The electrometer and its connections are charged to a potential V₁ by a battery, and the deflection d₁ of the needle is noted. By means of an insulated key, the capacity of the standard condenser is added in parallel with the electrometer system. Let V₂ be the potential of the system, and d₂ the new deflection.

Then

A simple standard capacity for this purpose can be constructed of two concentric brass tubes the diameters of which can be accurately measured. The external cylinder D (Fig. 19) is mounted on a wooden base, which is covered with a sheet of metal or tinfoil connected to earth. The tube C is supported centrally on ebonite rods at each end. The capacity is given approximately by the formula

where b is the internal diameter of D, a the external diameter of C, and l the length of the tubes.

The following method can be used in some cases with advantage. While a testing vessel is in connection with the electrometer, a sample of uranium is placed on the lower plate A. Let d₂ and d₁ be the number of divisions passed over per second by the needle with and without the standard capacity in connection.

This method has the advantage that the relative capacities are expressed in terms of the motion of the needle under the actual conditions of measurement.

69. Steady deflection method. The methods of measurement previously described depend upon the rate of angular movement of a suspended gold-leaf or of an electrometer needle. The galvanometer can only be employed for measurements with intensely active matter. A need, however, has long been felt for a method in which ordinary ionization currents can be measured by means of a steady deflection of an electrometer needle. This is especially the case, where measurements have to be made with active substances whose activity alters rapidly in the course of a few minutes.

A simple calculation shows that the resistance required is very great. Suppose, for example, that a current is to be measured corresponding to a rate of movement of the needle of 5 divisions per second, with a sensibility of 1000 divisions per volt, and where the capacity of the electrometer system is 50 electrostatic units. This current is equal to 2·8 × 10^-13 amperes. If a steady deflection of 10 divisions is required, which corresponds to a rise of potential of the system of ¹⁄₁₀₀ of a volt, the resistance should be 36,000 megohms. For a deflection of 100 divisions, the resistance should be 10 times as large. Dr Bronson^[109], working in the laboratory of the writer, has recently made some experiments in order to devise a practical method for measurements of this character. It is difficult to obtain sufficiently high and constant resistances to answer the purpose. Tubes of xylol had too great a resistance, while special carbon resistances were not sufficiently constant. The difficulty was finally got over by the use of what may be called an “air resistance.” The arrangement of the experiment is shown in Fig. 20.

The electrometer system was connected with the upper of two insulated parallel plates AB, on the lower of which was spread a layer of a very active substance. An active bismuth plate, coated with radio-tellurium, which had been obtained from Sthamer of Hamburg, proved very convenient for this purpose.

The lower plate B was connected to earth. The charge communicated to the upper plate of the testing vessel CD and the electrometer system leaked away in consequence of the strong ionization between the plates AB, and a steady deflection was obtained when the rate of supply was equal to the rate of discharge.

This air resistance obeyed Ohm’s law over a considerable range, i.e. the steady deflection was proportional to the current. It is advisable, in such an arrangement, to test whether the deflection is proportional to the ionization current over the range required for measurement. This can readily be done by the use of a number of metal vessels filled with a constant radio-active substance like uranium oxide. The effect of these, when placed in the testing vessel, can be tested separately and in groups, and in this way the scale can be calibrated accurately.

The plates AB were placed inside a closed vessel to avoid air currents. The contact difference of potential between the plates AB, which shows itself by a steady deflection when no radio-active matter is present in CD, was for the most part eliminated by covering the surface of the plates A and B with very thin aluminium foil.

This method proved very accurate and convenient for measurement of rapid changes in activity, and possesses many advantages over the ordinary rate-method of use of an electrometer. A thin layer of radium of moderate activity would probably serve in place of the radio-tellurium, but the emanation and the β and γ rays emitted from it would be a possible source of disturbance to the measurements. The deflection of the electrometer needle in this arrangement is independent of the capacity of the electrometer system, and thus comparative measurements of current can be made without the necessity of determining the capacity in each case.

70. Quartz piezo-electrique. In measurements of the strength of currents by electrometers, it is always necessary to determine the sensibility of the instrument and the capacity of the electrometer and the apparatus attached thereto. By means of the quartz piezo-electrique devised by the brothers MM. J. and P. Curie^[110], measurements of the current can be made with rapidity and accuracy over a wide range. These measurements are quite independent of the capacity of the electrometer and external circuit.

The essential part of this instrument consists of a plate of quartz which is cut in a special manner. When this plate is placed under tension, there is a liberation of electricity equal in amount but opposite in sign on the two sides of the plate. The plate of quartz AB (Fig. 21) is hung vertically and weights are added to the lower end. The plate is cut so that the optic axis of the crystal is horizontal and at right angles to the plane of the paper.

The two faces A and B are normal to one of the binary axes (or electrical axes) of the crystal. The tension must be applied in a direction normal to the optic and electric axes. The two faces A and B are silvered, but the main portion of the plate is electrically insulated by removing a narrow strip of the silvering near the upper and lower ends of the plate. One side of the plate is connected with the electrometer and with the conductor, the rate of leak of which is to be measured. The quantity of electricity set free on one face of the plate is accurately given by

where L is the length of the insulated portion of the plate, b the thickness AB, and F the weight attached in kilogrammes. Q is then given in electrostatic units.

Suppose, for example, that it is required to measure the current between the plates CD (Fig. 21) due to some radio-active material on the plate C, for a given difference of potential between C and D. At a given instant the connection of the quadrants of the electrometer with the earth is broken. The weight is attached to the quartz plate, and is held in the hand so as to apply the tension gradually. This causes a release of electricity opposite in sign to that given to the plate D. The electrometer needle is kept at the position of rest as nearly as possible by adjusting the tension by hand. The tension being fully applied, the moment the needle commences to move steadily from zero is noted. The current between the plates CD is then given by Q/t where t is the time of the observation. The value of Q is known from the weight attached.

In this method the electrometer is only used as a detector to show that the system is kept at zero potential. No knowledge of the capacity of the insulated system is required. With practice, measurements of the current can be made in this way with rapidity and certainty.