MEASUREMENTS AT TELEPHONIC FREQUENCIES. 113 



Finally, the vector OQ' represents the maximum impedance of 

 2357 'x 20°. 26'. 49" ohms. It is in cophase with the vector OP of 

 apparent resonance. 



If we invert the impedance graph L'P'H'Q' with respect to the 

 origin O, by plotting reciprocals of the corresponding vectors, we 

 obtain the total admittance graph of Fig. 90?. This pursues the cir- 

 cular locus IpkJun, as c varies from o to x. This may also be re- 

 garded as a main current graph to a suitable scale of amperes, with 

 the voltage at reference phase OG. The vector admittance and cur- 

 rent will have a maximum at Op, the point of apparent resonance, 

 cophase points at k and h, minimum at q and local internal reso- 

 nances of the Ic loop at ^i and s. 



Fig. yb shows the circular locus observations in the main current 

 corresponding to Fig. gd; while Fig. 8, deduced from yh, corre- 

 sponds to Fig. 9c. It is therefore brought out experimentally, with 

 the new potentiometer, what has perhaps hitherto been known only 

 in abstract theory, that the variation of pure reactance in a branch 

 circuit gives rise to circular-locus current variations in the main 

 circuit. 



The experimental case, presented in Fig. 7, corresponds to that 

 of a radio receiving system, in which L and C correspond to the 

 antenna path to ground. The loop circuit Ic then corresponds to 

 an oscillation circuit conductively connected with the antenna, c 

 being tuned to bring about maximum antenna current. 



Composition and Resolution of Vector Circular Loci. 



The vector loci of current in the fixed inductance / and the con- 

 denser c, as the latter is adjusted from zero to infinity, are presented 

 in Fig. yc. These take the form of circles marked respectively /? 

 and Ic- The vector sum, /„,, or main current in the circuit LC of 

 Fig. ya, is reproduced from Fig. yb to e.m.f. standard phase. It 

 may be noted that in these three circles the maximum or diametral 

 values of current strength occur at dififerent condenser settings. Im 

 has its maximum near f ^0.5/xf., Ii near 0.7 /xf., and Ic near 0.9 /^f. 



It has already been shown that the circular variation of impe- 

 dance in the condenser, by reason of its adjustment, gives rise to a 



PROC. AMER. PHIL. SOC, VOL. LVUI, H, JULY 22, I9I9. 



