Coefficient of Coupling of Oscillation Transformers. 765 

 The measured values were as follows : — 





Li= 



= L + 2M + N = 62576 centims 





L 2 = 



= L-2M + N=49621 „ 

 N =55445 „ 



Whence we 



have M =3239 „ 



and 





L + N =56098 „ 



therefore 





L =653 



and 





N =55445 „ 



Therefore 





M/^/LS =0-54 



The coupling would therefore be called " close/' as it is usual 

 to call the coupling " close " or " tight " when the coefficient 

 exceeds 0'5, and " loose " when it is smaller. 



The theory of the instrument is involved in that of oscillation 

 transformers generally. The case of two inductively coupled 

 circuits, each consisting of an inductance of negligible 

 resistance placed in series with a condenser has been fully 

 treated by A. Overbeck *. It has also been discussed by 

 G. Seibt. If we assume, as we may do, that all the currents and 

 electromotive forces vary in simple sinoidal manner, we may 

 employ complex quantities to represent the vectors with which 

 we are concerned. Suppose then that V represents the 

 potential-difference of the condenser-plates, I the current in 

 the circuit, whilst C, L, and M denote the capacity, induct- 

 ance, and mutual inductance. The symbols stand for the 

 maximum values of the periodic quantities, and suffixes 1 or 

 2 have reference to the primary or secondary circuits. Then 

 neglecting the energy dissipation by resistance we can write 

 the vector equations connecting these variables and constants 

 for the two circuits in the form 



V 2 +.;>L 2 T 2 + i ;pMI 1 =0, 



I 2 =.;>C2V 2 , 



where j has the usual significance of the sign of perpendicu- 

 larity, and p = 27r times the frequency. 



* See A. Overbeck, Wied. Ann. der Physik, vol. lv. p. (327 (1895). 



Phil. Mag. S. 6. Vol. 9. No. 54. June 1905. 3 E 



