456 KENNELLY, TAYLOR— PROPERTIES OF 



or the vector X2=^0F, is displaced from the vector .r,„=OC by a 

 phase angle equal to the angle of the primary impedance 2, which is 

 itself the angle AOC. In other words, the factor n/^ is a complex 

 quantity whose argument is the negative of that of s. Owing to the 

 presence of r.-, in the denominator of (31), the angular deviation of 

 x.^ from ix'm will be always somewhat less than the angle ^^OC of 

 z; so that the vector CE parallel to FO of secondary resonance, 

 always intersects the diameter OA at a point a little nearer to the 

 origin than the center of the main impedance circle. 



The theory also explains why a distortion loop, when the sec- 

 ondary frequency is much below the primary frequency, is very 

 small, and near to the origin on the right ; also, as the resonant fre- 

 quencies are made to approach, the loop enlarges, falling nearer to 

 the main diameter, and finally, as the resonant frequencies pass each 

 other and again diverge, the loop shrinks in size, and passes off 

 towards the origin on the left. In (29), if secondary resonance 

 occurs much above or below primary resonance, the loop due to this 

 resonance will appear remote from the diametrical point A, Zo again 

 reduces to r,, and 



Z \ S + ^2 / 



^-2=-(^7^r7j- ^mesA, (33) 



since r, is then certainly small by comparison with z, this is approxi- 

 mate to Fr^/z- ; or varies inversely as the square of the impedance 

 modulus. On the other hand, as the primary and secondary reso- 

 nances approach, z approaches r, and x., finally attains a maximum 

 possible value at Fr.^/r{r -\-r^). If r.^ = pr, this becomes 



rvo 



This shows that in order to have a secondary absorption velocity 

 nearly equal to the primary velocity, it is necessary to have the two 

 resonant frequencies n^ and n^r, nearly coincident, and p large by 

 comparison with unity ; or the secondary resistance large by com- 

 parison with the primary resistance. In such a case, if the two 

 frequencies do not quite coincide, there will be nearly zero velocity 

 and amplitude near to the secondary frequency and a maximum 

 velocity on each side of this, as in Figs. 14 and 15. 



