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XVII. The Construction of Non-inductive Resistances. 

 By Prof. W. E. Aykton, F.B.S., and T. Mathek*. 



[Plate IV.] 



WITH all electric methods devised for measuring the 

 power given by a varying current to a circuit that 

 may possess inductance or capacity it is necessary to employ 

 a resistance which shall have zero inductance, consequently it 

 is important to consider how such resistances may most easily 

 be made. 



If the inductance of this nominally non-inductive resistance 

 be not zero, the error thus introduced into the measurement 

 can still be made relatively unimportant if the time-constant 

 of this portion of the circuit be made small. For, as shown 

 by Dr. Sumpner and one of us, in a paper j read before this 

 Society on June 12th of this year, the following proportion 

 holds true in all the nine methods of measuring power there 

 considered: — 



the watts as measured _ 1 + tan 6 . tan <fi 

 the true watts 1 + tan 2 <f> ' 



where 6 and <f> are the angles of phase-difference between the 

 current and the P.D. for the circuit the power given to which 

 we desire to measure, and for the auxiliary circuit respectively. 



Now for any given configuration of a circuit, the time- 

 constant will be the smaller the higher the specific resistance 

 of the conductive material ; hence it is very desirable to use a 

 material of high specific resistance, like carbon. For this 

 reason, glow-lamps constitute valuable small time- constant 

 resistances, but carbon has the disadvantage that its resistance 

 varies rapidly with temperature. Hence, since with the 

 methods of measuring power referred to it is necessary to 

 know the resistance of the non-inductive circuit at the moment 

 of making the measurement, it follows that if carbon be 

 employed an extra measurement has to be made. 



When the non-inductive resistance is put in series with the 

 circuit the power given to which we desire to measure, as, for 

 example, with the three-voltmeter method of measuring power, 

 a measurement of the resistance of the glow-lamps merely 

 means the reading of an extra instrument at the moment the 

 power-test is made ; but when the two circuits are joined in 

 parallel, as, for example, with the one-voltmeter and two- 

 ammeter method of measuring power, a measurement of the 



* Communicated by the Physical Society : read June 26, 1891. 

 t "Alternate Current and Potential Difference Analogies in the 

 Methods of Measuring- Power, ' Phil. Mag. August 1891, p. 20-i. 



