MEASUREMENTS AT TELEPHONIC FREQUENCIES. 99 



sistance r ohms, as indicated at BC, in Fig. i, is measured imme- 

 diately after U ^b, we have 



UBc = Ip{Ro + i^^), r.m.s. volts Z (3) 



Then 



Uab^R±JX_ 

 Ubc Ro+jXo 



numeric Z (4) 



In this way, the relative numerical values of the p.d.'s on different 

 parts of the working circuit can be evaluated, preferably in terms of 

 the p.d. on a standard resistance, without requiring a measurement 

 of the potentiometer current I p. 



As thus far described, the instrument can only measure vector 

 p.d.'s confined to a single quadrant. By means of reversing switches, 

 however, on X and on the entire potentiometer, all four quadrants 

 in the voltage complex plane can be explored. 



A more detailed description of the instrument, and of its mode 

 of operation, technique and limitations, appears in a paper by the 

 writers published* elsewhere ; so that only a brief outline of this part 

 of the subject will here be necessary, in order to present more fully 

 in this paper some of the results which have been secured with the 

 instrument, at telephonic frequencies, in the laboratory. 



Simple Series Circuit of Resistance, Inductance and Capaci- 

 tance, AT Constant Frequency and Varied Capacitance. 



In Fig. 2 the connections are shown of a simple working circuit 

 containing an inductance L of 0.8106 henry, a total resistance R of 

 3183 ohms, and an adjustable condenser C. Such a circuit may 

 briefly be described as a RLC circuit. The connections pp' to the 

 potentiometer are also indicated. The inductance L was very loosely 

 coupled with the Vreeland oscillator Osc, and the oscillator fre- 

 quency was maintained at Soo^-'. 



With the condenser C shorted ; i.e., made infinite, the poten- 

 tiometer reading on 100 ohms in r was the vector OA, as obtained 

 from rectangular coordinates in R and — jX, viz. — 22.5 — /176 mil- 

 livolts. This is indicated as a vector of 179.4 millivolts, at a slope 



* Bibliography 14. 



