Galvanometer for Alternate Current Circuits. 313 



frequency can be represented by the measured values of the 

 quantity (3) for a deflexion of 200 mm. If this quantity 

 when multiplied by 10,000 be called Q, then for the arrange- 

 ment »i = 4000, n — 200, the value of Q is 1*62 for 50 cycle 

 circuits, 1/61 for 100 cycle circuits, and 1*73 for 25 cycle 

 circuits. That is, the deflexion for a given value of V 2 is 

 essentially the same for all frequencies above 50 cycles per 

 second, but is 6^ per cent, less if the frequency is dropped 

 to 25 cycles per second. For the arrangement m = 200, 

 7i= 4000, a change of frequency produces greater effect. The 

 deflexion for a given value of "V 2 is 5*2 per cent, greater for 

 100 cycles, and 18*6 per cent, less for 25 cycles, than it is for 

 50 cycles. When the main coil is used for both voltage and 

 condenser (m = ?i = 4000) there is no appreciable change of 

 constant for frequencies between these limits. 



The effect of frequency on the value of Q is mainly due to 

 the phase error represented approximately by the ratio of 

 resistance to impedance of the coil to which the voltage is 

 applied. This ratio on 50 cycle circuits is 2*6 per cent, for 

 the 4000 turn coil, and 10*6 per cent, for the 200 turn coil. 

 But Q is also affected by slight amounts of magnetic leakage 

 (between the windings) dependent on the arrangement of 

 coils used. Other properties of the magnet are deducible 

 from the data that on 50 cycle circuits the power factor of 

 the magnetizing coil is 0'14 ; the ampere turns needed for the 

 magnet are 6 u ; and the flux density in the iron is 80 u ; 

 where u is the number representing the voltage applied per 

 1000 turns, or the millivolts per turn. For special uses of 

 the instrument the phase error of the magnet can be reduced 

 by applying a suitable condenser direct to one of the field 

 windings. Thus the power factor of the 200 turn coil can 

 be raised to unity on 50 cycle circuits by applying a condenser 

 of 1*1 m.f. to the 4000 turn coil, the ratio of resistance to 

 impedance is reduced from 10*6 per cent, to 1*5 per cent., 

 and the phase error is reduced to zero. 



Use with Null Me t hods. 



Figs. 2-7 illustrate the ordinary bridge methods for com- 

 paring inductances and capacities. In these methods a 

 ballistic galvanometer is used as an indicator, and to test the 

 balance the current A through the arms of the bridge is made 

 or broken by a key. The equation representing the condition 

 for inductive balance is indicated in each case beside the 

 figure. The zero deflexion condition for steady currents 



Phil. Mag. S. 6. Vol 20. No. 116. Aug. 1910. Y 



