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planes of the condenser, and c the principal axis of the sensitive strip. Similarly at $A',k_{1},p_{1},a_{1},c_{1}$ are new positions of these elements due to any constant rotation of all of the elements of the second system except k' . If now there be any damping of the electric oscillations, the effect of the one condenser on the polarized ray for, say, the first oscillation, may be made equal to that of the other condenser for the second oscillation by such a rotation, and so on. Thus these two condensers become an equivalent "crossed" system, the one compensating completely the effect of the other, even if the electric stresses in each are not the same. This would hold for electric oscillations which produce successive stresses that are in a constant ratio to each other. If now the interval of passage of the beam of light between k and k' is any multiple of a half period of the vibration, we may obtain compensation, and hence retain the settings for a match in the two half-shade systems c and c' . If there should be any difference in the interval of passage in the two opposite directions, we should not obtain a match in the one if we set for the same in the other, after the frequency had been varied so as to give this exact multiple of the half period in this latter system. This would be determined by noting when the intensity of the field approximated a minimum intensity.

For low frequencies sunlight has been used; but for the higher frequencies this source has not given satisfactory results on account of the very brief duration of the spark in the exciter, and, consequently, the integral time of the electric stresses due to such a discharge. In this case the spark itself may be used to advantage, since here we have a very much greater intensity during the period of the electric stresses. The greater uniformity and intensity of a vapour spark-gap, e. g. of mercury, recommend its use in connexion with the half-shade system. To maintain greater uniformity in the amplitude of the oscillations, and hence in the Kerr "effect," a secondary or resonance circuit itself, with its condenser system, may be used, as this will give sufficient double refraction in the dielectric to make accurate settings. Such a half-shade system, where the photometric sensibility is as low, say, as 2 per cent., will show a change of phase of $0.3\times 10^{-4}\lambda$.^[1] Since now the maxima of the Kerr "effect" occur every half oscillation, the distance between the condenser k and k' needs only to be equal to the space traversed by the ray in half an oscillation, or $d={\tfrac {1}{2}}L$, where L is the wavelength of an electric oscillation. This would give us a change of phase in the one direction of $0.3\times 10^{-4}\lambda$ and an

1. Phys. Rev. vol. xviii. p. 85.