its hour of maximum). The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes. That the 8-hour and 6-hour waves, though small near midsummer, represent more than mere accidental irregularities, seems a safe inference from the regularity apparent in the annual variation of their phase angles.
Table V.—Fourier Series Amplitudes and Phase Angles.
| Place. | Period. | Winter. | Summer. | ||||||
| c1. | c2. | a1. | a2. | c1. | c2. | a1. | a2. | ||
Kew ” Bureau Central Eiffel Tower Sonnblick (22) Karasjok Kremsmünster (23) Potsdam |
1862–64 1898–1904 1894–98 1896–98 1902–3 1903–4 1902 1904 |
0·283 ·102 ·220 .. .. ·356 ·280 ·269 |
0·160 ·103 ·104 .. .. ·144 ·117 ·101 |
° 184 206 223 .. .. 189 224 194 |
° 193 180 206 .. .. 155 194 185 |
0·127 ·079 ·130 ·133 ·208 ·165 ·166 ·096 |
0·229 ·213 ·200 ·085 ·120 ·093 ·153 ·152 |
° 111 87 95 216 178 141 241 343 |
° 179 186 197 171 145 144 209 185 |
9. Table V. gives some data for the 24-hour and 12-hour Fourier coefficients, which will serve to illustrate the diversity between different stations. In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season. “Winter” means generally the four midwinter, and “summer” the four midsummer, months; but at Karasjok three, and at Kremsmünster six, months are included in each season. The results for the Sonnblick are derived from a comparatively small number of days in August and September. At Potsdam the data represent the arithmetic means derived from the Fourier analysis for the individual months comprising the season. The 1862–1864 data from Kew—due to J. D. Everett (19)—are based on “all” days; the others, except Karasjok to some extent, represent electrically quiet days. The cause of the large difference between the two sets of data for c1 at Kew is uncertain. The potential gradient is in all cases lower in summer than winter, and thus the reduction in c1 in summer would appear even larger than in Table V. if the results were expressed in absolute measure. At Karasjok and Kremsmünster the seasonal variation in a1 seems comparatively small, but at Potsdam and the Bureau Central it is as large as at Kew. Also, whilst the winter values of a1 are fairly similar at the several stations the summer values are widely different. Except at Karasjok, where the diurnal changes seem somewhat irregular, the relative amplitude of the 12-hour term is considerably greater in summer than in winter. The values of a2 at the various stations differ comparatively little, and show but little seasonal change. Thus the 12-hour term has a much greater uniformity than the 24-hour term. This possesses significance in connexion with the view, supported by A. B. Chauveau (21), F. Exner (24) and others, that the 12-hour term is largely if not entirely a local phenomenon, due to the action of the lower atmospheric strata, and tending to disappear even in summer at high altitudes. Exner attributes the double daily maximum, which is largely a consequence of the 12-hour wave, to a thin layer near the ground, which in the early afternoon absorbs the solar radiation of shortest wave length. This layer he believes specially characteristic of arid dusty regions, while comparatively non-existent in moist climates or where foliage is luxuriant. In support of his theory Exner states that he has found but little trace of the double maximum and minimum in Ceylon and elsewhere. C. Nordmann (25) describes some similar results which he obtained in Algeria during August and September 1905. His station, Philippeville, is close to the shores of the Mediterranean, and sea breezes persisted during the day. The diurnal variation showed only a single maximum and minimum, between 5 and 6 p.m. and 4 and 5 a.m. respectively. So again, a few days’ observations on the top of Mont Blanc (4810 metres) by le Cadet (26) in August and September 1902, showed only a single period, with maximum between 3 and 4 p.m., and minimum about 3 a.m. Chauveau points to the reduction in the 12-hour term as compared to the 24-hour term on the Eiffel Tower, and infers the practical disappearance of the former at no great height. The close approach in the values for c1 in Table V. from the Bureau Central and the Eiffel Tower, and the reduction of c2 at the latter station, are unquestionably significant facts; but the summer value for c2 at Karasjok—a low level station—is nearly as small as that at the Eiffel Tower, and notably smaller than that at the Sonnblick (3100 metres). Again, Kew is surrounded by a large park, not devoid of trees, and hardly the place where Exner’s theory would suggest a large value for c2, and yet the summer value of c2 at Kew is the largest in Table V.
10. Observations on mountain tops generally show high potentials near the ground. This only means that the equipotential surfaces are crowded together, just as they are near the ridge of a house. To ascertain how the increase in the voltage varies as the height in the free atmosphere increases, it is necessary to employ kites or balloons. At small heights Exner (27) has employed captive balloons, provided with a burning fuse, and carrying a wire connected with an electroscope on the ground. He found the gradient nearly uniform for heights up to 30 to 40 metres above the ground. At great heights free balloons seem necessary. The balloon carries two collectors a given vertical distance apart. The potential difference between the two is recorded, and the potential gradient is thus found. Some of the earliest balloon observations made the gradient increase with the height, but such a result is now regarded as abnormal. A balloon may leave the earth with a charge, or become charged through discharge of ballast. These possibilities may not have been sufficiently realized at first. Among the most important balloon observations are those by le Cadet (1) F. Linke (28) and H. Gerdien (29). The following are samples from a number of days’ results, given in le Cadet’s book. h is the height in metres, P the gradient in volts per metre.
| Aug. 9, 1893 |
| |||||||||
h P |
824 37 |
830 43 |
1060 43 |
1255 41 |
1290 42 |
1745 34 |
1940 25 |
2080 21 |
2310 18 |
2520 16 |
| Sep. 11, 1897 |
| |||||||||
h P |
1140 43 |
1378 38 |
1630 33 |
1914 25 |
2370 22 |
2786 21 |
3136 19 |
3364 19 |
3912 14 |
4085 13 |
The ground value on the last occasion was 150. From observations during twelve balloon ascents, Linke concludes that below the 1500-metre level there are numerous sources of disturbance, the gradient at any given height varying much from day to day and hour to hour; but at greater heights there is much more uniformity. At heights from 1500 to 6000 metres his observations agreed well with the formula
dV/dh＝34 − 0·006 h,
V denoting the potential, h the height in metres. The formula makes the gradient diminish from 25 volts per metre at 1500 metres height to 10 volts per metre at 4000 metres. Linke’s mean value for dV/dh at the ground was 125. Accepting Linke’s formula, the potential at 4000 metres is 43,750 volts higher than at 1500 metres. If the mean of the gradients observed at the ground and at 1500 metres be taken as an approximation to the mean value of the gradient throughout the lowest 1500 metres of the atmosphere, we find for the potential at 1500 metres level 112,500 volts. Thus at 4000 metres the potential seems of the order of 150,000 volts. Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.
11. At most stations a negative potential gradient is exceptional, unless during rain or thunder. During rain the potential is usually but not always negative, and frequent alternations of sign are not uncommon. In some localities, however, negative potential gradient is by no means uncommon, at least at some seasons, in the absence of rain. At Madras, Michie Smith (30) often observed negative potential during bright August and September days. The phenomenon was quite common between 9·30 a.m. and noon during westerly winds, which at Madras are usually very dry and dusty. At Sodankylä, in 1882–1883, K. S. Lemström and F. C. Biese (31) found that out of 255 observed occurrences of negative potential, 106 took place in the absence of rain or snow. The proportion of occurrences of negative potential under a clear sky was much above its average in autumn. At Sodankylä rain or snowfall was often unaccompanied by change of sign in the potential. At the polar station Godthaab (32) in 1882–1883, negative potential seemed sometimes associated with aurora (see Aurora Polaris).
Lenard, Elster and Geitel, and others have found the potential gradient negative near waterfalls, the influence sometimes extending to a considerable distance. Lenard (33) found that when pure water falls upon water the neighbouring air takes a negative charge. Kelvin, Maclean and Gait (34) found the effect greatest in the air near the level of impact. A sensible effect remained, however, after the influence of splashing was eliminated. Kelvin, Maclean and Galt regard this property of falling water as an objection to the use of a water-dropper indoors, though not of practical importance when it is used out of doors.
12. Elster and Geitel (35) have measured the charge carried by raindrops falling into an insulated vessel. Owing to observational difficulties, the exact measure of success attained is a little difficult to gauge, but it seems fairly certain that raindrops usually carry a charge. Elster and Geitel found the sign of the charge often fluctuate repeatedly during a single rain storm, but it seemed more often than not opposite to that of the simultaneous potential gradient. Gerdien has more recently repeated the experiments, employing an apparatus devised by him for the purpose. It has been found by C. T. R. Wilson (36) that a vessel in which freshly fallen rain or snow has been evaporated to dryness shows radioactive properties lasting for a few hours. The results obtained from equal weights of rain and snow seem of the same order.
13. W. Linss (6) found that an insulated conductor charged either positively or negatively lost its charge in the free atmosphere; the potential V after time t being connected with its initial value V0 by a formula of the type V = V0e−at where a is constant. This was confirmed by Elster and Geitel (7), whose form of dissipation apparatus has been employed in most recent work. The percentage of the