222 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



for this kind of degeneracy become manifold in multi-terminal devices, 

 and some degree of degeneracy is the rule rather than the exception. 

 Consider an entirely practical example: that of an amplifier chassis from 

 which the tubes have been removed.* Here the degeneracy is essential 

 and intrinsic ; it would be highly artificial to regard it as the mere acci- 

 dent of a limiting case. Tioie, given any particular degenerate network, 

 there is usually evident a method for representing or describing its be- 

 havior. What is needed, however, is a mode of representation which is 

 applicable generally to any 2w-pole without a priori knowledge of its 

 structure or peculiar degeneracies. 



2.72 The mode of representation adopted in this paper, embodied in 

 the notions of general 2n-pole (Section 4) and linear correspondence 

 (Section 6), is an obvious one, and so completely general that it solves 

 no problems other than the elemental one for which it was introduced. 

 It provides a definite mathematical construct whose properties one can 

 discuss with mathematical precision. This is all that we ask of it. 



Realizability theory begins and ends with the study of these proper- 

 ties. It would be more accurate to say that the notion of general 2/?-pole 

 describes a particular, but still very large, class of mathematical en- 

 tities; realizability theory consists in the study of certain subclasses of 

 the whole class of these entities, the particular subclasses being distin- 

 guished by special, and to us interesting, properties. 



2.73 Despite its avowed aim at generality, the paper is oriented toward 

 the realizability theory of finite passive networks. It ultimately provides 

 a proof of 1.1 and indeed a complete characterization of finite passive 

 2n-poles, however degenerate. This characterization is accomplished in 

 a sequence of postulates, each one delineating a property of general 

 2n-poles, i.e., a subclass consisting of all 2n-poles having this property. 

 The class of 2n-poles having all of these properties is then identified 

 with the class of 2w-poles obtained from finite passive networks. 



2.74 If we have succeeded here in our hope to set an adequate founda- 

 tion for the realizability theory of devices with many terminals, it will 

 be because of the nature and organization of the postulates themselves. 

 They describe what at present seem to be individually significant prop- 

 erties of 2n-poles, of progressively greater specificity, which in the 

 aggregate characterize finite passive devices. Bj' eliminating them in 

 various combinations one obtains larger classes of objects. Furtlier re- 



* It is exactly this example, and the practical need of an adequate theory for 

 it, which led the author first to study the realizability theor}- of passive multi- 

 terminal devices. 



