166 Measurement of Small Differences of Phase. 



used to step up the volts from Y x to V 2 , the other to step down 

 from V 2 to V 3 . The arrangement of the circuits is shown in the 

 diagram at the top of fig. 4. A noninductive resistance was put 

 across Y ly and the phase- difference between Y x and Y s was 

 tested by the two-voltmeter method already described. The 

 phase-difference found is for the double transformation and is 

 approximately twice that for each transformer. The load for the 

 first curve was composed of lamps, and is noninductive ; that 

 for the second curve consisted of a hedgehog transformer, the 

 secondary of which was, for the first test, open-circuited, but 

 afterwards closed through a number of lamps in parallel. 

 The primary took a current of nearly 25 amperes at a power 

 factor of 0*09 when the secondary was open- circuited ; but as 

 the lamp-load on the latter was increased the primary current 

 and power factor each rose. The voltages Y 1 and V 3 used, 

 instead of being about 100 at 100 cycles, for which the trans- 

 formers were designed, were about 50 volts at about 50 

 cycles, so that the magnetic fluxes in the cores were about 

 the same as if the normal voltages and frequencies had been 

 used. The full-load current is 30 amperes for each of the 

 low-voltage coils. The phase-difference between Vi and V 3 

 for the two transformers with the second on open circuit, is 

 only 0*109 degree or O054 degree per transformer. For a 

 noninductive load it increases regularly with the current. 

 For the full-load current of 30 amperes it is 9*4 degrees, and 

 for 50 amperes it is 11*5 degrees. For the inductive load 

 there was a remarkable, and sharply defined, minimum of 

 0*36 degree for a current of 25*5 amperes at low-power 

 factor. This minimum was carefully tested. It occurred for 

 a small load on the secondary which could be varied very 

 gradually, the corresponding change in the primary current 

 being only just measurable. For larger loads on the secondary, 

 and therefore for power factors approaching unity as the 

 current increased, the phase-difference curve is seen to 

 approach that corresponding with a noninductive load. The 

 portion of the curve for small inductive currents was not 

 tested owing to the absence of a suitable load, but two 

 special tests were made for lower currents at a power factor 

 of about 0*1, as shown on the dotted portion of the curve, 

 which of course must have the same starting-point for zero 

 current as the curve for noninductive load. ]n all pro- 

 bability the dotted part of the curve denotes a u leading " 

 condition of current, and the rest of it a " lagging" state of 



current 



In conclusion the writer desires to express his thanks to 

 Mr. David Owen for much valuable assistance in carrying 

 out several of the measurements above referred to. 



