686 BELL SYSTEM TECHNICAL JOURNAL 



While llu' mclhod of solution employed in the second part is largely 

 that of the operational calculus, I have not hesitated to employ 

 developmcjits and extensions not to be found in Hca\iside. Fcr 

 exani|)le, the formulation of the problem as a Poisson integral ecjuation 

 is an original de\clopment which has proved quite useful in the actual 

 numerical solution of complicated problems. The same ma\- be said 

 of the Chapter on \'ariable Electric Circuit Theory. 



In view of its two-fold aspect this work may therefore be regarded 

 either as an exposition and development of the operational calculus 

 with applications to electric circuit theory, or as a contribution to 

 advanced electric circuit theory, depending on whether the leader's 

 viewpoint is that of the mathematician or the engineer. 



1 have not at li-m|)lc<l in the text to gi\-e adecjuate reference to the 

 literaturi' ol the sulijtTt, now lairU' extensive. In an appendix, 

 howe\er, there is furnished a list of original papers and memoirs, for 

 which, however, no claim to completeness is made. 



CHAPTER I 

 The Funi).\mi:nt.\i.s of Ei.f.ctkic Circuit Thkory 



While a knowledge, on the reader's part, of the elements of ekririi- 

 circuit theory will be assumed, it seems well to start with a brief 

 review of the fundamental physical principles of circuit theory, the 

 mode of formulating the equations, and some general theorems which 

 will prove useful subsequently. 



First, the circuit elements are resistances, inductances, and con- 

 densers. The network is a connected system of circuits or branches 

 each of which may include resistance, inductance and capacitance 

 elements together with mutual inductance, and mutual branches. 



The equations ol circuit theory may be established in a number 

 of different wa\s. For example, they may be based on Maxwell's 

 dynamical theory. In accordance with this method, the network 

 forms a dynamic system in which the currents play the role of veloci- 

 ties. If we therefore .set up the expressions for the kinetic energy, 

 potential energ\- and dissipation, the network etiiialions are deducible 

 from general dynamic ecjuations. 



The simplest, and for ouv jnii poses, a t|uite satisfactory basis for 

 the eciualions of circuit lluory arc found in KirchhofT's Laws. These 

 laws state that 



1. The total impressed force taken around aiu' closed loop or 

 ciicuit in the network is equal to the potential drop due to (a) resist- 

 ance, (b) inductive reaction and (c) capacitivc reactance. 



