If <i>k</i> is the mechanical restoring force per unit displacement of the fiber, the actual restoring force per unit displacement may readily be shown to be <i>k</i>-<i>CX</i><sup>2</sup>, where <i>C</i> is the capacity of the fiber and <i>X</i> the field between the plates. The deflecting force due to a change of potential δ<i>V</i> in the fiber is <i>CX</i>δ<i>V</i>, so that the sensitivity <i>S</i> is <i>S</i>=<i>CX</i>/(<i>k</i>-<i>CX</i><sup>2</sup>). If <i>k</i> is less than <i>CX</i><sup>2</sup> the instrument is unstable, and the fiber flies to either one plate or the other. The sensitivity becomes very large if <i>k</i>-<i>CX</i><sup>2</sup> is small; and in obtaining high sensitivity from the instrument, this condition is usually satisfied, even though the fact may not be realized. It is a bad condition since it results in large variations in <i>S</i> for small variations in either <i>k</i> or <i>X</i>. If we desire to restrict ourselves to the case <i>k</i>-<i>CX</i><sup>2</sup>=<i>k</i>/2, so that we draw upon the term <i>CX</i><sup>2</sup> to the extent of no more than doubling the sensitivity which we should obtain in its absence, <i>S</i> reduces to the very simple expression <i>S</i>=1/<i>X</i> which, under a magnification of 100, gives a deflection of 1000 mm per volt for a field of one volt per cm between the plates. High sensitivity consistent with great constancy necessitates a small field between the plates and correspondingly small value of <i>k</i>. An instrument meeting the required conditions is described. As an illustration of the performance of the electroscope one experiment gave, with a magnification of 600, and a potential difference of 6 volts between plates, a sensitivity of 3500 eyepiece divisions per volt and a period so short that the fiber assumed a steady reading in less than ¾ second after application of the potential. Moreover, the linearity of the calibration curve over the whole range of the eyepiece scale was so perfect that departures from linearity could not be observed within the limits of accuracy of the readings.
W. F. G. SWANN, "THE THEORY OF THE SINGLE FIBER ELECTROSCOPE AND A NEW DESIGN OF THE INSTRUMENT," J. Opt. Soc. Am. 11, 375-391 (1925)