Bible Encyclopedias
Atmospheric Electricity

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

Sodankyl. (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

r08

123

Kew (12), 1898 - 1904.. .

127

141

113

87

77

70

61

72

76

96

126

153

Greenwich (13), 1893-1894, 1896

I10

112

127

107

83

71

76

84

83

104

104

139

Florence (14), 1883-1886. .

132

Ho

98

84

86

81

77

90

89

99

129

125

Perpignan (15), 1886-1888 .

121

112

108

89

91

92

89

82

74

99

122

121

Lisbon (16), 1884-1886. .

104

105

104

92

91

93

87

92

loc.

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.), 1887-1890.

97

115

155

127

129

105

79

62

69

79

90

93

, 1 (7.8 m.) 1890-1895

Ioo

89

103

120

98

103

85

99

73

101

117

112

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 themselves in practice. It requires a radium salt of high radioactivity to be at all comparable in effectiveness with a good water-dropper. Experiments by F. Linke (8) indicated that a water-dropper 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. are often too rapid to be satisfactorily dealt with by an ordinary [[Table I]]. - Annual Variation Potential Gradient. 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, however, 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 sometimes electrometer, 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 riot 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 somewhat precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions. At Potsdam, G. Liideling (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 Kremsmunster for 1902 P. B. Zolss (11) 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 Kremsmtinster, 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 Boo Are Occasionally Met With.

Station.	Karasjok.	Sodankyla.	Kew (19, 12).		Greenwich.	Florence.	Perpignan.	Lisbon.	Tokyo.	Batavia.		Cape Horn (20).		Period.	1903 4.	1882 83.	1 864.	19 O 4	1893 96.	1883 85.	1886 88.	1884 86.	1900 I. 8	189 O	9 5.	1882 83.		Days.		All.	All.	Quiet.	All.	All.	Fine.	All.	All.	Dry.	Dry.	Pos.		It		3 O	3.5	3'35	3.O		8.4	3 O	1.7	2	8	3.5		L	5	2.5	I 0	I .3	1.8		1.5	0.5	2.0			2.0		Hour. 1	83	91	87	93	97	92	78	84	101	147	125	82		2	73	85	79	88	89	83	72	80	98	141	114	73		3	66	82	74	84	87	77	71	78	97	135	10 9	85		4	63	84	72	83	86	75	72	81	99	128	102	81		5	60	89	71	85	86	74	77	83	121	127	101	85		6	68	91	77	93	92	82	92	92	154	137	11 7	95		7	81	97	92	103	100	100	107	Ioi	167	158	147	106		8	87	100	106	112	102	I12	114	105	149	104	119	118		9	94	98	107	115	100	113	Iii	104	117	67	82	119		10	Ioi	102	100	I12	Ioi	107	100	104	87	42	55	123		Ii	99	98	90	Rot	96	100	96	102	70	35	46	123		Noon.	103	102	92	94	97	95	99	108	61	30	43	115		I	106	105	90	89	96	92	99	Iii	54	30	42	112		2	108	107	91	87	94	90	97	114	49	30	43	94		3	108	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	'Jo	108	1 O	99	102	94	113	108	76	67	73	84		6	119	I10	121	108	108	113	126	Iii	95	91	108	I10		7	129	102	134	115	Iii	121	131	116	107	120	145	107		8	136	Iii	139	118	115	129	129	114	114	137	1 55	123		9	139	Iii	138	119	117	132	120	109	119	146	155	I12		10	133	104	128	115	117	127	109	102	120	148	1 47	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 Central (21). Eiffel Tower(21) Perpignan (21). Batavia . (2 M.) 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 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 82 87 90 78 94 75 94 78 72 92 132 123 6 61 83 80 114 86 97 Wi 82 Ioi 83 106 87 84 107 138 136 7 78 89 86 117 95 109 113 94 107 98 118 97 104 114 166 153 8 $2 93 95 122 104 118 120 97 Iii Iii 120 103 122 108 118 92 9 90 93 91 109 Iii 119 119 98 102 113 106 I10 126 100 74 64 10 104 93 106 101 114 I10 I10 102 98 Iii 94 109 114 93 43 40 Ii 102 92 98 97 107 95 97 103 86 108 84 107 98 90 35 36 Noon. 119 90 98 100 102 86 87 107 94 106 77 104 99 95 31 30 I 116 94 116 97 99 81 80 107 85 112 79 107 96 93 29 33 2 118 97 113' 97 97 80 76 109 82 112 81 Ii() 94 90 28 32 3 119 100 121 93 99 82 76 Iii 78 Iii 78 107 95 88 24 41 4 115 99 Iii 96 103 88 80 116 81 113 80 105 102 92 30 49 5 120 106 105 106 108 96 87 112 93 120 85 106 115 98 60 74 6 131 104 115 92 Iii 109 98 114 98 124 97 109 128 I10 88 94 7 136 Iio 118 102 114 120 Iii 117 99 124 123 113 133 122 119 122 8 134 113 117 106 112 124 123 113 108 116 134 I Io 131 127 138 135 9 137 125 115 90 Iii 123 129 Iii 118 104 130 109 124 125 145 147 Io 125 135 112 90 108 118 125 I10 124 97 122 105 Iii 117 148 148 Ii 114 126 113 103 103 109 116 1.02 120 90 115 Ioi 96 108 149 152 12 96 Iii 95 85 96 99 105 93 116 83 108 94 83 95 148 146 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 too. 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° II' 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 [[Table Ii]].-Diurnal Variation Potential Gradient. Table IiI.-Diurnal Variation Potential Gradient. 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 24 hourly values being taken as loo. 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 pp P.M., the principal minimum in the morning from 3 to 5 A.M. At some stations the minimum in the afternoon is indistinctly 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 100. By " summer " is meant April to Sep -?? 100 tember at Sodankyla., IllEFIMEM' 90 Greenwich and ust at via; May to August at 111 100 Kew, Bureau Central so (Paris), Eiffel Tower and Perpignan; and May to July at Karasjok. " Winter " in- ,00 eludes October to arch at Sod, so Greenwich and Batavia; November to February at Kew ky and M Kew '110 Bureau Central; December 100, 100 November to January ' at Karasjok, and December and Janu ary at Perpignan. Kew 110 Mean results from June 100 ? - 1 ,00 March, April, Septem ber and October at so Kew are assigned to 110 " Equinox." Kew At Batavia the Potential 100 , - ? 100 difference between r 00 winter and summer is comparatively small. Elsewhere there is a ? inn tendencyforthe double period, usually so prominent in summer, to become less pro- 6 Noon 6 Mid- nounced in winter, the a.m. p.m. night 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. 1. 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 pecuiiar to Paris, being seen, for instance, at Lisbon in summer. The December and June 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 III 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 c 1 sin ( t+ a l) +c2 sin ( 2t+ a 2)+c 3 sin ( 3t+a3)+c4 sin (4t+a 4)+.. . where t denotes time counted from (local) midnight, c 1, c 2, c 4 ,.. are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; al, a2, a 3, a 4, are the corresponding phase angles. One hour of time t is counted as 15°, and a delay of one hour in the time of maximum answers to a diminution of 15° in a l, of 30° in a2, and so on. If a l, say, varies much throughout the year, or if the ratios of i c4, ... to c 1, 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 60-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. Jan. Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. Dec. Mean Potential Gradient 201 224 180 138 123 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 60 54 63 52 82 C I 22 22 17 13 18 9 6 6 9 7 14 30 21 33 34 31 22 23 24 26 23 30 17 21 Amplitudes of Fourier waves c 3 7 10 5 5 3 I 3 2 3 6 5 7 3 5 6 4 1 4 3 4 3 2 3 0 0 ° ° o 0 0 0 ° o 0 0 a, a 2 206 170 204 171 123 186 72 1 93 86 188 79 183 48 185 142 182 154 199 192 206 202 212 208 175 Phase angles of Fourier waves a 3 11 9 36 96 loo 125 124 107 16 18 38 36 a 4 2 35 225 307 314 314 277 293 313 330 288 238 249 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 [[Table Iv]]. - Absolute Potential Data at Kew (12). .110 Eiffel 100 Tower Summer 110 100 Bureau Central Winter Bureau Central 110 Summer 100 110 Kew Barometric 100 Pressure 90 night 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 c l at [[Table V]]. - Fourier Series Amplitudes and Phase Angles. Kew is uncertain. The potential gradient is in all cases lower in summer than winter, and thus the reduction in c 1 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 a i seems comparatively small, but at Potsdam and the Bureau Central it is as large as at Kew. Also, whilst the winter values of a i 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 a 2 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 c l in Table V. from the Bureau Central and the Eiffel Tower, and the reduction of e 2 at the latter station, are unquestionably significant facts; but the summer value for c 2 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 c 2 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 Copyright Statement These files are public domain. Bibliography Information Chisholm, Hugh, General Editor. 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