+------------------+---------+-------------------------+-------------------------+
| | | Winter. | Summer . |
| Place. | Period. +------+------+-----+-----+------+------+-----+-----+
| | | c1. | c2. | a1. | a2. | c1. | c2. | a1. | a2. |
+------------------+---------+------+------+-----+-----+------+------+-----+-----+
| | | | | deg.| deg.| | | deg.| deg.|
| Kew | 1862-64 |0.283 |0.160 | 184 | 193 |0.127 |0.229 | 111 | 179 |
| " |1898-1904| .102 | .103 | 206 | 180 | .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) | 1902-03 | .. | .. | .. | .. | .208 | .120 | 178 | 145 |
| Karasjok | 1903-04 | .356 | .144 | 189 | 155 | .165 | .093 | 141 | 144 |
| Kremsmunster (23)| 1902 | .280 | .117 | 224 | 194 | .166 | .153 | 241 | 209 |
| Potsdam | 1904 | .269 | .101 | 194 | 185 | .096 | .152 | 343 | 185 |
+------------------+---------+------+------+-----+-----+------+------+-----+-----+
9. Table V. gives some data for the 24-hour and 12-hour Fourier
coefficients, which will serve to illustrate the diversity between
different stations. In this table, unlike Table IV., amplitudes are
all expressed as decimals of the mean value of the potential gradient
for the corresponding season. "Winter" means generally the four
midwinter, and "summer" the four midsummer, months; but at Karasjok
three, and at 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 c1 at
Kew is uncertain. The potential gradient is in all cases lower in
summer than winter, and thus the reduction in c1 in summer would
appear even larger than in Table V. if the results were expressed in
absolute measure. At Karasjok and Kremsmunster the seasonal variation
in a1 seems comparatively small, but at Potsdam and the Bureau Central
it is as large as at Kew. Also, whilst the winter values of a1 are
fairly similar at the several stations the summer values are widely
different. Except at Karasjok, where the diurnal changes seem somewhat
irregular, the relative amplitude of the 12-hour term is considerably
greater in summer than in winter. The values of a2 at the various
stations differ comparatively little, and show but little seasonal
change. Thus the 12-hour term has a much greater uniformity than the
24-hour term. This possesses significance in connexion with the view,
supported by A.B. Chauveau (21), F. Exner (24) and others, that the
12-hour term is largely if not entirely a local phenomenon, due to the
action of the lower atmospheric strata, and tending to disappear even
in summer at high altitudes. Exner attributes the double daily
maximum, which is largely a consequence of the 12-hour wave, to a thin
layer near the ground, which in the early afternoon absorbs the solar
radiation of shortest wave length. This layer he believes specially
characteristic of arid dusty regions, while comparatively non-existent
in moist climates or where foliage is luxuriant. In support of his
theory Exner states that he has found but little trace of the double
maximum and minimum in Ceylon and elsewhere. C. Nordmann (25)
describes some similar results which he obtained in Algeria during
August and September 1905. His station, Philippeville, is close to the
shores of the Mediterranean, and sea breezes persisted during the day.
The diurnal variation showed only a single maximum and minimum,
between 5 and 6 P.M. and 4 and 5 A.M. respectively. So again, a few
days' observations on the top of Mont Blanc (4810 metres) by le Cadet
(26) in August and September 1902, showed only a single period, with
maximum between 3 and 4 P.M., and minimum about 3 A.M. Chauveau points
to the reduction in the 12-hour term as compared to the 24-hour term
on the Eiffel Tower, and infers the practical disappearance of the
former at no great height. The close approach in the values for c1 in
Table V. from the Bureau Central and the Eiffel Tower, and the
reduction of c2 at the latter station, are unquestionably significant
facts; but the summer value for c2 at Karasjok--a low level
station--is nearly as small as that at the Eiffel Tower, and notably
smaller than that at the Sonnblick (3100 metres). Again, Kew is
surrounded by a large park, not devoid of trees, and hardly the place
where Exner's theory would suggest a large value for c2, and yet the
summer value of c2 at Kew is the largest in Table V.
10. Observations on mountain tops generally show high potentials near
the ground. This only means that the equipotential surfaces are
crowded together, just as they are near the ridge of a house. To
ascertain how the increase in the voltage varies as the height in the
free atmosphere increases, it is necessary to employ kites or
balloons. At small heights Exner (27) has employed captive balloons,
provided with a burning fuse, and carrying a wire connected with an
electroscope on the ground. He found the gradient nearly uniform for
heights up to 30 to 40 metres above the ground. At great heights free
balloons seem necessary. The balloon carries two collectors a given
vertical distance apart. The potential difference between the two is
recorded, and the potential gradient is thus found. Some of the
earliest balloon observations made the gradient increase with the
height, but such a result is now regarded as abnormal. A balloon may
leave the earth with a charge, or become charged through discharge of
ballast. These possibilities may not have been sufficiently realized
at first. Among the most important balloon observations are those by
le Cadet (1) F. Linke (28) and H. Gerdien (29). The following are
samples from a number of days' results, given in le Cadet's book. h is
the height in metres, P the gradient in volts per metre.
Aug. 9, 1893 / h 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 from day to day and hour to
hour; but at greater heights there is much more uniformity. At heights
from 1500 to 6000 metres his observations agreed well with the formula
dV/dh = 34 - 0.006h,
V denoting the potential, h the height in metres. The formula makes
the gradient diminish from 25 volts per metre at 1500 metres height to
10 volts per metre at 4000 metres. Linke's mean value for dV/dh at the
ground was 125. Accepting Linke's formula, the potential at 4000
metres is 43,750 volts higher than at 1500 metres. If the mean of the
gradients observed at the ground and at 1500 metres be taken as an
approximation to the mean value of the gradient throughout the lowest
1500 metres of the atmosphere, we find for the potential at 1500
metres level 112,500 volts. Thus at 4000 metres the potential seems of
the order of 150,000 volts. Bearing this in mind, one can readily
imagine how close together the equipotential surfaces must lie near
the summit of a high sharp mountain peak.
11. At most stations a negative potential gradient is exceptional,
unless during rain or thunder. During rain the potential is usually
but not always negative, and frequent alternations of sign are not
uncommon. In some localities, however, negative potential gradient is
by no means uncommon, at least at some seasons, in the absence of
rain. At Madras, Michie Smith (30) often observed negative potential
during bright August and September days. The phenomenon was quite
common between 9.30 A.M. and noon during westerly winds, which at
Madras are usually very dry and dusty. At Sodankyla, in 1882-1883,
K.S. Lemstrom and F.C. Biese (31) found that out of 255 observed
occurrences of negative potential, 106 took place in the absence of
rain or snow. The proportion of occurrences of negative potential
under a clear sky was much above its average in autumn. At 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 sometimes associated with aurora (see AURORA
POLARIS).
Lenard, Elster and Geitel, and others have found the potential
gradient negative near waterfalls, the influence sometimes extending
to a considerable distance. Lenard (33) found that when pure water
falls upon water the neighbouring air takes a negative charge. Kelvin,
Maclean and Gait (34) found the effect greatest in the air near the
level of impact. A sensible effect remained, however, after the
influence of splashing was eliminated. Kelvin, Maclean and Galt regard
this property of falling water as an objection to the use of a
water-dropper indoors, though not of practical importance when it is
used out of doors.
12. Elster and Geitel (35) have measured the charge carried by
raindrops falling into an insulated vessel. Owing to observational
difficulties, the exact measure of success attained is a little
difficult to gauge, but it seems fairly certain that raindrops usually
carry a charge. Elster and Geitel found the sign of the charge often
fluctuate repeatedly during a single rain storm, but it seemed more
often than not opposite to that of the simultaneous potential
gradient. Gerdien has more recently repeated the experiments,
employing an apparatus devised by him for the purpose. It has been
found by C.T.R. Wilson (36) that a vessel in which freshly fallen rain
or snow has been evaporated to dryness shows radioactive properties
lasting for a few hours. The results obtained from equal weights of
rain and snow seem of the same order.
13. W. Linss (6) found that an insulated conductor charged either
positively or negatively lost its charge in the free atmosphere; the
potential V after time t being connected with its initial value V0 by
a formula of the type V = V0e^(-at) where a is constant. This was
confirmed by Elster and Geitel (7), whose form of dissipation
apparatus has been employed in most recent work. The percentage of the
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 denoted by
a[+-] or simply by a, while q is employed for the ratio a-/a+. Some
observers when giving mean values take [Sigma](a-/a+) as the mean
value of q, while others take [Sigma](a-)/[Sigma](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-
without 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.