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XIV. The Measurement of Small Differences of Phase. 

 By W. E. Sumpnbr, 2>.£c* 



1 VTH1LE investigating recently the behaviour of watt- 

 ▼ » meters, transformers, and similar apparatus, the 

 "writer has found it necessary to measure small phase-differ- 

 ences occurring in the working of alternating-current plant. 

 The methods hitherto available for such measurements are not 

 at all satisfactory when the angles to be determined are small. 

 Phase-meters have been constructed for commercial purposes, 

 but the angular deflexion of the pointer of these instruments 

 is. as a rule, smaller than the phase-difference to be measured, 

 so that when the latter is as small, or smaller, than one degree, 

 such instruments, even if perfectly accurate, are quite unsuited 

 for the purpose. All other known methods necessitate the 

 simultaneous reading of three instruments. The best-known 

 method needs a wattmeter, a voltmeter, and an ammeter. 

 Among wattmeters we may include all instruments of the 

 double current, or double voltage, type, whether dynamo- 

 meters, current-balances, or electrometers. In all these cases 

 the value of cos 0, where 6 is the angle of phase to be deter- 

 mined, is measured by dividing the wattmeter reading by the 

 product of the readings of the other two instruments. The 

 percentage error made in measuring cos 6 is thus greater than 

 the corresponding errors made in reading the separate 

 instruments. The method only gives fair results when the 

 angle 6 is large, and instruments of suitable range are 

 available. When 6 is small the method is hopeless, for since 

 cos 1° is -99985. and cos 0°'5 is '99996, it is clear that no such 

 method involving the measurement of three deflexions can be 

 anything like accurate enough for determining values of 

 les- than one degree. 



All other known methods are based upon the three-volt- 

 meter method of measuring power factor, or phase-difference. 

 This method has been much criticised at different times, but 

 its limitation^ were all fully pointed out in the original paper 

 (see Proc. Roy. Soc. vol. xlix. March 1891) in which Professor 

 Ayrton and the present writer first drew attention to it. It 

 is a method for measuring power, or power factor, which 

 cannot compare in ease or simplicity with the wattmeter 

 method, when a suitable wattmeter is available, and the 

 accuracy of the instrument is not in doubt. But wattmeters 

 and other alternating-current meters, owing to the absence 

 of iron-cored magnetic circuit-, are not nearly so sensitive 



* Communicated by the Physical Society: read November 'Jo, l!)i>4. 



