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It is necessary at the outset of this lecture to I apologize to this assemblage of mature theoreticians for talking about an essentially engineering subject. My excuse for doing so is that whereas my subject represents one of the most important current applicaI tions of the theory of linear graphs, it is all too clear I from the literature that a number of misconceptions about it are be ing passed along from person to person. A word of warning is in order also. The subject I am to discuss is like a multifaced ge m in that it has many facets , eac h of which can add to an appreciation of the beauty of the whole objec t. Indeed whole books have been written on a r es tricted aspect of the total subject; the application of linear graphs to electric networks for example . This being the case, it is foolish to think that I can give a definitiv e exposition of the subjec t in less than an hour. At most, it will be possible only to touch upon those ideas and concepts whic h either are rather basic or are often overlooked by so me people who use the techniques . It is well at the outset to bear in mind that the theory oflinear graphs is used, in the application under discussion, as an aid, and as a unifying co ncept in the analysis of what can be called hereafter, an engineering sys tem. In particular, the techniques are applicable to those engineering systems which can be described, with adequate precision, by a finite number of physical variables. This limitation assures us that we shall be dealing only with finit e linear graphs as will become more evident later. These remarks suggest, or rather demand, that we look carefully at engineering analyses and extract from them those concepts and operations that are pertinent to the problem at hand. By thi s it is meant that our problem is to justify, in so me logical fashion, just how the properties of linear graphs, whic h after all are only lines on a sheet of paper, can be used in a meaningful way in the analysis of a finite engineering sys tem. Surely no one in thi s audience believes that a linear graph drawn on the blackboard in thi s room and, say, a motor-ge nerator down th e hall are the same object. And surely more than one person here is wondering why such a trite remark has been made. There are two reasons. In the first place some trite remarks emphasize fundamental concepts.

On the connection between properties of oriented linear graphs and analyses of lumped physical systems