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Xf I T. On the use of Vector Methods in the Derivation of the 

 Formulae used in Inductance and Capacity Measurements. 

 ByM. H. Poole, Sc.D.* 



I^HE various formula? used in methods, such as Anderson's, 

 for the comparison of Inductances and Capacities are 

 usually obtained in the text-books by the use of algebraic 

 methods. It does not seem to be generally recognized how 

 easily these expressions can be obtained geometrically from 

 the vector diagrams representing the currents in the various 

 arms. This method possesses the advantage of enabling a 

 better mental picture to be formed of the currents in the 

 various arms and their mutual phase relationships. 



A few examples are given here of the derivation of the 

 required expressions in some important cases. We assume 



that an alternating current generator of frequency ^— is 



used as a source, and any form of detector, such as a tele- 

 phone or vibration galvanometer. We further assume that 

 the system is balanced, i. e. that the two terminals of the 

 telephone are represented by a single point on the P.D. 

 vector diagrams, for a pure sine wave of the given frequency. 

 We find that in order that this may be true, certain relation- 

 ships must exist between the various arms, but that these 

 relationships are independent of co ; and hence, if the system 

 is balanced for one frequency, it is balanced for all. More- 

 over, as any disturbances can be resolved into sinusoidal dis- 

 turbances of suitable amplitudes and frequencies, the system 

 will be balanced for any disturbance whatever. 



This will only be the case if the inductances and capacities 

 used are independent of the frequency. This will be very 

 nearly true of inductances which do not contain iron, at 

 musical or lower frequencies, but will not be true for in- 

 ductances containing iron cores. The capacity of a condenser 

 with a solid dielectric generally varies slightly with the fre- 

 quency. This causes a slight variation in the balance for 

 the various harmonics in the rather complex wave emitted 

 by a buzzer and transformer, so that perfect silence is rarely 

 attained, and the predominant note of the telephone changes 

 its pitch in passing through the point of balance. A similar 

 effect may occur with inductances owing to the capacity 

 between different layers of windings, which may cause an 

 appreciable change in the effective inductance for the 



* Communicated by the Author. 



Phil. Mao. S. 6. Vol. 40. No. 240. Dec. 1920. 3 F 



