514 



Mr. W. Duddell. On the Resistance and 



true resistance. In fact, frequencies up to 120,000 periods per second 

 were finally used. Owing to experimental difficulties in employing 

 the above method with much higher frequencies, a fresh method was 

 adopted. 



Basis of Method adopted. 



An apparatus A is considered which has resistance and E.M.F., but 

 no self-induction, or capacity, and through which a steady current is 

 flowing. There is mixed with the steady current an alternating testing 

 current. It is shown that, if the apparatus A possess a true resistance, 

 and if the frequency of the testing current be such that the conditions 

 of the apparatus are not in any way changed by it, then the resistance of A 

 will be a constant over the range of variation of the current, and 

 equal to the impedance of A to the superposed alternating current. 



A criterion that the apparatus A has a constant resistance is that the 

 power factor of A with respect to the alternating testing current must 

 be unity. It is concluded that in order to prove that the arc has a 

 true resistance and to find its value it is necessary to show : — First that 

 it is possible to find a value of the frequency of the testing current for 

 which the power factor of the arc with respect to this current is unity ; 

 second, that the power factor remains unity and the impedance con- 

 stant, even when the f requency*is greatly increased above this value ; 

 thirdly, to determine the value of the impedance of the arc under 

 these conditions, which will be its true resistance. 



Method of Measuring the Impedance and Power Factor. 



Owing to the high frequency of the testing current finally used, viz., 

 120,000 periods per second, it was difficult to devise a satisfactory 

 method of measuring the impedance, and power factor ; wattmeters and 

 dynamometers could not be used, as at these high frequencies' their 

 windings behaved more like insulators than conductors, owing to their 

 self-induction. The method finally adopted was the well-known three 

 voltmeter method, for which three pieces of special apparatus were 

 used — 



(1) An alternator to produce the high frequency currents. 



(2) A new measuring instrument called a " Thermo-galvanometer " to 

 measure the three voltages. 



(3) A standard resistance with which the impedance of the arc was 

 compared, which had a time constant of only 2*7 x 10~ 7 second. 



The High Frequency Alternator. 



The alternator is of the inductor type ; it was belt driven from two 

 discs by means of a figure of 8 drive, each disc being separately belted 

 to the source of power so as to balance, as far as possible, the pull on 



