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Originally appearing in Volume V02, Page 870 of the 1911 Encyclopedia Britannica.
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ATMOSPHERIC ELECTRICITY. 1. It was not until the middle of the 18th century that experiments due to Benjamin Franklin showed that the electric phenomena of the atmosphere are not fundamentally different from those produced in the laboratory.. For the next century the rate of progress was slow, though the ideas of Volta in Italy and the instrumental devices of Sir Francis Ronalds in England merit recognition. The invention of the portable electrometer and the water-dropping electrograph by Lord Kelvin in the middle of the 19th century, and the greater definiteness thus introduced into observational results, were notable events. Towards the end of the 19th century came the discovery made by W. Linss (6)1 and by J. Elster and H. Geitel (7) that even the most perfectly insulated conductors lose their charge, and that this loss depends on atmospheric conditions. Hard on this came the recognition of the fact that freely charged positive and negative ions are always present in the atmosphere, and that a radioactive emanation can be collected. Whilst no small amount of observational work has been done in these new branches of atmospheric electricity, the science has still not developed to a considerable extent beyond preliminary stages. Observations have usually been limited to a portion of the year, or to a few hours of the day, whilst the results from different stations differ much in details. It is thus difficult to form a judgment as to what has most claim to acceptance as the general law, and what may be regarded as local or exceptional. 2. Potential Gradient.—In dry weather the electric potential in the atmosphere is normally positive relative to the earth, and increases with the height. The existence of earth currents (q. v.) shows that the earth, strictly speaking, is not all at one potential, but the natural differences of potential between points on the earth's surface a mile apart are insignificant compared to the normal potential difference between the earth and a point one foot above it. What is aimed at in ordinary observations of atmospheric potential is the measurement of the difference of potential between the earth and a point a given distance above it, or of the difference of potential betweeen two points in the same vertical line a given distance apart. Let a conductor, say a metallic sphere, be supported by a metal rod of negligible electric capacity whose other end is earthed. As the whole conductor must be at zero (i.e. the earth's) potential, there must be an induced charge on the sphere, producing at its centre a potential equal but of opposite sign to what would exist at the, same spot in free air. This neglects any charge in the air 1 See Authorities below. displaced by the sphere, and assumes a statical state of conditions and that the conductor itself exerts no disturbing influence. Suppose now that the sphere's earth connexion is broken and that it is carried without loss of charge inside a building at zero potential. If its potential as observed there is -V (volts), then the potential of the air at the spot occupied by the sphere was +V. This method in one shape or another has been often employed. Suppose next that a fixed insulated conductor is somehow kept at the potential of the air at a given point, then the measurement of its potential is equivalent to a measurement of that of the air. This is the basis of a variety of methods. In the earliest the conductor was represented by long metal wires, supported by silk or other insulating material, and left to pick up the air's potential. The addition of sharp points was a step in advance; but the method hardly became a quantitative one until the sharp points were replaced by a flame (fuse, gas, lamp), or by a liquid jet breaking into drops. The matter leaving the conductor, whether the products of combustion or the drops of a liquid, supplies the means of securing equality of potential between the conductor and the air at the spot where the matter quits electrical connexion with the conductor. Of late years the function of the collector is discharged in some forms of apparatus by a salt of radium. Of flame collectors the two best known are Lord Kelvin's portable electrometer with a fuse, or F. Exner's gold leaf electroscope in conjunction with an oil lamp or gas flame. Of liquid collectors the representative is Lord Kelvin's water-dropping electrograph; while Benndorf's is the form of radium collector that has been most used. It cannot be said that any one form of collector is superior all round. Flame collectors blow out in high winds, whilst water-droppers are apt to get frozen in winter. At first sight the balance of advantages seems to lie with radium. But while gaseous products and even falling water are capable of modifying electrical conditions in their immediate neighbourhood, the " infection " produced by radium is more insidious, and other drawbacks present them-selves in practice. It requires a radium salt of high radioactivity to be at all comparable in effectiveness with a good water-dropper. Experralents by F. Zz.z e rirdcated That a water-dropper /are often too raprafto 6e sathfactorlfydealt with 6y an ordr"nary Place and Period. Jan. Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. Dec. Karasjok (10), 1903-1904 . 143 150 137 94 74 65 70 67 67 87 120 126 Sodankyla (31),1882-1883• 94 133 148 155 186 93 53 77 47 72 71 71 Potsdam (9), 1904 . . . . 167 95 118 88 93 72 73 65 97 101 Io8 123 Kew (12),1898-1904 . . 127 141 113 87 77 70 61 72 76 96 126 153 Greenwich (13),1893-1894,1896 110 112 127 107 83 71 76 84 83 104 104 139 Florence (14), 1883-1886 . . 132 110 98 84 86 81 77 90 89 99 129 125 Perpignan (15), 1886-1888 . . 121 112 Io8 89 91 92 89 82 74 99 122 121 Lisbon (16),1884–1886 . . . 104 105 104 92 91 93 87 92 too 99 115 117 Tokyo(17),1897-1898,1900-1901 165 145 117 86 62 58 41 59 59 97 134 176 Batavia (18)(2 m.), 1887–189o. 97 115 155 127 129 105 79 62 69 79 90 93 „ (7.8 m.) 1890-1895 too 89 103 120 98 103 85 99 73 101 117 112 there are external buildings or trees sufficiently near to influence the potential. It is thus futile to compare the absolute voltages met with at two stations, unless allowance can be made for the influence of the environment. With a view to this, it has become increasingly common of late years to publish not the voltages actually observed, but values deduced from them for the potential gradient in the open in volts per metre. Observations are made at a given height over level open ground near the observatory, and a comparison with the simultaneous results from the self-recording electrograph enables the records from the latter to be expressed as potential gradients in the open. In the case, however, of many observatories, especially as regards the older records, no data for reduction exist; further, the reduction to the open is at best only an approximation, the success attending which probably varies considerably at different stations. This is one of the reasons why in the figures for the annual and diurnal variations in Tables I., II. and III., the potential has been expressed as percentages of its mean value for the year or the day. In most cases the environment of a collector is not absolutely invariable. If the shape of the equipotential surfaces near it is influenced by trees, shrubs or grass, their influence will vary throughout the year. In winter the varying depth of snow may exert an appreciable effect. There are sources of uncertainty in the instrument itself. Unless the insulation is perfect, the potential recorded falls short of that at the spot where the radium is placed or the water jet breaks. The action of the collector is opposed by the leakage through imperfect insulation, or natural dissipation, and this may introduce a fictitious element into the apparent annual or diurnal variation. The potentials that have to be dealt with are often hundreds and sometimes thousands of volts, and insulation troubles are more serious than is generally appreciated. When a water jet serves as collector, the pressure under which it issues should be practically constant. If the pressure alters as the water tank empties, a discontinuity occurs in the trace when the tank is refilled, and a fictitious element may be introduced into the diurnal variation. When rain or snow is falling, the potential frequently changes rapidly. These changes having a number of fine holes, or having a fine jet under a considerable pressure, picks up the potential in about a tenth of the time required by the ordinary radium preparation protected by a glass tube. These fine jet droppers with a mixture of alcohol and water have proved very effective for balloon observations. 3. Before considering observational data, it is expedient to mention various sources of uncertainty. Above the level plain of absolutely smooth surface, devoid of houses or vegetation, the equipotential surfaces under normal conditions would be strictly horizontal, and if we could determine the potential at one metre above the ground we should have a definite measure of the potential gradient at the earth's surface. The presence, how-ever, of apparatus or observers upsets the conditions, while above uneven ground or near a tree or a building the equipotential surfaces cease to be horizontal. In an ordinary climate a building seems to be practically at the earth's potential; near its walls the equipotential surfaces are highly inclined, and near the ridges they may lie very close together. The height of the walls in the various observatories, the height of the collectors, and the distance they project from the wall vary largely, and sometimeselectrometer, and they sometimes leave hardly a trace on the photographic paper. Again rain dripping from exposed parts of the apparatus may materially affect the record. It is thus customary in calculating diurnal inequalities either to take no -account of days on which there is an appreciable rainfall, or else to form separate tables for " dry " or " fine " days and for " all " days. Speaking generally, the exclusion of days of rain and of negative potential comes pretty much to the same thing, and the presence or absence of negative potential is not infrequently the criterion by reference to which days are rejected or are accepted as normal. 4. The potential gradient near the ground varies with the season of the year and the hour of the day, and is largely dependent on the weather conditions. It is thus difficult to form even a rough estimate of the mean value at any place unless hourly readings exist, extending over the whole or the greater part of a year. It is even some-what precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions. At Potsdam, G. Ludeling (9) found for the mean value for 1904 in volts per metre 242. At Karasjok in the extreme north of Norway G. C. Simpson (10) in 1903–1904 obtained 139. At Kremsm~nsterfor 1902 P. B. Z~isslJ 1) gives 98. At Kew (12) the mean for individual years from 1898 to 1904 varied from 141 in 1900 to 179 in 1899, the mean from the seven years combined being 159. The large difference between the means obtained at Potsdam and Kremsmunster, as compared to the comparative similarity between the results for Kew and Karasjok, suggests that the mean value of the potential gradient may be much more dependent on local conditions than on difference of latitude. At any single station potential gradient has a wide range of values. The largest positive and negative values recorded are met with during disturbed weather. During thunderstorms the record from an electrograph shows large sudden excursions, the trace usually going off the sheet with every flash of lightning when the thunder is near. Exactly what the potential changes amount to under such circumstances it is impossible to say; what the trace shows depends largely on the type of electrometer. Large rapid changes are also met with in the absence of thunder during heavy rain or snow fall. In England the largest values of a sufficiently steady character to be shown correctly by an ordinary electrograph occur during winter fogs. At such times gradients of -400 or +500 volts per metre are by no means unusual at Kew, and voltages of 700 or 800 are occasionally met with. 5. Annual Variation.-Table I. gives the annual variation of the potential gradient at a number of stations arranged according to latitude, the mean value for the whole year being taken in each case as loo. Karasjok as already mentioned is in the extreme north of Norway (69° 17' N.); Sodankyla was the Finnish station of the international polar year 1882-1883. At Batavia, which is near the equator (6° IT' S.) the annual variation seems somewhat irregular. Further, the results obtained with the water-dropper at two heights -viz. 2 and 7.8 metres-differ notably. At all the other stations the difference between summer and winter months is conspicuous. From the European data one would be disposed to conclude that Station. Karasjok. Sodankyla. Kew (19, 12). Greenwich. Florence. Perpignan. Lisbon. Tokyo. Batavia. Cape Horn (20). Period. 1903-4. 1882-83. 1864. 1904. 1893-96. 1883-85. 1886-88. 1884-86. 19070_18' 1 890. 1895. 1882-83. Days. All. All. Quiet. All. All. Fine. All. All. Dry. Dry. Pos. h 5.5 3.0 3'5 3.35 3.0 8.4 3.0 1.7 2 7.8 3.5 2.5 1.0 I.3 1.8 1.5 0.5 2.0 2.0 Hour. I 83 91 87 93 97 92 78 84 101 147 125 82 2 73 85 79 88 89 83 72 8o 98 141 114 73 3 66 82 74 84 87 77 71 78 97 135 109 85 4 63 84 72 83 86 75 72 81 99 128 102 81 5 6o 89 71 85 86 74 77 83 121 127 101 85 6 68 91 77 93 92 82 92 92 154 137 117 95 7 81 97 92 I03 I00 I0o I07 I01 167 158 147 I06 8 87 Ioo 106 II2 102 II2 114 I05 149 104 I19 I18 9 94 98 107 115 loo 113 III 104 117 67 82 119 IO I01 IO2 I00 II2 I01 I07 Ioo I04 87 42 55 123 II 99 98 90 101 96 loo 96 102 70 35 46 123 Noon. 103 102 92 94 97 95 99 108 61 30 43 115 Io6 105 90 89 96 92 99 III 54 30 42 112 2 Io8 107 91 87 94 90 97 114 49 30 43 94 3 Io8 108 92 88 95 89 99 109 53 33 46 '89 4 109 108 98 93 97 89 105 108 61 41 53 88 5 IIo 108 108 99 102 94 113 Io8 76 67 73 84 6 119 Ho I21 I08 I08 I13 I26 III 95 91 108 II0 7 129 IO2 134 I15 III I2I 131 116 I07 I20 145 I07 8 136 III 139 118 115 129 129 114 114• 137 155 123 9 139 III 138 119 117 132 120 109 119 146 155 112 to 133 104 128 115 117 127 I09 102 120 148 147 99 II 121 108 113 108 III 114 97 92 119 151 143 85 12 102 93 99 99 104 Too 86 85 112 147 130 98 (Station. Karasjok. Sodankyla. Kew. Greenwich. Bureau Eiffel Perpignan(21). Batavia. (2 m.) Central (21). Tower(21) Period. 1903-4. 1882-83. 1898-1904. 1894 and '96. 1894-99. 1896-98. 1885-95. 1887-90. Winter. Summer. Winter. Summer. Winter. Equinox. Summer. Winter. Summer. Winter. Summer. Summer. Winter. Summer. Winter. 'Summer. Hour. I 76 104 90 99 91 93 96 87 I10 79 102 90 72 88 145 149 2 66 96 79 84 86 88 90 84 101 71 92 83 67 83 139 142 3 57 89 78 90 82 85 85 76 98 70 88 79 66 81 137 135 4 55 83 74 99 81 84 84 77 96 69 84 76 67 83 131 127 5 50 79 74 III 82 87 90 78 94 75 94 78 72 92 132 123 6 61 83 8o 114 86 97 101 tot 83 Io6 87 84 107 138 136. 7 78 89 86 117 95 109 113 94 107 98 118 97 104 114 166 153 8 82 93 95 122 104 118 120 97 III III 120 103 122 I08 I18 92 9 90 93 91 109 III 119 119 98 102 113 I06 110 126 100 74 64 10 104 93 106 101 114 110 IIo 102 98 III 94 109 114 93 43 40 11 102 92 98 97 107 95 97 103 86 Io8 84 107 98 90 35 36 Noon. 119 90 98 100 102 86 87 107 94 Io6 77 104 99 95 31 30 I 116 94 116 97 99 81 8o 107 85 I12 79 107 96 93 29 33 2 118 97 113 97 97 8o 76 109 82 112 81 IIo 94 90 28 32 3 119 100 121 93 99 82 76 11I 78 III 78 107 95 88 24 41 4 115 99 111 96 103 88 8o 116 81 113 8o 105 102 92 30 49 5 120 Io6 105 106 108 96 87 I12 93 120 85 Io6 115 98 6o 74 6 131 104 115 92 III 109 98 114 98 124 97 109 128 110 88 94 7 136 110 I18 102 114 120 III 117 99 124 123 I13 133 122 119 122 8 134 113 117 I06 112 124 123 113 I08 116 134 110 131 127 138 135 9 137 125 115 90 III 123 129 111 118 104 130 109 124 125 145 147 10 125 135 112 90 I08 118 125 110 124 97 122 105 III 117 148 148 II 114 126 113 103 103 109 116 102 120 90 115 101 96 108 149 152 12 96 III 95 85 96 99 105 93 116 83 108 94 83 95 148 146 it . —~~ itoo al r I ,9G a§n -WEE 90 • .r too so o too oo to too 90 the variation throughout the year diminishes as one approaches the equator. It is decidedly less at Perpignan and Lisbon than at Potsdam, Kew and Greenwich, but nowhere is the seasonal difference more conspicuous than at Tokyo, which is south of Lisbon. At the temperate stations the maximum occurs near mid-winter; in the Arctic it seems deferred towards spring. 6. Diurnal Variation.—Table II. gives the mean diurnal variation for the whole year at a number of stations arranged in order of latitude, the mean from the 29. hourly values being taken as too. The data are some from all ' days, some from quiet," " fine or dry " days. The height, h, and the distance from the wall, 1, where the potential is measured are given in metres when known. In most cases two distinct maxima and minima occur in the 24 hours. The principal maximum is usually found in the evening between 8 and Io P.M., the principal minimum in the morning from 3 to 5 A.M. At some stations the minimum in the afternoon is in-distinctly shown, but at Tokyo and Batavia it is much more conspicuous than the morning minimum. 7. In Table III. the diurnal inequality is shown for " winter " and " summer " respectively. In all cases the mean value for the 24 hours is taken as too. By " summer " is meant April to September at Sodankyla, Greenwich and Bata-via ; May to August at Kew, Bureau Central (Paris), Eiffel Tower and Perpignan; and May to July at Karasjok. ' Winter " includes October to March at Sodankyla, Greenwich and Bata-via ; November to February at Kew and Kew ' Bureau Central; December t November to January at Karasjok, and December and January at Perpignan. Mean results from March, April, September and October at Kew are assigned to " Equinox.Kew At Batavia the Potential ::i difference between winter and summer is comparatively small. Elsewhere there is a tendencyfor the double period, usually so pro- minent in summer, to become less pro- nounced in winter, the afternoon minimum tending to disappear. Even in summer the double period is not prominent in the arctic climate of Karasjok or on the top of the Eiffel Tower. The diurnal variation in summer at the latter station is shown graphically in the top curve of fig. t. It presents a remarkable resemblance to the adjacent curve, which gives the diurnal variation at mid-winter at the Bureau Central. The resemblance between these curves is much closer than that between the Bureau Central's own winter and summer curves. All three Paris curves show three peaks, the first and third representing the ordinary forenoon and afternoon maxima. In summer at the Bureau Central the intermediate peak nearly disappears in the profound afternoon depression, but it is still recognizable. This three-peaked curve is not wholly peculiar to Paris, being seen, for instance, at Lisbon in summer. The December and June Eiffel Tower Summer Bureau Cent Winter Bureau Cent Summer Kew June t New Barometric t Pressure Mid- night 6 a. m. Noon 6 p.m. Mid-night curves for Kew are good examples of the ordinary nature of the difference between midwinter and midsummer. The afternoon minimum at Kew gradually deepens as midsummer approaches. Simultaneously the forenoon maximum occurs earlier and the afternoon maximum later in the day. The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole. The somewhat remarkable resemblance between the diurnal variation for the two elements, first remarked on by J. D. Everett (19), is of interest in connexion with recent theoretical conclusions by J. P. Elster and H. F. K. Geitel and by H. Ebert. In the potential curves of the diagram the ordinates represent the hourly values expressed—as in Tables II. and III.—as percentages of the mean value for the day. If this be overlooked, a wrong impression may be derived as to the absolute amplitudes of the changes. The Kew curves, for instance, might suggest that the range maximum less minimum hourly value) was larger in June than in December. In reality the December range was 82, the June only 57 volts; but the mean value of the potential was 243 in December as against I I1 in June. So again, in the case of the Paris curves, the absolute value of the diurnal range in summer was much greater for the Eiffel Tower than for the, Bureau Central, but the mean voltage was 2150 at the former station and only 134 at the latter. 8. Fourier Coefficients.—Diurnal inequalities such as those of Tables II. and III. and intended to eliminate irregular changes, but they also to some extent eliminate regular changes if the hours of maxima and minima or the character of the diurnal variation alter throughout the year. The alteration that takes place in the regular diurnal inequality throughout the year is best seen by analysing it into a Fourier series of the type cl sin (t+a,)+es sin (21+as)-1-cs sin (3t+as)+c4 sin (41+x4)+. where t denotes time counted from (local) midnight, c1, c2, c3, c4,. are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; al, as, as, at, are the corresponding phase angles. One hour of time t is counted as 150, and a dela% of one hour in the time of maximum answers to a diminution of 15 in al, of 300 in as, and so on. If a1, say, varies much throughout the year, or if the ratios of c2, es, c4,... to ci, vary much, then a diurnal inequality derived from a whole year, or from a season composed of several months, represents a mean curve arising from the superposition of a number of curves, which differ in shape and in the positions of their maxima and minima. The result, if considered alone, inevitably leads to an underestimate of the average amplitude of the regular diurnal variation. It is also desirable to have an idea of the size of the irregular changes which vary from one day to the next. On stormy days, as already mentioned, the irregular changes hardly admit of satisfactory treatment. Even on the quietest days irregular changes are always numerous and often large. Table IV. aims at giving a summary of the several phenomena for a single station, Kew, on electrically quiet days. The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days. The hourly values are derived from smoothed curves, the object being to get the mean ordinate for a 6o-minute period. If the actual crests of the excursions had been measured the figures in the second line would have been even larger. The third line gives the range of the regular diurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed. These mean values, ranges• and amplitudes are all measured in volts per metre (in the open) The last four lines of Table IV. give the phase angles of the first four Fourier waves. It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November. At midwinter the 24-hour term is the largest, but near midsummer it is small compared to the 12-hour term. The 24-hour term is very variable both as regards its amplitude and its phase angle (and so Jan. Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. Dec. Mean Potential Gradient . 201 224 18o 138 123 III 98 114 121 153 200 243 . Mean of individual daily ranges 203 218 210 164 143 132 117 129 141 196 186 213 Range in Diurnal inequality 73 94 83 74 71 57 55 6o 54 63 52 82 c1 22 22 17 13 18 9 6 6 9 7 14 30 G2 21 33 34 31 22 23 24 26 23 30 17 21 Amplitudes of Fourier waves cs 7 to 5 5 3 I 3 2 3 6 5 7 C4 2 3 5 6 4 I 4 3 4 3 2 3 0 0 0 0 0 0 0 0 0 0 0 0 a, 206 204 123 72 86 79 48 142 154 192 202 208 II as 170 171 x86 193 188 183 185 182 199 206 212 175 Phase angles of Fourier waves as I t 9 36 96 100 125 124 107 t6 I8 38 36 a4 235 225 307 314 314 277 293 313 330 288 238 249 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. 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 Kremsmunster 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 ci at Kew is uncertain. The potential gradient is in all cases lower in summer than winter, and thus the reduction in ci in summer would appear even larger than in Table V. if the results were expressed in absolute measure. At Karasjok and Kremsmunster the seasonal variation in at seems comparatively small, but at Potsdam and the Bureau Central it is as large as at Kew. Also, whilst the winter values of al 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 el 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. 1o. 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 ors 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 gradientnearly 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 824 830 1060 1255 1290 1745 1940 2080 2310 2520 P 37 43 43 41 42 34 25 21 18 16 Sep.11, 1897 h 1140 1378 1630 1914 2370 2786 3136 3364 3912 4085 P 43 38 33 25 22 21 19 19 14 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 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•oo6 h, V denoting the potential, It 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 Sodankyla, in 1882—1883, K. S. Lemstrom and F. C. Biese (31) found that out of 255 observed occurrences of negative potential, ro6 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 Sodankyla 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 some-times 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 Galt (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 Vo by a formula of the type V = Voe— 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 Place. Period. Winter. Summer. Cl. C2. ai. a2. cis C2. ai• a2. O O O O Kew 1862—64 0.283 0•16o 184 193 0.127 0.229 III 179 1898—19o4 •102 .103 206 18o .079 .213 87 186 Bureau Central 1894—98 •220 .104 223 206 •130 •200 95 197 Eiffel Tower 1896—98 .. .. .. . 133 •085 216 171 Sonnblick (22) 1902—3 .. .. .208 •120 178 145 Karasjok . 1903—4 .356 .144 189 155 '165 •093 141 144 Kremsmunster (23). 1902 •28o .117 224 194 •166 .153 241 209 Potsdam 1904 .269 •101 194 185 .096 '152 343 185 from day to day and hour to hour; but at charge which is dissipated per minute is usually denoted by a+ or a_ according to its sign. The mean of a+ and a_ is usually de-noted by a± or simply by a, while q is employed for the ratio a_/a+. Some observers when giving mean values take E(a_/a+) as the mean value of q, while others take E(a_)/E(a+). The Elster and Geitel apparatus is furnished with a cover, serving to protect the dissipator from the direct action of rain, wind or sunlight. It is usual to observe with this cover on, but some observers, e.g. A. Gockel, have made long series of observations without it. The loss of charge is due to more than one cause, and it is difficult to attribute an absolutely definite meaning even to results obtained with the cover on. Gockel (37) says that the results he obtained without the cover when divided by 3 are fairly comparable with those obtained under the usual conditions; but the appropriate divisor must vary to some extent with the climatic conditions. Thus results obtained for a+ or a_ with-out the cover are of doubtful value for purposes of comparison with those found elsewhere with it on. In the case of q the uncertainty is much less. Table VI. gives the mean values of a± and q found at various places. The observations were usually confined to a few hours of the day, very commonly between II A.M. and I P.M., and in absence of in-formation as to the diurnal variation it is impossible to. say how much this influences the results. The first eight stations le inland; that at Seewalchen (38) was, however, adjacent to a large lake. The next five stations are on the coast or on islands. The final four are at high levels. In the cases where the observations were con-fined to a few months the representative nature of the results is more doubtful. On mountain summits q tends to be large, i.e. a negative charge is lost much faster than a positive charge. Apparently q has also a tendency to be large near the sea, but this phenomenon is not seen at Trieste. An exactly opposite phenomenon, it may be remarked, is seen near waterfalls, q becoming very small. Only Innsbruck and Mattsee give a mean value of q less than unity. Also, as later observations at Innsbruck give more normal values for q, some doubt may be felt as to the earlier observations there. The result for Mattsee seems less open to doubt, for the observer, von Schweidler, had obtained a normal value for q during the previous year at Seewalchen. Whilst the average q in at least the great majority of stations exceeds unity, individual observations making q less than unity are not rare. Thus in 1902 (51) the percentage of cases in which q fell short of I was 30 at Trieste, 33 at Vienna, and 35 at Kremsmunster; at Innsbruck q was less than I on 58 days out of 98. In a long series of observations, individual values of q show usually a wide range. Thus during observations extending over more than a year, q varied from 0.18 to 8.25 at Kremsmunster and from o.11 to 3.00 at Trieste. The values of a+, a_ and a+ also show large variations. Thus at Trieste a+ varied from 0.12 to 4.07, and a_ from 0.11 to 3.87; at Vienna a+ varied from 0.32 to 7.10, and a_ from o•78 to 5'42; at Kremsmunster a± varied from 0.14 to 5.83. 14. Annual Variation.-When observations are made at irregular hours, or at only one or two fixed hours, it is doubtful how representative they are. Results obtained at noon, for example, probably differ more from the mean value for the 24 hours at one season than at another. Most dissipation results are exposed to considerable uncertainty on these grounds. Also it requires a long series of years to give thoroughly representative results for any element, and few stations possess more than a year or two's dissipation data. II. 28Table VII. gives comparative results for winter (October to March) and summer at a few stations, the value for the season being the arithmetic mean from the individual months composing it. At Karasjok (10), Simpson observed thrice a day; the summer value there is nearly double the winter both for a+ and a_. The Kremsmunster (42) figures show a smaller but still distinct excess in the summer values. At Trieste (47), Mazelle's data from all days of the year show no decided seasonal change in a+ or a_; but when days on which the wind was high are excluded the summer value is decidedly the higher. At Freiburg (43), q seems decidedly larger in winter than in summer; at Karasjok and Trieste the seasonal effect in q seems small and uncertain. 15. Diurnal Variation.-P. B. Zoiss (41, 42) has published dirunal variation data for Kremsmunster for more than one year, and independently for midsummer (May to August) and midwinter (December to February). His figures show a double daily period in both a+ and a_, the principal maximum occurring about i or 2 P.M. The two minima occur, the one from 5 to 7 A.M., the other from 7 to 8 P.M.; they are nearly equal. Taking the figures answering to the whole year, May 1903 to 1904, a+ varied throughout the day from o•82 to 1.35, and a_ from o•85 to 1.47. At midsummer the extreme hourly values were 0.91 and 1.45 for a+, 0.94 and i•6o for a_. The corresponding figures at midwinter were 0.65 and 1.19 for a+, 0.61 and 1.43 for a_. Zoiss' data for q show also a double daily period, but the apparent range is small, and the hourly variation is somewhat irregular. At Karasjok, Simpson found a+ and a_ both larger between noon and I P.M. than between either 8 and 9 A.M. or 6 and 7 P.M. The 6 to 7 P.M. values were in general the smallest, especially in the case of a+; the evening value for q on the average exceeded the values from the two earlier hours by some 7 %. Summer observations on mountains have shown diurnal variations very large and fairly regular, but widely different from those observed at lower levels. On the Rothhorn, Gockel (43) found a+ particularly variable, the mean 7 A.M. value being 41 times that at I P.M. q (taken as E(a_/a+) varied from 2.25 at 5 A.M. and 2.52 at 9 P.M. to 7.82 at 3 P.M. and 8.35 at 7 P.M. On the Sonnblick, in early September, V. Conrad (22) found somewhat similar results for q, the principal maximum occur-ring at 1 P.M., with minima at 9 P.M. and 6 A.M.; the largest hourly value was, however, scarcely double the least. Conrad found a_ largest at 4 A.M. and least at 6 P.M., the largest value being double the least; a+ was largest at 5 A.M. and least at 2 P.M., the largest value being fully 22 times the least. On Mont Blanc, le Cadet (43) found glargest from I to 3 P.M., the value at either of these hours being more than double that at 11 A.M. On the Patscherkofel, H. yon Ficker and A. Defant (52), observing in December, found q largest from I to 2 P.M. and least between 11 A.M. and noon, but the largest value was only I a times the least. On mountains much seems to depend on whether there are rising or falling air currents, and results from a single season may not be fairly representative. 16. Dissipation seems largely dependent on meteorological conditions, but the phenomena at different stations vary so much as to suggest that the connexion is largely indirect. At most stations a+ and a_ both increase markedly as wind velocity rises. From the observations at Trieste in 1902-1903 E. Mazelle (47) deduced an increase of about 3% in a+ for a rise of i km. per hour in wind velocity. The following are some of his figures, the velocity v being in kilometres per hour:- V 0to4. 20to24 40to49.6oto69. a - 0.64 1 03 1.38 0.33 q 1.13 1.19 1'00 0'96 For velocities from o to 24 km. per hour q exceeded unity in 74 cases out of ioo; but for velocities over 5o km. per hour q exceeded unity II Winter. Summer. Place. a+ a_ a+ q a+ a_ a± g Karasjok 1903-1904 2'28 2'69 2.49 I•18 4'38 4'94 4'65 1.13 Kremsmunster 1903 I •14 I .30 P22 I. 14 I .38 I-56 1 .47 112 Freiburg . . .. .., .. 1.57 . . .. .. 1.26 Trieste 1902-1903 0.56 0.59 0.58 I•07 0.55 o•61 0.58 1.13 „ calm days . .. .. 0.35 .. .. .. 0.48 Place. Period. Season. Observer or at q Authority. Authors y. Karasjok 1903-4 Year Simpson (10) 3'57 1'15 Wolfenbuttel Year Elster and Geitel(39) 1.33 1.05 Potsdam 1904 Year Ludeling (40) 1.13 1.33 Kremsmunster 1902 Year Z~Iss (41) I.32 1.18 1903 Year Zoiss (42) P35 1.14 Freiburg Year Gockel (43) .. I.41 Innsbruck 1902 Czermak (44) I.95 0.94 1905 Jan. to June Defant (45) 1.47 1.17 Mattsee (Salzburg) 1905 July to Sept. von Schweidler (46) .. 0'99 Seewalchen 1904 July to Sept. von Schweidler (38) 1.18 Trieste . . 1902-3 Year Mazelle (47) 0.58 I.09 Misdroy. 1902 Ludeling (40) 1.09 1.58 Swinemunde 1904 Aug. and Sept. Ludeling (40) I.23 I.37 Heligoland (sands) 1903 Summer Elster and Geitel (40) 1.14 1.71 plateau „ (40) 3.07 I.50 Juist (Island) ,, (48) 1.56 1.56 Atlantic and German Ocean 1904 August Boltzmann (49) 1.83 2.69 Arosa (1800 m.) . 1903 Feb. to April Saake (50) i•79 I.22 Rothhorn (2300 m.) 1903 September Gockel (43) .. 5.31 Sonnblick (3100 m.) . 1903 September Conrad (22) .. 1'75 Mont Blanc (4810 m.) 1902 September le Cadet (43) .. I0•3 in only 40 cases out of Ioo. Simpson got similar results at Karasjok; the rise in a+ and a_ with increased wind velocity seemed, however, larger in winter than in summer. Simpson observed a fall in q for wind velocities exceeding 2 on Beaufort's scale. On the top of the Sonnblick, Conrad observed a slight increase of a± as the wind velocity increased up to 20 km. per hour, but for greater velocities up to 8o km. per hour no further decided rise was observed. At Karasjok, treating summer and winter independently, Simpson (10) found a+ and a_ both increase in a nearly linear relation with temperature, from below -20° to + 15° C. For ex-ample, when the temperature was below -2o° mean values were 0.76 for a+ and 0.91 for a_; for temperatures between -10° and -5° the corresponding means were 2.45 and 2.82; while for temperatures between +to° and +15° they were 4.68 and 5.23. Simpson found no certain temperature effect on the value of q. At Trieste, from 470 days when the wind velocity did not exceed 20 km. per hour, Mazelle (47) found somewhat analogous results for temperatures from o° to 3o° C.; a_, however, increased faster than a+, i.e. q increased with temperature. When he considered all days irrespective of wind velocity, Mazelle found the influence of temperature obliterated. On the Sonnblick, Conrad (22) found a± increase appreciably as temperature rose up to 4° or 5° C.; but at higher temperatures a decrease set in. Observations on the Sonnblick agree with those at low-level stations in showing a diminution of dissipation with increase of relative humidity. The decrease is most marked as saturation approaches. At Trieste, for example, for relative humidities between 90 and loo the mean a± was less than half that for relative humidities under 40. With certain dry winds, notably Fohn winds in Austria and Switzerland, dissipation becomes very high. Thus at Innsbruck Defant (45) found the mean dissipation on days of Fohn fully thrice that on days without Fohn. The increase was largest for a+, there being a fall of about 15% in q. In general, a+ and a_ both tend to be less on cloudy than on bright days. At Kiel (53) and Trieste the average value of q is considerably less for wholly overcast days than for bright days. At several stations enjoying a wide prospect the dissipation has been observed to be specially high on days of great visibility when distant mountains can be recognized. It tends on the contrary to be low on days of fog or rain. The results obtained as to the relation between dissipation and barometric pressure are conflicting. At Kremsmunster, Zolss (42) found dissipation vary with the absolute height of the barometer, a± having a mean value of 1.36 when pressure was below the normal, as against 1.20 on days when pressure was above the normal. He also found a± on the average about to % larger when pressure was falling than when it was rising. On the Sonnblick, Conrad (22) found dissipation increase decidedly as the absolute barometric pressure was larger, and he found no difference between days of rising and falling barometer. At Trieste, Mazelle (47) found no certain connexion with absolute barometric pressure. Dissipation was above the average when cyclonic conditions prevailed, but this seemed simply a consequence of the increased wind velocity. At Mattsee, E. R. von Schweidler (46) found no connexion between absolute barometric pressure and dissipation, also days of rising and falling pressure gave the same mean. At Kiel, K. Kaehler (53) found a+ and a_ both greater with rising than with falling barometer. V. Conrad and M. Topolansky (54) have found a marked connexion at Vienna between dissipation and ozone. Regular observations were made of both elements. Days were grouped according to the intensity of colouring of ozone papers, o representing no visible effect, and 14 the darkest colour reached. The mean values of a+ and a_ answering to 12 and 13 on the ozone scale were both about double the corresponding values answering to o and t on that scale. 17. A charged body in air loses its charge in more than one way. The air, as is now known, has always present in it ions, some carrying a positive and others a negative charge, and those having the opposite sign to the charged body are attracted and tend to discharge it. The rate of loss of charge is thus largely dependent on the extent to which ions are present in the surrounding air. It depends, however, in addition on the natural mobility of the ions, and also on the opportunities for convection. Of late years many observations have been made of the ionic charges in air. The best-known apparatus for the purpose is that devised by Ebert. A cylinder condenser has its inner surface insulated and charged to a high positive or negative potential. Air is drawn by an aspirator between the surfaces, and the ions having the opposite sign to the inner cylinder are deposited on it. The charge given up to the inner cylinder is known from its loss of potential. The volume of air from which the ions have been extracted being known, a measure is obtained of the total charge on the ions, whether positive or negative. The conditions must, of course, be such as to secure that no ions shall escape, otherwise there is an underestimate. I+ is used to denote the charge on positive ions, I_ that on negative ions. The unit t4 which they are ordinarily referred is t electrostatic unit of electricity per cubic metre of air. For the ratio of the mean value of I+ to the mean value of I_, the letter Q is employed by Gockel (55), who has made an unusually complete study of ionic charges at Freiburg. Numerous observations were also made by Simpson (10)—thrice a day—at Karasjok, and von Schweidler has made a good many observations about 3 P.M. at Mattsee (46) in 1905, and Seewalchen (38) in 1904 Station. Authority. I+ I_ Q Freiburg . . . . Gockel 0.34 0.24 1.41 Karasjok . Simpson 0.38 0.33 1.17 These will suffice to give a general idea of the mean values met itGockel's mean values of I+ and Q would be reduced to 0.31 and Mattsee . . . . von Schweidler 0.35 0.29 1.19 Seewalchen . . . 0.45 0.38 1.17 1.38 respectively if his values for July—which appear abnormal—were omitted. I+ and L both show a considerable range of values, even at the same place during the same season of the year. Thus at Seewalchen in the course of a month's observations at 3 P.M., I+ varied from 0.31 to 0.67, and I_ from 0.17 to o•67. There seems a fairly well marked annual variation in ionic contents, as the following figures will show. Summer and winter represent each six months and the results are arithmetic means of the monthly values. Freiburg. Karasjok. I+ I_ Q I+ I_ Q Winter . 0.29 O.2I 1.49 0.33 0.27 I.22 Summer . . 0.39 o•28 1.34 0.44 0.39 1.13 If the exceptional July values at Freiburg were omitted, the summer values of I+ and Q would become 0.33 and 1.25 respectively. 18. Diurnal Variation.—At Karasjok Simpson found the mean values of I+ and L throughout the whole year much the same between noon and I P.M. as between 8 and 9 A.M. Observations between 6 and 7 P.M. gave means slightly lower than those from the earlier hours, but the difference was only about 5 % in I+ and to % in L. The evening values of Q were on the whole the largest. At Freiburg, Gockel found I+ and I_ decidedly larger in the early afternoon than in either the morning or the late evening hours. His greatest and least mean hourly values and the hours of their occurrence are as follows: Winter. Summer. I+ I+ L Max. Min. Max. Min. Max. Min. Max. ,Min. 0.333 0.193 0.242 0.130 0.430 0.244 0'333 0.192 2 P.M. 7 P.M. 2 P.M. 8 P.M. 4 P.M. 9 t0 4 P.M. 9 to to P.M. 10 P.M. Gockel did not observe between to P.M. and 7 A.M. 19. Ionization seems to increase notably as temperature rises. Thus at Karasjok Simpson found for mean values: Temp. less than—2o° — I0° to -5° to° to 15° I+=o•18, I_=o•16 I+=o•36, I_=0.30 I+=O.45, I-=0.43 Simpson found no clear influence of temperature on Q. Gockel; observed similar effects at Freiburg—though he seems doubtful whether the relationship is direct—but the influence of temperature on I+ seemed reduced when the ground was covered with snow. Gockel found a diminution of ionization with rise of relative humidity. Thus for relative humidities between 4o and 5o mean values were x.306 for I+ and 0.219 for I_; whilst for relative humidities between 90 and too the corresponding means were respectively 0.222 and 0.134. At Karasjok, Simpson found a slight decrease in I_ as relative humidity increased, but no certain change in I+. Specially large values of I+ and I_ have been observed at high levels in balloon ascents. Thus on the 1st of July 1901, at a height of 2400 metres, H. Gerdien (29) obtained o•86 for I+ and 1.09 for L. 20. In 1901 Elster and Geitel found that a radioactive emanation is present in the atmosphere. Their method of measuring the radio-activity is as follows (48) : A wire not exceeding I mm. in diameter, charged to a negative potential of at least 2000 volts, is supported between insulators in the open, usually at a height of about 2 metres. After two hours' exposure, it is wrapped round a frame supported in a given position relative to Elster and Geitel's dissipation apparatus, and the loss of charge is noted. This loss is proportional to the length of the wire. The radioactivity is denoted by A, and A =1' signifies that the potential of the dissipation apparatus fell t volt in an hour per metre of wire introduced. The loss of the dissipation body due to the natural ionization of the air is first allowed for. Suppose, for instance, that in the absence of the wire the potential falls from 264 to 255 volts in 15 minutes, whilst when the wire (to metres long) is introduced it falls from 264 to 201 volts in io minutes, then 10A=(264—201) x6—(264—255)x4=342; or A=34.2. The values obtained for A seem largely dependent on the station. At Wolfenbuttel, a year's observations by Elster and Geitel (56) made A vary from 4 to 64, the mean being 20. In the island of Juist, off the Friesland coast, from three weeks' observations they obtained only 5.2 as the mean. On the other hand, at Altjoch, an Alpine station, from nine days' observations in July 1903 they obtained a mean of 137, the maximum being 224, and the minimum 92. At Freiburg, from 15o days' observations near noon in 1903-1904, Gockel (57) obtained a mean of 84, his extreme values being 10 and 420. At Karasjok, observing several times throughout the day for a good many months, Simpson (10) obtained a mean of 93 and a maximum of' 432. The same observer from four weeks' observations at Hammerfest got the considerably lower mean value 58, with a maximum of 252. At this station much lower values were found for A with sea breezes than with land breezes. Observing on the pier at Swinemunde in August and September 1904, Ludeling (40) obtained a mean value of 34. Elster and Geitel (58), having found air drawn from the soil highly radioactive, regard ground air as the source of the emanation in the atmosphere, and in this way account for the low values they obtained for A when observing on or near the sea. At Freiburg in winter Gockel (55) found A notably reduced when snow was on the ground, I+ being also reduced. When the ground was covered by snow the mean value of A was only 42, as compared with 81 when there was no snow. J. C. McLennan (59) observing near the foot of Niagara found A only about one-sixth as large as at Toronto. Similarly at Altjoch, Elster and Geitel (56) found A at the foot of a waterfall only about one-third of its normal value at a distance from the fall. 21. Annual and Diurnal Variations.-At Wolfenbuttel, Elster and Geitel found A vary but little with the season. At Karasjok, on the contrary, Simpson found A much larger at midwinter-notwithstanding the presence of snow-than at midsummer. His mean value for November and December was 129, while his mean for May and June was only 47. He also found a marked diurnal variation, A being considerably greater between 3 and 5 A.M. or 8.3o to 10.30 P.M. than between Io A.M. and noon, or between 3 and 5 P.M. At all seasons of the year Simpson found A rise notably with increase of relative humidity. Also, whilst the mere absolute height of the barometer seemed of little, if any, importance, he obtained larger values of A with a falling than with a rising barometer. This last result of course is favourable to Elster and Geitel's views as to the source of the emanation. 22. For a wire exposed under the conditions observed by Elster and Geitel the emanation seems to be almost entirely derived from radium. Some part, however, seems to be derived from thorium, and H. A. Bumstead (60) finds that with longer exposure of the wire the relative importance of the thorium emanation increases. With three hours' exposure he found the thorium emanation only from 3 to 5% of the whole, but with 12 hours' exposure the percentage of thorium emanation rose to about 15. These figures refer to the state of the wire immediately after the exposure; the rate of decay is' much more rapid for the radium than for the thorium emanation. 23. The different elements-potential gradient, dissipation, ionization and radioactivity- are clearly not independent of one another. The loss of a charge is naturally largely dependent on the richness of the surrounding air in ions. This is clearly shown by the following results obtained by Simpson (10) at Karasjok for the mean values of a+ corresponding to certain groups of values of If. To eliminate the disturbing influence of wind, different wind strengths are treated separately. Wind to o•1. 0•I to 0.2 to 0.3 0.3 t0 0.4. 0.4 t0 0.5. . Strength. o to 1 0.45 0•6o 1.26 2.04 3.03 I ,, 2 0.65 I•o8 1.85 2.92 3'83 2 „ 3 .. .. 2.70 3.88 5'33 If we regard the potential gradient near the ground as representing a negative charge on the earth, then if the source of supply of that charge is unaffected the gradient will rise and become high when the operations by which discharge is promoted slacken their activity. A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient. Table IX. associates with rise in potential gradient a reduced number of both positive and negative ions and a diminished rate of dissipation whether of a negative or a positive charge. The rise in q and Q indicates that the diminished rate of dissipation is most marked for positive charges, and that negative ions are even more reduced then positive. At KremsmunsterZolss (41) finds a considerable similarity between the diurnal variations in q and in the potential gradient, the hours of the forenoon and afternoon maxima being nearly the same in the two cases. No distinct relatic nship has yet been established between potential gradient and radioactivity. At Karasjok Simpson (10) found fairly similar mean values of A for two groups of observations, one confined to cases when the potential gradient exceeded +400 volts, the other confined to cases of negative gradient. At Freiburg Gockel (55, 57) found that when observations were grouped according to the value of A there appeared a distinct rise in both a_ and I+ with increasing A. For instance, when A lay between loo and 150 the mean value of a_ was 1.27 times greater than when A lay between o and 5o ; while when A lay between 120 and 150 the mean value of I+ was 1.53 times larger than when A lay between o and 30. These apparent relationships refer to mean values. In individual cases widely different values of a_ or I+ are associated with the same value of A. 25. If V be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth's centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have r-1(d/dr) (r dV/dr) +4rrp = 0. For practical purposes we may treat r2 as constant, and replace d/dr by d/dh, where h is height in centimetres above the ground. We thus find p= - (I/41r)d2V/dh2. If we take a tube of force 1 sq. cm. in section, and suppose it cut by equipotential surfaces at heights hl and h2 above the ground, we have for the total charge M included in the specified portion of the tube 4irM = (dV/dh)hl - (dV/dh)h2. Taking Linke's (28) figures as given in § It), and supposing h1=o, h2 =15 X lo', we find for the charge in the unit tube between the ground and 1500 metres level, remembering that the centimetre is now the unit of length, M=(I/4r) (125-25)/100. Taking I volt equal 1/300 of an electrostatic unit, we find M =0.000265. Between 1500 and 4000 metres the charge" inside the unit tube is much less, only 0.000040. The charge on the earth itself has its surface density given by u= - (I/42r) X I25 volts per metre, =0.000331 in electrostatic units. Thus, on the view now generally current, in the circumstances answering to Linke's experiemnts we have on the ground a charge of -331 X10-6 C.G.S. units per sq. cm. Of the correspondingg positive charge, 265 X10-6 lies below the 1500 metres level, 40 X10--between between this and the 4000 metres level, and only 26)00-6 above 4000 metres. Thereis a difficulty in reconciling observed values of the ionization with the results obtained from balloon ascents as to the variation of the potential with altitude. According to H. Gerdien (61), near the ground a mean value for d2V/dh2 is -(1/10) volt/(metre)2. From this we deduce for the charge p per cubic centimetre (I f 42r) X IO-6 (volt/cm2), or 2.7 X10-9 electrostatic units. But taking, for example, Simpson's mean values at Karasjok, we have observed - p- l+- Ii =0.05 X (cm./metre)3 = 5 X 10-8, and thus (calculated p)/(observed p) = 0.05 approximately. Gerdien himself makes I+-I_ considerably larger than Simpson, and concludes that the observed value of p is from 30 to 50 times that calculated. The presumption is either that d2V/dh2 near the ground is much larger numerically than Gerdien supposes, or else that the ordinary instruments for measuring ionization fail to catch some species of ion whose charge is preponderatingly negative. 26. Gerdien (61) has made some calculations as to the probable average value of the vertical electric current in the atmosphere in fine weather. This will be composed of a conduction and a convection current, the latter due to rising or falling air currents carrying ions. He supposes the field near the earth to be loo volts per metre, or 1/300 electrostatic units. For simplicity, he assumes I+ and I_ each equal 0.25 X 10-6 electrostatic units. The specific velocities of the ions-i.e. the velocities in unit field-he takes to be 1.3 X300 for the positive, and I•6X3oo for the negative. The positive and Simspon concluded that for a given wind velocity dissipation is practically a linear function of ionization. 24. Table IX. will give a general idea of the relations of potential gradient to dissipation and ionization. Potential q Karasjok (Simpson (10)). gradients volts per Kremsmunster(41). Freiburg (43). Rothhorn (43): a+ a_ I+ I_ Q metre. 0 to 5o 1.12 5o „ loo 1.14 1.31 .. 4.29 4.67 0.43 0.39 I.II 100 ,, 150 1.24 1.69 3.38 3.93 0.37 0.32 1.15 150 ,, 200 1.48 1.84 .. 1.85 2.58 0.36 0.28 1.28 200 ,, 300 .. .. 3.21 1.37 I.58 o•26 0.19 I.42 300 ,, 400, .. 4'33 o•6o 0.85 .. .. .. 400 ,, 500 5.46 .. . . 500 „ 7001 .. 8.75 negative ions travel in opposite directions, so the total current is (1 /30o) (o.25 X 10-0) (1.3 X 300+ I.6 X 300), or 73 X Io-6 in electrostatic measure, otherwise 2.4 X10-" amperes per sq. cm. As to the convection current, Gerdien supposes-as in § 25-p=2.7 X 10-9 electrostatic units, and on fine days puts the average velocity of rising air currents at lo cm. per second. This gives a convection current of 2.7X10-6 electrostatic units, or about 1/27 of the conduction current. For the total current we have approximately 2.5 X10-" amperes per sq. cm. This is insignificant compared to the size of the currents which several authorities have calculated from considerations as to terrestrial magnetism (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=ant, where q is the number of ions of one sign made in I cc. of air per second by the emanation, a 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 r4 as a mean value. Taking for a Townsend's value 1.2 +10-6, Mache finds n =1800. The charge on an ion being 3.4 X io 10 Mache deduces for the ionic charge, I+ or I_, per cubic metre 1800X3.4 X io '° X 106, or o.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 a 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 theappears 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 Tooth 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." Inhabitants. Hungary 7.7 Upper Missouri and Plains . 15 Netherlands 2.8 Rocky Mountains and Plateau Io England, N.1\4. 1.8 South Atlantic . . 8 1.3 Central Mississippi . 7 „ E. S.M.. . 1.2 Upper " 7 York and W.M. 1.1 Ohio Valley . 7 N 1.o Middle Atlantic 6 Wales. . 0.9 Gulf States 5 England, S.E. . o•8 New England 0.7 Pacific Coast . . End of Article: ATMOSPHERIC ELECTRICITY
ATMOSPHERE (Gr. fir µ6r, vapour; orkaipa, a sphere...

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