1. In a previous note (McCrea, 1936) the following problem was enunciated: A rectangular lattice is given; a particle P moves from one lattice-point to another in such a way that, when it is at any interior point, it is equally likely to move to any of its four neighbouring points. P is liberated at any given lattice-point and it is required to find the probability that it will ultimately reach any stated point in the boundary of the lattice, assuming that on arrival at a boundary point its movement ceases.

In fine weather the diurnal variation of electric potential gradient shows at most places a double oscillation in the course of the twenty-four hours. At Kew Observatory, for example, the potential gradient is high in the evening a t 2011. and in the morning at gh. ; it is low in the early morning and in the early afternoon. The two maxima are about equal, but the morning minimum is the lower. In the polat regions however where, especially in winter, the meteorological elements change but little during the day, the variation of potential gradient is of a simpler type with only one masimum and one minimum.The observations at seven places, four in the Arctic regions and three in the Antarctic, were compared by Hoffmann when he published' the results obtained in Spitzbergen in 1913-14. Hoffmann noticed that when the observatioiis a t the several stations were referred to local time the hours a t which the maxima and minima occurred differed widely, but when he referred the daily variations a t all the stations to universal time he found that all the principal maxima and minima agreed.Shortly afterwards S. J. Mauchly, of the Carnegie Institution, published2 his discussion of the results obtained during the cruises . of the " Carnegie" and showed that the diurnal variation of potential gradient was of the same simple type. Moreover, hIauchly ' s analysis of the readings at observatories in various parts of the world indicated that there was some general cause tending to produce a simple synchronous oscillation even though it might be modified by local conditions. Additional support for Mauchly's generalization is provided by the observations made by Sverdrup 1 K. Hoffmann. Beitr. Pliysik Atmosph., Leipzig, 11, 1923, p. 1. Apparently it was consideration of the fact that the mean potential gradient was highest at the same season (the southern summer) in both hemispheres that led HorImann to the idea that direct local solar influence was unimportant and that the diurnal variation might be governed by a universal cause. S.J. Mauchly. Terr. Mag., Baltimore, 28, 1923, p. 61: Washington, Res. DeQ. Terr. Mag., Carnegie Inst., 5, 1926, p. 385. The first evidence for the simultaneous wave of potential gradient over the oceans mas published by Mauchly in 1921. Physic. Rev., 18, 1921, pp. 161, 477.

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Wilson's theory of the acquisition of charges by drops falling through a region containing ions is worked out in detail ; diagrams of the paths of ions and curves of the rates of acquisition of charge are drawn. The applications of the theory to the building up of fields in clouds and to the charging of raindrops are briefly discussed.