766 Dr. Fleming on the Determination of the 



Then, eliminating I 1? Lj, Y lf V 2 , we have 



V 4 2 ^L^CgLg 1 



Hence 



p2= 2CA(L7L7^M 2 ) * ( C i L i + G 2 "L 2 ) + •(Cf 1 L l -CiI*)»+4C l C i M»J 



Suppose now that the two circuits have independently and 

 separately the same oscillation constant or same natural time- 

 period T . ^ Then 0^=0^2 = 01^, and if we call k the co- 

 efficient of coupling so that M 2 = FL 1 L 2 , we have for the 

 value of p 2 the expression 



2_J_ 1±* 



Hence if k has a value different from zero, there will be two 

 oscillations of different frequency induced which have fre- 

 quencies given by the equations 



i 



where n = l/27r \/CL is the natural frequency of each circuit 

 separately. Consequently 



n\(l-k) = n* t n 2 2 (l + k) = n 



are two equations which determine the relation of the com- 

 ponent frequencies of the complex oscillation set up when 

 two circuits of equal natural time-period are inductively con- 

 nected. It is evident therefore, that if a circuit has in it oscil- 

 lations of a certain frequency w , and we couple it inductively 

 with another circuit which can be adjusted to have the same 

 oscillation constant ( VCL) ; in order that oscillations of only 

 one single frequency equal to n should be induced in this 

 adjustable circuit, it is essential that the coefficient of coupling 

 k of the two circuits should be very small. Otherwise two 

 oscillations of different frequency are excited, the frequency 

 of one being greater and that of the other being less than that 

 of the free independent original frequency n it is desired to 

 determine. 



In the form of cymometer here described, this necessary 



