340 MR. W. DUDDELL ON THE RESISTANCE AND 



above -assumptions will not be true, and the resistance as measured at such low 

 frequencies will differ from that measured at much higher frequencies. 



In order to investigate this matter, the arc was replaced by an electrolytic cell, and 

 its impedance and power-factor tested in a similar way to those of the arc, except 

 that no direct current was sent through the cell. To make the polarisation effects 

 important compared with the ohmic drop, the resistance of the cell must be small, 

 therefore sulphuric acid was chosen as the electrolyte. The cell used was a glass 

 trough 100 millims. long, 104 millims. deep, and having a mean thickness of 

 15 '53 millims. The electrodes were two platinum plates 90 millims. apart (not 

 platinised) which fitted the trough tightly and extended to the bottom. 



The mean depth of the electrolyte was 61 '6 millims. So that the liquid whose 

 resistance was measured was a rectangular parallelepiped, having a length of 

 9 centims. and a mean cross-section of 9 '5 7 sq. centime. 



The temperature was kept constant at 20 C. to within 0'1 C. during the test, by 

 immersing the trough in a water-bath. The results of the tests of the impedance 

 and power-factor at different frequencies are given in Curve VIII. 



With the above cell, neither the impedance nor the power-factor are independent 

 of the frequency at ordinary frequencies, and it is evident that the polarisation in 

 this electrolyte occurs so rapidly that it is not until the frequency is well above 

 10,000 -- per second that it is unable to follow the variations of the testing current, 

 and that the electrolyte behaves like an ordinary resistance. If the resistance of 

 this cell were tested in the ordinary way, at a frequency of about 100 -- per second, 

 the value obtained would be over twice the true resistance of the cell. 



The slight drop in impedance observed when the frequency is increased from 50,000 

 to 100,000 ^ per second is possibly due to the electrostatic capacity of the plates 

 and liquid in the cell, and to the water-bath surrounding it acting as a shunt to the 

 cell. Attempts were made to determine experimentally the exact value of this 

 correction, which indicated that it was less than 1 per cent, at 100,000 per 

 second. 



The possible errors due to polarisation, even when using alternating currents, were 

 thoroughly appreciated by KOHLRAUSCH, and in the ' Leitvermogen der Elektrolyte,' 

 by KOHLUAUSCH and HOLBORN, means are described for minimising these errors. By 

 interpolation from their results the conductivity of sulphuric acid of the same 

 density and at the same temperature as that used in this experiment is 

 0758 (ohm X centim.)" 1 , or a specific resistance of 1'319 X 10 c.g.s., which 

 confirms the value of 1'30 X 10 obtained in the present experiment at a frequency 

 of 50,000 per second. 



The fact that the power-factor is not unity at low frequencies proves that at 

 these frequencies the electrolyte does not behave like an ordinary resistance, and 

 consequently all the instantaneous values of the P.D. between the terminals of the 

 telephone sometimes used in the Kohlrausch method cannot be made to vanish at 



