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 negative ions travel in opposite directions, so the total current is (1⁄300)(0·25 × 10−6)(1·3 × 300 + 1·6 × 300), or 73 × 10−8 in electrostatic measure, otherwise 2·4 × 10−16 amperes per sq. cm. As to the convection current, Gerdien supposes—as in § 25—ρ＝2·7 × 10−9 electrostatic units, and on fine days puts the average velocity of rising air currents at 10 cm. per second. This gives a convection current of 2·7 × 10−8 electrostatic units, or about 1⁄27 of the conduction current. For the total current we have approximately 2·5 × 10−16 amperes per sq. cm. This is insignificant compared to the size of the currents which several authorities have calculated from considerations as to (q.v.). Gerdien’s estimate of the convection current is for fine weather conditions. During rainfall, or near clouds or dust layers, the magnitude of this current might well be enormously increased; its direction would naturally vary with climatic conditions.

27. H. Mache (62) thinks that the ionization observed in the atmosphere may be wholly accounted for by the radioactive emanation. If this is true we should have q＝αn², where q is the number of ions of one sign made in 1 cc. of air per second by the emanation, α the constant of recombination, and n the number of ions found simultaneously by, say, Ebert’s apparatus. Mache and R. Holfmann, from observations on the amplitude of saturation currents, deduce q＝4 as a mean value. Taking for Townsend’s value 1·2 × 10−6, Mache finds n＝1800. The charge on an ion being 3·4 × 10−10 Mache deduces for the ionic charge, I+ or I−, per cubic metre 1800 × 3·4 × 10−10 × 106, or 0·6. This is at least of the order observed, which is all that can be expected from a calculation which assumes I+ and I− equal. If, however, Mache’s views were correct, we should expect a much closer connexion between I and A than has actually been observed.

28. C. T. R. Wilson (63) seems disposed to regard the action of rainfall as the most probable source of the negative charge on the earth’s surface. That great separation of positive and negative electricity sometimes takes place during rainfall is undoubted, and the charge brought to the ground seems preponderatingly negative. The difficulty is in accounting for the continuance in extensive fine weather districts of large positive charges in the atmosphere in face of the processes of recombination always in progress. Wilson considers that convection currents in the upper atmosphere would be quite inadequate, but conduction may, he thinks, be sufficient alone. At barometric pressures such as exist between 18 and 36 kilometres above the ground the mobility of the ions varies inversely as the pressure, whilst the coefficient of recombination varies approximately as the pressure. If the atmosphere at different heights is exposed to ionizing radiation of uniform intensity the rate of production of ions per cc., q, will vary as the pressure. In the steady state the number, n, of ions of either sign per cc. is given by n＝√q/, and so is independent of the pressure or the height. The conductivity, which varies as the product of n into the mobility, will thus vary inversely as the pressure, and so at 36 kilometres will be one hundred times as large as close to the ground. Dust particles interfere with conduction near the ground, so the relative conductivity in the upper layers may be much greater than that calculated. Wilson supposes that by the fall to the ground of a preponderance of negatively charged rain the air above the shower has a higher positive potential than elsewhere at the same level, thus leading to large conduction currents laterally in the highly conducting upper layers.

29. Thunder.—Trustworthy frequency statistics for an individual station are obtainable only from a long series of observations, while if means are taken from a large area places may be included which differ largely amongst themselves. There is the further complication that in some countries thunder seems to be on the increase. In temperate latitudes, speaking generally, the higher the latitude the fewer the thunderstorms. For instance, for Edinburgh (64) (1771 to 1900) and London (65) (1763 to 1896) R. C. Mossman found the average annual number of thunderstorm days to be respectively 6·4 and 10·7; while at Paris (1873–1893) E. Renou (66) found 27·3 such days. In some tropical stations, at certain seasons of the year, thunder is almost a daily occurrence. At Batavia (18) during the epoch 1867–1895, there were on the average 120 days of thunder in the year.

As an example of a large area throughout which thunder frequency appears fairly uniform, we may take Hungary (67). According to the statistics for 1903, based on several hundred stations, the average number of days of thunder throughout six subdivisions of the country, some wholly plain, others mainly mountainous, varied only from 21·1 to 26·5, the mean for the whole of Hungary being 23·5. The antithesis of this exists in the United States of America. According to A. J. Henry (68) there are three regions of maximum frequency: one in the south-east, with its centre in Florida, has an average of 45 days of thunder in the year; a second including the middle Mississippi valley has an average of 35 days; and a third in the middle Missouri valley has 30. With the exception of a narrow strip along the Canadian frontier, thunderstorm frequency is fairly high over the whole of the United States to the east of the 100th meridian. But to the west of this, except in the Rocky Mountain region where storms are numerous, the frequency steadily diminishes, and along the Pacific coast there are large areas where thunder occurs only once or twice a year.

30. The number of thunderstorm days is probably a less exact measure of the relative intensity of thunderstorms than statistics as to the number of persons killed annually by lightning per million of the population. Table X. gives a number of statistics of this kind. The letter M stands for “Midland.”

.—Deaths by Lightning, per annum, per million Inhabitants.

The figure for Hungary is based on the seven years 1897–1903; that for the Netherlands, from data by A. J. Monné (69) on the nine years 1882–1890. The English data, due to R. Lawson (70), are from twenty-four years, 1857–1880; those for the United States, due to Henry (68), are for five years, 1896–1900. In comparing these data allowance must be made for the fact that danger from lightning is much greater out of doors than in. Thus in Hungary, in 1902 and 1903, out of 229 persons killed, at least 171 were killed out of doors. Of the 229 only 67 were women, the only assignable explanation being their rarer employment in the fields. Thus, ceteris paribus, deaths from lightning are much more numerous in a country than in an industrial population. This is well brought out by the low figure for London. It is also shown conspicuously in figures given by Henry. In New York State, where the population is largely industrial, the annual deaths per million are only three, but of the agricultural population eleven. In states such as Wyoming and the Dakotas the population is largely rural, and the deaths by lightning rise in consequence. The frequency and intensity of thunderstorms are unquestionably greater in the Rocky Mountain than in the New England states, but the difference is not so great as the statistics at first sight suggest.

.—Annual Variation of Thunderstorms.

31. Even at the same place thunderstorms vary greatly in intensity and duration. Also the times of beginning and ending are difficult to define exactly, so that several elements of uncertainty exist in data as to the seasonal or diurnal variation. The monthly data in Table XI. are percentages of the total for the year. In most cases the figures are based on the number of days of thunder at a particular station, or at the average station of a country; but the second set for Hungary relates to the number of lightning strokes causing fire, and the figures for the United States relate to deaths by lightning. The data for Edinburgh, due to R. C. Mossman (64), refer to 130 years, 1771 to 1900. The data for London (1763–1896) are also due to