 Amer. Math. Soc, -10, 545-582 (1934). Many references to the earlier work are 

 given. 



7. R. E. Langer, On the Connection Formulas and the Solutions of the Wave Equation, 



Phys. Rev., 51, 669-676 (1937). 



8. R. E. Langer, The Boundarv Problem of an Ordinary Linear Differential Sj'stem in 



the Complex Domain, Trans. Am. Math. Soc, 46, 151-190 (1939). 



9. E. C. Titchmarsh, Eigen-function Transformations, Oxford (1946). 



10. H. Jeffreys, On Certain Approximate Solutions of Linear Differential Equations of 



the Second Order, Proc. London Math. Soc, (2), 23, 428-436 (1924). 



11. W. H. Furry, Two Notes on Phase Integral Methods, Phys. Rev., 71, 360-371 (1947). 



12. G. D. Birkhoff and R. E. Langer, The Boundary Problems and Developments Asso- 



ciated with a System of Ordinary Linear Differential Equations of the First Order, 

 Proc Amer. Acad. Arts and Sci.,'58, 49-128 (1923). 



13. H. E. Newell, The Asymptotic Forms of the Solutions of an Ordinary Linear Matric 



Differential Equation in the Complex Domain, Duke Math. JL, 9, 245-258 (1942) 

 and 10, 705-709 (1943). 



14. See, for example, Frank and von Mises, Differential und Integralgleichungen, Vol. 1, 



page 56, Braunschweig (1930). 



15. J. C. Slater, Microwave Transmission, page 74, McGraw-Hill (1942). 



16. Poritsky and Blewett, A Method of Solution of Field Problems bv Means of Over- 



lapping Regions, Quart. Jl. Appl. Math. 3, 336-347 (1946). 



17. Barrow and Chu, Theory of the Electromagnetic Horn, Proc. I.R.E., 27, 51-64 (1939). 



18. N. H. Frank, Reflections from Sections of Tapered Transmission Lines and Wave 



Guides, Radiation Lab. Rep. 43-17, Jan. 6, 1943. 



19. Whittaker and Robinson, Calculus of Observations, page 64, Blackie (1926). 



