and C = C1 --------
d1 – d2
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.
This can obviously be secured if the electrometer system (one pair of quadrants being earthed) is connected to earth through a suitable high resistance. A steady deflection of the electrometer needle will be obtained when the rate of supply of electricity to the electrometer system is balanced by the loss due to conduction through the resistance. If the high resistance obeys Ohm’s law, the deflection should be proportional to the ionization current to be measured.
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].
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.