



The Calibration of WaveMeters for RadioTelegraphy, by G W O Howe. Proceedings of the Physical Society of London, Vol 24, issue 1, 1st Dec. 1911*, p251259. * The Journal is dated 1911, but the paper is headed "Read May 31 1912". Hence it is often cited with 1912 as the date. A wavemeter, consisting of a coil, a variable air capacitor, and a resonance indicator such as a gasdischarge tube or an ammeter, can be calibrated approximately by calculation if the inductance and capacitance are known. The inductance can be made independent of frequency by use of thin or stranded wire, and the air dielectric ensures that the capacitance is independent of frequency. A source of error however is the capacitance between neighbouring portions of the coil. Even when the capacitor is removed, the coil has a definite natural frequency, the ends acting as the plates of a capacitor and the central portion as an inductance, the two functions being distributed over the coil. Drude 1902 implies the existence of an equivalent circuit comprising an effective inductance and an effective selfcapacitance. Drude assumes that the effective inductance is 2/π × total inductance, but it is shown that for practical purposes, the effective inductance is the same as the total inductance. If the selfcapacitance calculated from the natural frequency on this basis is added to the capacitance of the variable capacitor, the remaining error in the wavemeter calibration is reduced to < 1%. A plot of the square of the selfresonant wavelength vs. parallel capacitance is a straight line that is offset by an amount equal to the selfcapacitance. Thus the selfcapacitance can be measured by resonating the coil against a series of known capacitances and extrapolating. Note: Howe correctly establishes that the effective inductance for the selfcapacitance determination is the same as the uniformcurrent inductance. Drude's inductance factor of 2/π is not supported empirically. This observation however leads to a longstanding fallacy; which is due to the fact that the extrapolation measurement is made with the coil always terminated by a capacitor, the effect of which is to render the current distribution substantially uniform. It is not difficult to show that the true selfresonance frequency (SRF) of a coil is not the same as that predicted by the combination of uniform current inductance and self capacitance, but the discrepancy is later attributed to poor measurement technique by Willis Jackson^{[1]}. Investigators then continue to attempt to fit freecoil and extrapolated resonance measurements to the same model for many years. The issue is resolved in selfresonance and self capacitance of solenoids. [1] The selfcapacitance of singlelayer coils, W Jackson. Phil. Mag. Ser. 7, Vol. 19, 128, April 1935, p823835. 



