1134 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



change of state may be the weak magnetization of an originally un- 

 magnetized specimen occupying a substantial part of the structure, or 

 the introduction of a very small specimen with arbitrarily large mag- 

 netization into the originally empty structure. Under the heading, 

 "Small Magnetization — Arbitrary Sample-Size," we shall discuss the 

 propagation constant for a pencil of ferrite of any radius, coaxial with a 

 cylindrical waveguide, the space between guide wall and pencil being 

 filled wth an isotropic medium whose dielectric constant equals that of 

 the ferrite. This is discussed in preparation for the practically more 

 important case of a ferrite pencil of any radius in an air-filled guide. Here 

 the unperturbed state of the system, when the pencil is unmagnetized 

 and therefore isotropic, is already rather complicated and recjuire some 

 preliminary calculations. Under the heading "Small Sample-Size — Ar- 

 bitrary Magnetization," we consider the case of a thin pencil of ferrite 

 in an originally empty guide. 



Another topic, not easily treated except by perturbation methods, is 

 that concerning end effects in samples of finite length. After a prelim- 

 inary discussion of internal reflections in an extended slab of ferrite (a 

 problem which can be treated rigorously), two cases are considered: a 

 ferrite slug of arbitrary length, closely fitting a cylindrical guide, and a 

 thin disc normal to the guide axis, of arbitrary size. In these cases in- 

 terest centers around the effect of sample length on Faraday rotation, 

 though for the ferrite slug a subsidiary effect, that of mode conversion, 

 is also mentioned briefly. 



It should be emphasized that the perturbation methods employed here 

 are not in themselves novel. They are standard to most linear eigenvalue 

 problems of physics, and have been used in connection M'ith electromag- 

 netic problems by many authors. 



The remainder of the paper is devoted to a discussion of a ferrite-filled 

 "cable" in plane parallel form, using the methods of Part I. The treat- 

 ment is kept in terms of saturation magnetization and magnetizing field, 

 and is based on Polder's equations. The paper concludes with an adden- 

 dum to Part I, which reports some calculations and graphs of field pat- 

 terns in a cylindrical waveguide completely filled Avith ferrite. 



1. PERTURBATION METHODS 



1.1 General Method 



A number of authors have made applications of perturbation theory 

 to the problems of propagation in gyromagnetic media and the exposi- 

 tion w^hich follows is included mainly for completeness. We shall develop 

 the subject in the follo^\ing fashion: it ^^^ll be supposed that the unper- 



