The paper deals with the problems which arose in the adaptation ofthe Schering bridge network for service at radio frequencies, anddescribes the finalform taken by the arrangement of components, screened high-frequencysource, and screened detector-amplifier, which has given a satisfactory performance at frequencies as high as 1 million cycles per sec. The steps which had to be taken to ensure a simultaneity of the main and the auxiliary bridge balances and to expedite the convergence of the succession of balances upon the final simultaneousbalance are explained.An account is given of the modifications which have been introduced into the well-known Schering bridge network, and of the provisions which had to be made in the disposition and the linking-up of the component parts to render the bridge capable of precision measurements.The arrangement described is essentially an equal-arm bridge composed of two capacitance arms, two resistance ratio-arms, and two auxiliary resistance ratio-arms, the latter forming part of a Wagner earthing system. The resistance arms are provided with condensers in parallel for phase-angle adjustments. Tappings are brought out in the main arms which permit of a choice of resistance for the whole arm and for the fraction across which the condensers are shunted. The artifice of connecting the power-factormeasuring condenser across only a fraction of the main resistance was adopted in order to supply a means of maintaining the changes of capacitance which are required when dealing with a large variety of power-factor differences over a large range of frequencies, always of the same convenient order of magnitude.The procedure followed in the measurements is strictly one of substitution of a variable air condenser for an actual, or an effective, capacitance of approximately the same value. Apparatus such as coils are tested in series or in parallel with such a value of the capacitance in the arm as brings the effective capacitance of the composite arm to the value required for a bridge balance. Observations are taken of the change in reading of the standard air condenserand of the difference in setting of one of the power-factor-measuring condensers required by the inclusion and the exclusion of the impedance under test. From these two differences the two components of the impedance may be computed. In the case of condensers, the condenser is replaced by the variable air condenser. The capacitance is obtained directly from the settings of the latter. The power factor is derived from the formulaΔθ = 1/ρ2RΔCωKT/KSwhere R is the resistance of the ratio-arm, and 1/ρ is the fraction across which the differenceΔCis observed.KTrepresents the total capacitance forming the arm, andKSthe substituted capacitance under test. The corrections to the simpler formulæ, when the ratio-arms and the arm under measurement possess large phase angles, are discussed and evaluated. In order to reduce the phase angles of the resistance arms to a minimum, the latter have been provided with a shield, independently earthed, in preference to a separate screen connected to their common point.The successful performance of the arrangement is to be attributed in the first place to the attention which has been given to the design of the high-frequency screened source and of the detector-amplifier, and secondly to the arrangement of the component parts of the network and of the system of wiring which has been developed. .The adoption of toroidal forms for the tuning coils of the source and of the high-frequency stage of the amplifier, together with the screening arrangements employed, has practically eliminated all stray inductive and any capacitative coupling between the source and the bridge arms or the amplifier, respectively. Reversal of the leads from the source at 1 million cycles per sec. affects the power-factor balance by only 0.000002.In approaching the final balanced state of the bridge, the usual procedure is followed of adjusting two vectors in the main network for a balance of the main bridge, alternately with the adjustment of two vectors in the Wagner earthing system for balance of the auxiliary Wagner bridge. In practice a large number of alternations have to be made. The fewer that are necessary, the more convergent is the balancing process. The entry of parasitic voltages into the detector system (which is inconsistent with a condition of simultaneous balance of both systems) was found to retard the process very seriously, and when the impedances composing the bridge arms exceeded a certain value the process even became divergent. Consequently, the detector points of the main bridge, and the Wagner bridge, respectively, have been brought close together, and the whole detector circuit has been so designed as to contain no open loops. All exposed points in the amplifier have also been carefully screened. In order to ensure satisfactory conditions for convergence it became necessary to connect the filament of the input stage of the amplifier to the detector point located at the junction of the capacitance-arms. The grid is therefore transferred between the two remaining detector points in the course of the balancing alternations. It was discovered that the convergence could be regulated and further improved by the suitable choice of a resistance which is inserted across these detector points at the amplifier end. The bridge thereupon became easily workable, and the balance was found to be almost independent of the values of the impedances connecting the detector points to earth. The potentials of all three detector points are therefore very close to earth potential.In its present form it is considered that the bridge arrangement is capable of measuring, to an accuracy of 1 per cent, power factors lying between the limits 0.001 and 0.1, and differences in power factor of precision air condensers to an accuracy of 0.00001 at all frequencies up to 1 million cycles per sec.The paper concludes with a list of a.c. measurements for which the bridge is recommended.A solution of the general bridge equations, taking account of impedances from all four corners of the network to earth, is included as an Appendix.