(13) 



502 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



the usual case of the Tesla coil, where only the longer oscillation 

 plays much part. For a further treatment of this example, the 

 reader is referred to articles by Oberbeck* and Bliimckef. 



We shall now consider the forced oscillation. Let there be 

 an impressed force JE cos wt in the primary circuit, there being 

 none in the secondary. Then we have for the secondary 



= 

 1 



+ i^ 

 The amplitude of the secondary current / 2 (0) = co . \ a 2 \ is 



We get resonance when co 2 is one of the roots of the quadratic 



In case there is no condenser in the secondary, we have 

 and there is then but one frequency for resonance, 



<'5> "^.(ZA-jfy 



This is the practical case of a transformer or induction coil, and 

 is treated by J. J. Thomson in his Recent Researches in Electricity 

 and Magnetism, Chapter VI., to which the student is referred for 

 further examples of this subject. For a treatment at length of the 

 subject of oscillations, the student may consult Rayleigh, Theory 

 of Sound, Chapters IV, V. and X.B, and Routh, Advanced Rigid 

 Dynamics, Chapter II. 



* Oberbeck. "Ueber den Verlauf der electrischen Schwingungen bei den Tesla'- 

 schen Versucken." Wied. Ann. 55, p. 623, 1895. 



t Bliimcke. "Bemerkung zu der Abkandhmg des Hrn. A. Oberbeck." Wied. 

 Ann. 58, p. 405, 1896. 



