The general expression for the voltage between the terminals A and B of the voltmeter is therefore The voltage indicated on a voltmeter of infinite input resistance is then which will be a minimum with respect to variations in M when .sx With reasonable assumptions regarding the order of magnitude of the quantities involved , it is shown in the appendix that the value of M giving minimum voltage is given by for which value of M the recorded voltage is .sx The primary and secondary coil self-capacities lead , therefore , to an apparent condenser resistance in excess of the actual , while the effect of the mutual capacity may be to increase or decrease , but generally to decrease , this value depending on the magnitude of the constants of the mutual .sx The accuracy with which r can be determined depends on the extent to which these capacity errors can be kept small in the design of the mutual .sx The value chosen for the inductance L1 of the primary coil of the mutual is bound up with the size of the test condenser C and the frequency , or wavelength , range over which measurements are to be carried out , since it must be possible to adjust the circuit L1CL3 to resonance at all desired frequencies in this range .sx This resonant condition is specified because of the need to obtain large current values in the measuring circuit for accurate recording of the required minimum voltage , and at the same time to ensure as much freedom from harmonics as possible in the working current .sx This current must further be provided with a small coupling coil L3 , if similar settings of the mutual are to serve for the provision of minimum voltmeter reading in the independent measurement at the same frequency of both condenser and primary coil resistance .sx The respective values of M in the two cases are given approximately by and L1,3 values which approach equality at resonance of the L1CL3 circuit as L3 is made small compared with L1 .sx The secondary coil inductance must now be chosen so that , when coupled to L1 , it can be arranged to give a mutual inductance M somewhat in excess of L1 .sx The value of L0 is , therefore , dependent on the chosen value for L1 and on the manner of coupling the two coils .sx Equation ( 5 ) brings out the need for keeping the coil self capacities C1 and C2 and the mutual capacity C12 , small , so that single layer construction and end-to-end coaxial location of L1 and L2 is desirable .sx With this arrangement L2 is , of necessity , much larger than L1 for the provision of the required value of mutual inductance .sx In winding the coils it is also important to ensure that their high frequency resistances , R1 and R2 , shall be small , a consideration which also makes single layer construction important .sx The details of the mutual inductance finally adopted for the purpose of making measurements on a laboratory variable .sx air condenser of maximum capacity 2000 micro-microfarads in the region of 1000 metres wavelength were as given in the following table .sx Both the primary and secondary coils were wound single layer on cylindrical paxolin former using silk covered wire .sx The effect of silk covering and the use of paxolin former on the high frequency resistance of such coils had been found previously to be small .sx The primary coil was fixed on the base of the mutual , and the secondary arranged for relative coaxial movement under coarse and vernier control .sx The latter is essential in order that there may be no difficulty in adjustment for minimum voltmeter reading .sx The vernier control was made remote so as to ensure freedom from hand capacity effects .sx In order to reduce the mutual capacity between the coils , the common point was obtained by joining their adjacent ends .sx Without introducing the complication of a calibrated amplifier , a thermionic voltmeter fulfilling the requirement of infinite input resistance does not lend itself to the accurate measurement of voltages of less than about 0.5 volt .sx For measurement of a condenser resistance of the order of 1.0 ohm , therefore , working currents up to 1.0 ampere become necessary .sx The generation of high frequency currents of this order does not offer any difficulty with the valve oscillator .sx Complete screening of the oscillator is essential , however , to ensure freedom from direct voltage injection into either the secondary coil of the mutual or the voltmeter circuit .sx As a further precaution the thermionic voltmeter was also screened , and its valve de-capped with a view to reducing its input circuit capacity .sx Since the voltage across the condenser C is many times greater than the phase component of voltage to be measured as its resistance drop , care is necessary in adjusting the circuit conditions for measurement , if damage to the volt-meter is to be avoided .sx For example , should the condenser C have a power factor of 1 10-3 , the total voltage across C is 1000 times the voltage to be measured , so that slightly incorrect adjustment of the mutual , when the measuring circuit is carrying currents of the order of 0.5 ampere , is sufficient to cause the voltmeter scale to be exceeded .sx The procedure adopted was to commence with very weak coupling of L3 to the oscillator and to tune the circuit on C to the desired wavelength with the voltmeter inoperative .sx This was possible with circulating currents of only a few milli-amperes since the thermal ammeter in use was multirange .sx On introducing the voltmeter an approach to the final adjustment of the mutual was possible without danger to the voltmeter .sx The desired working current and the final mutual setting were then attained by successively increasing the coupling of L3 to the oscillator and appropriately re-adjusting M. .sx The results of a series of measurements taken over a wavelength range of 800 to 1350 metres are given in Fig. 2 , and the condenser power factor calculated therefrom in Fig. 3 , to which further reference is made later .sx It has been shown that the resistance values of Fig. 2 are subject to an error which can be estimated from the known constants of the mutual by use of equation ( 5) .sx Taking for R1 and R2 the calculated high frequency resistances of the primary and secondary coils , a procedure which is justified by the subsequent measurements , the effect of the self capacities C1 and C2 on the apparent condenser resistance at 1100 metres is given by calculation from this equation as an increase of 0.096 ohm .sx A reliable measurement of the mutual capacity C12 is not possible , but this may be taken as small , since , at the setting for minimum voltmeter reading , the adjacent ends of L1 and L2 were more than 1.0 cm .sx apart .sx As the calculated decrease in apparent resistance per micro-microfarad of C12 is 0.016 ohm , the net error as calculated is not likely to be in excess of 0.05 ohm , which , with the condenser under test , corresponds to an apparent resistance 4 per cent .sx high .sx The effects on the apparent condenser resistance at 1100 metres of artificial increase of the self and mutual capacities in turn are shown in Fig. 4 , and are of interest in view of the mathematical expectations .sx It is seen that the nature of the effects is as predicted , although the measured change resulting from large variation of C2 is somewhat greater than that expected .sx PRIMARY COIL RESISTANCE MEASUREMENT .sx The method adopted for measurement of the primary coil resistance R1 was essentially that developed in the previous paper , and required modification of the circuit of Fig. 1 to that of Fig. 5 .sx The method consists in the measurement of the phase component of voltage across the primary coil following neutralisation of the quadrature component by appropriate adjustment of the mutual inductance M. As the mutual inductance between L1 and L2 is varied , the voltmeter reading passes through a minimum value for .sx For an ideal mutual , devoid of secondary coil resistance and self capacities , this minimum voltage gives a measure of the primary coil resistance in the form .sx When , however , these quantities are taken into account the resistance value provided is an apparent primary resistance .sx from which it is seen that C1 and C12 are responsible for positive , and C2 for a negative , error in the deduced resistance R, .sx Observance of the precautions previously discussed in connection with the construction of the mutual serve to keep these errors of small relative magnitude .sx The results of a series of measurements over the same .sx wavelength range as before are recorded in Fig. 6 , along with the curve of calculated coil resistance as derived from Butterworth's theoretical formula .sx Definite agreement occurs between the measured and calculated curves , and it is of interest to analyse the difference to determine whether it can be accounted for by the errors resulting from impurity in the mutual .sx In this case it is possible to determine the mutual capacity C12 with reasonable accuracy .sx In the circuit of Fig. 5 , the thermionic voltmeter is connected virtually across the outer .sx ends of the primary and secondary coils of the mutual , so that C12 may be taken as the capacity of the input circuit of the voltmeter .sx With the voltmeter valve de-capped , this was measured under operating conditions of the voltmeter as 10.8 micro-microfarads .sx Using the calculated high frequency values of R1 and R2 , the error due to self and mutual capacities can be calculated from equation ( 6 ) , and provides the curve of R1 in Fig. 6 .sx The agreement with the measured values is now more marked except at the lower wavelengths , where the effect of C2 in decreasing the apparent resistance appears more pronounced than has been estimated .sx The results showing the effect on the primary coil resistance of artificially increasing the self and mutual capacities in turn appear in Fig. 7 , where it is seen that the effect of C , and C12 in increasing , and of C2 in decreasing , the apparent resistance is as indicated by equation ( 6) .sx " RESISTANCE VARIATION " MEASUREMENTS .sx The primary coil of the mutual and the test condenser were finally associated , and their combined resistance measured by the " resistance-variation " method over the same wave-length range .sx The results are shown in Fig. 8 along with a curve representing the calculated primary coil resistance .sx Since this latter has been found to represent a close approach to the true resistance of the coil , the difference between the two curves may be taken as a measure of the condenser loss resistance .sx Due to the absence in these measurements of the coupling coil L3 present in the resonant circuit of the mutual method , the condenser settings at a given frequency of measurement were slightly different in the two cases , but have been recorded in the corresponding resistance-wavelength curves .sx The condenser power factor as calculated from the above results is plotted in Fig. 3 , where it is seen that good agreement occurs between the values as determined by the two methods of measurement , the difference over the frequency range concerned being never in excess of 6 per cent .sx In drawing conclusions from this agreement as to the utility of the mutual method of condenser resistance measurement,it should be remembered that the resistance values provided are virtually the sum of the condenser resistance desired and the impurity in the mutual .sx The accuracy obtainable in a measurement of the former depends , therefore , on the relative magnitude of the latter .sx Since small self and mutual capacities are inherently present in a mutual inductance , the method will always require very careful experimental development , and offer increasing difficulty with increase in frequency and when accurate measurements are attempted on condensers of very low power factor .sx Although theoretically the in- .sx dividual components of the impurity error may be made self eliminating by artificial increase of the mutual capacity C13 , this adjustment is not of practical convenience over a range of frequency , since variation of the coil resistances with frequency would demand a variable correction .sx The author's thanks are due to the authorities of the College of Technology , Manchester , for the facilities provided in the Electrical Engineering department for the carrying out of the recorded work , and to Professor Miles Walker for his constant encouragement .sx