

[ 35 ] 



III. On the Theory of the Oscillations in Three Coupled 

 Electric Circuits. By L. C. Jackson, B.Sc* 



Introduction. 



THE problem of two coupled electric circuits has been 

 the subject of a considerable number of investigations 

 both from the experimental and theoretical standpoint. The 

 question has been attacked fro in the theoretical point of 

 view by J. v. Greitler, A. Overbeck, V. Bjerknes, P. Drude, 

 F. Kiebitz, and others. The corresponding problem of 

 three coupled electric circuits does not seem to have 

 received any very great amount of attention. Apart from 

 the work of B. Macku t and E. Bellini J, the literature 

 of the subject is very scanty. 



In view of the growing importance of the use of systems 

 containing three coupled circuits in wireless telegraphy and 

 for the determination of various physical constants §, it 

 seems desirable that the question should receive further 

 investigation. 



The purpose of the present paper is to obtain a solution 

 •of the problem by a simple method not involving any 

 considerable amount of complicated mathematical analysis. 



Notation. 

 The following notation will be used throughout the present 

 work : — 



Li, L 2 , L 3 = Self-inductances of circuits 1, 2, and 3 

 respectively. 

 M 12} M 23 , M 31 = Mutual inductances between circuits 1 

 and 2, 2 and 3, 3 and 1 respectively. 

 C 1? C 2 , C 3 = Capacities in circuits 1, 2, and 3, 

 R l5 R 2 , R3 = Resistances of circuits 1, 2, and 3. 



e u e 2i e z = Charges on condensers in circuits 1, 2, 



and 3. 

 ^1? h-> h — Currents in circuits 1, 2, and 3. 

 a, /3, 7 = Coefficients of coupling. 

 I, m, n = Frequencies of the simple oscillations in cir- 

 cuits if entirely separate from each other. 

 p, «>!, g) 2 j w 3 = Frequencies of oscillation in coupled 

 circuits. 

 q, r, s = Damping factors. 

 9 <£, yfr .= Phase angles. 



* Communicated by the Author. 



1- Jahrbuch der Drahtlosen Telegraphie, iv. pp. 188-195 (Dec. 1910). 

 \ * Electrician/ lxxxv. p. 78 (July 1G, 1920). 



§ Cf. J. H. Vincent, Proc. Phys. Soc. vol. xxxii. pp. 84-90 (Feb. 1919) ; 

 andL. Pungsand G. Premier, Phys. Zeits. xx. pp. 543-545 (Dec. I, 1919), 



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