MEASUREMENTS AT TELEPHONIC FREQUENCIES. 115 



capacitance c, the vector sum of Ii and Ic, corresponding thereto, is 

 equal to the value of Im then existing. IMoreover, the vector sum 

 of 00c and 00 1, which are respectively the vectors from the origin 

 to the centers of the branch current circles, is equal to 00m, the 

 vector to the center of the main current circle. 



This process of splitting a main current vector circular locus into 

 branch current circular loci can be indefinitely extended, by sub- 

 dividing the admittance of any one branch into any desired number 

 of equivalent branch admittances. Thus, by following the known 

 electrical rules of splitting admittances, a vector circular locus, fol- 

 lowed by the main current, can be resolved into any desired number 

 of component vector circular loci. 



Conversely, when a number of branch circuits, forming divisions 

 of a main circuit containing a steady e.m.f ., connect a pair of termi- 

 nals, and one of them has its impedance varied circularly, the cur- 

 rents in all will undergo circular variation in locus. The vector 

 sum of all the currents in the unvaried branches can be obtained 

 by replacing their several fixed admittances by a single joint admit- 

 tance, and determining, from electrical considerations, the vector 

 circular locus established in this joint admittance by the circular 

 variation of impedance in the outstanding branch. 



Voltage Distribution Along a Series of High-Resistance 

 Coils at 2010^. 



A series of high-resistance coils, such as a megohm box, divided 

 into a number of sections, develops an interesting electrical condi- 

 tion, when used with alternating currents, which does not obtrude 

 itself upon the attention of the observer when such resistances are 

 used in continuous-current tests. This condition is a superposed 

 alternating-current distribution in the coils, due to their distributed 

 capacitance and the relatively high a.-c. potentials which are im- 

 pressed upon their terminals. In the continuous-current case, the 

 capacitances and applied potentials are present, but the charges are 

 fixed, and these do not interfere with the testing current. The a.-c. 

 phenomenon has been noticed and studied, but does not appear to 

 have been presented in the light of potentiometer measurements. 



