Chapter IV: Part 4

At Batavia the difference between winter and summer is comparatively
small. Elsewhere there is a tendency for the double period, usually so
prominent in summer, to become less pronounced 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. 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 peculiar 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 111 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

c1 sin(t + a1) + c2 sin(2t + a2) + c3 sin(3t + a3) +
+ c4 sin(4t + a4) + ...

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; a1, a2, a3, a4, are the corresponding phase angles.
One hour of time t is counted as 15 deg., and a delay of one hour in
the time of maximum answers to a diminution of 15 deg. in a1, of 30
deg. in a2, and so on. If a1, say, varies much throughput the year, or
if the ratios of c2, c3, c4, ... to c1, 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.

TABLE IV.--_Absolute Potential Data at Kew_ (12).

+--------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | Jan.| Feb.| Mar.| Apr.| May | June| July| Aug.| Sep.| Oct.| Nov.| Dec.|
+--------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Mean Potential Gradient | 201 | 224 | 180 | 138 | 123 | 111 | 98 | 114 | 121 | 153 | 200 | 243 |
| Mean of individual daily ranges| 203 | 218 | 210 | 164 | 143 | 143 | 117 | 129 | 141 | 196 | 186 | 213 |
| Range in Diurnal inequality | 73 | 94 | 83 | 74 | 71 | 57 | 55 | 60 | 54 | 63 | 52 | 82 |
| / c1 | 22 | 22 | 17 | 13 | 18 | 9 | 6 | 6 | 9 | 7 | 14 | 30 |
| Amplitudes of Fourier | c2 | 21 | 33 | 34 | 31 | 22 | 23 | 24 | 26 | 23 | 30 | 17 | 21 |
| waves < c3 | 7 | 10 | 5 | 5 | 3 | 1 | 3 | 2 | 3 | 6 | 5 | 7 |
| \ c4 | 2 | 3 | 5 | 6 | 4 | 1 | 4 | 3 | 4 | 3 | 2 | 3 |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | deg.| deg.| deg.| deg.| deg.| deg.| deg.| deg.| deg.| deg.| deg.| deg.|
| / a1 | 206 | 204 | 123 | 72 | 86 | 79 | 48 | 142 | 154 | 192 | 202 | 208 |
| Phase angles of Fourier | a1 | 170 | 171 | 186 | 193 | 188 | 183 | 185 | 182 | 199 | 206 | 212 | 175 |
| waves < a3 | 11 | 9 | 36 | 96 | 100 | 125 | 124 | 107 | 16 | 18 | 38 | 36 |
| \ a1 | 235 | 225 | 307 | 314 | 314 | 277 | 293 | 313 | 330 | 288 | 238 | 249 |
+--------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

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 its hour of
maximum). The 12-hour term is much less variable, especially as
regards its phase angle; its amplitude shows distinct maxima near the
equinoxes. That the 8-hour and 6-hour waves, though small near
midsummer, represent more than mere accidental irregularities, seems a
safe inference from the regularity apparent in the annual variation of
their phase angles.

TABLE V.--_Fourier Series Amplitudes and Phase Angles._

+------------------+---------+-------------------------+-------------------------+
| | | 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.

TABLE VI.--_Dissipation. Mean Values._

+--------------------------+-------+--------------+---------------------+------+------+
| Place. |Period.| Season. | Observer or | a[+-]| q |
| | | | Authority. | | |
+--------------------------+-------+--------------+---------------------+------+------+
| Karasjok | 1903-4| Year | Simpson (10) | 3.57 | 1.15 |
| Wolfenbuttel | Year | Elster & Geitel (39)| 1.33 | 1.05 |
| Potsdam | 1904 | Year | Ludeling (40) | 1.13 | 1.33 |
| Kremsmuster | 1902 | Year | Zolss (42) | 1.32 | 1.18 |
| " | 1903 | Year | Zolss (41) | 1.35 | 1.14 |
| Freiburg | | Year | Gockel (43) | .. | 1.41 |
| Innsbruck | 1902 | | Czermak (44) | 1.95 | 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 | 1.09 |
| Misdroy | 1902 | | Ludeling (40) | 1.09 | 1.58 |
| Swinemunde | 1904 |Aug. and Sept.| Ludeling (40) | 1.23 | 1.37 |
| Heligoland (sands) | 1903 | Summer | Elster & Geitel (40)| 1.14 | 1.71 |
| " plateau | " | " | " " (40)| 3.07 | 1.50 |
| 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) | 1.79 | 1.22 |
| 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) | .. |10.3 |
+--------------------------+-------+--------------+---------------------+------+------+

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 11 A.M. and 1 P.M., and in absence of
information as to the diurnal variation it is impossible to say how
much this influences the results. The first eight stations lie 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 confined 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 1 was 30 at Trieste,
33 at Vienna, and 35 at Kremsmunster; at Innsbruck q was less than 1
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 0.11 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 0.78 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. Table 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.

TABLE VII.--_Dissipation._

+--------------------+---------------------------+---------------------------+
| | Winter. | Summer. |
+--------------------+------+------+------+------+------+------+------+------+
| Place. | a+ | a- | a[+-]| q | a+ | a- | a[+-]| q |
+--------------------+------+------+------+------+------+------+------+------+
| Karasjok 1903-1904 | 2.28 | 2.69 | 2.49 | 1.18 | 4.38 | 4.94 | 4.65 | 1.13 |
| Kremsmuster 1903 | 1.14 | 1.30 | 1.22 | 1.14 | 1.38 | 1.56 | 1.47 | 1.12 |
| Freiburg | .. | .. | .. | 1.57 | .. | .. | .. | 1.26 |
| Trieste 1902-1903 | 0.56 | 0.59 | 0.58 | 1.07 | 0.55 | 0.61 | 0.58 | 1.13 |
| " calm days | .. | .. | 0.35 | .. | .. | .. | 0.48 | .. |
+--------------------+------+------+------+------+------+------+------+------+

15. _Diurnal Variation._--P.B. Zolss (41, 42) has published diurnal
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 1 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 0.82 to 1.35, and a- from
0.85 to 1.47. At midsummer the extreme hourly values were 0.91 and
1.45 for a+, 0.94 and 1.60 for a-. The corresponding figures at
midwinter were 0.65 and 1.19 for a+, 0.61 and 1.43 for a-. Zolss' 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 1 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 4-1/2 times that at 1 P.M. q
(taken as [Sigma](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 occurring 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 2-1/2 times the least.
On Mont Blanc, le Cadet (43) found q largest from 1 to 3 P.M., the
value at either of these hours being more than double that at 11 A.M.
On the Patscherkofel, H. von Ficker and A. Defant (52), observing in
December, found q largest from 1 to 2 P.M. and least between 11 A.M.
and noon, but the largest value was only 1-1/2 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 1 km. per hour in wind velocity. The following
are some of his figures, the velocity v being in kilometres per
hour:--

+-----+---------+-----------+-----------+-----------+
| v | 0 to 4. | 20 to 24. | 40 to 49. | 60 to 69. |
+-----+---------+-----------+-----------+-----------+
| a | 0.33 | 0.64 | 1.03 | 1.38 |
| q | 1.13 | 1.19 | 1.00 | 0.96 |
+-----+---------+-----------+-----------+-----------+

For velocities from 0 to 24 km. per hour q exceeded unity in 74 cases
out of 100; but for velocities over 50 km. per hour q exceeded unity
in only 40 cases out of 100. 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 80 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 deg. to +15 deg. C. For example, when the
temperature was below -20 deg. mean values were 0.76 for a+ and 0.91
for a-; for temperatures between -10 deg. and -5 deg. the
corresponding means were 2.45 and 2.82; while for temperatures between
+10 deg. and +15 deg. 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 0 deg. to
30 deg. 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 deg. or 5 deg. 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 100 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 recognize 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 10% 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, 0 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 0 and 1 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 to which they are ordinarily
referred is 1 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. These will suffice to give
a general idea of the mean values met with.

+------------+-----------------+------+------+------+
| Station. | Authority. | I+ | I- | Q |
+------------+-----------------+------+------+------+
| Freiburg | Gockel | 0.34 | 0.24 | 1.41 |
| Karasjok | Simpson | 0.38 | 0.33 | 1.17 |
| Mattsee | von Schweidler | 0.35 | 0.29 | 1.19 |
| Seewalchen | " | 0.45 | 0.38 | 1.17 |
+------------+-----------------+------+------+------+

Gockel's mean values of I+ and Q would be reduced to 0.31 and 1.38
respectively if his values for July--which appear abnormal--were
omitted. I+ and I- 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 0.67.

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 | 0.21 | 1.49 | 0.33 | 0.27 | 1.22 |
| Summer | 0.39 | 0.28 | 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 I- throughout the whole year much the same between noon and 1
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 10% in I-. 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- | I+ | I- |
+-------+-------+-------+-------+-------+-------+-------+-------+
| 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 to | 4 P.M.| 9 to |
| | | | | |10 P.M.| |10 P.M.|
+-------+-------+-------+-------+-------+-------+-------+-------+

Gockel did not observe between 10 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 -20 deg. -10 deg. to -5 deg. 10 deg. to 15 deg.
I+ = 0.18, I- = 0.36 I+ = 0.36, I- = 0.30 I+ = 0.45, 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 40 and 50 mean values were 0.306 for I+
and 0.219 for I-; whilst for relative humidities between 90 and 100
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 0.86 for I+ and 1.09 for I-.

20. In 1901 Elster and Geitel found that a radioactive emanation is
present in the atmosphere. Their method of measuring the radioactivity
is as follows (48): A wire not exceeding 1 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 1 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 (10 metres long) is
introduced it falls from 264 to 201 volts in 10 minutes, then

10A = (254 - 201) X 6 - (264 - 255) X 4 = 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 150 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 8.30 to 10.30 P.M. than between 10 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 I[+-]. To
eliminate the disturbing influence of wind, different wind strengths
are treated separately.

TABLE VIII.--_Mean Values of a[+-]._

+----------+--------------+----------+----------+----------+----------+
| Wind |I[+-]0 to 0.1.|0.1 to 0.2|0.2 to 0.3|0.3 to 0.4|0.4 to 0.5|
| Strength.| | | | | |
+----------+--------------+----------+----------+----------+----------+
| 0 to 1 | 0.45 | 0.60 | 1.26 | 2.04 | 3.03 |
| 1 " 2 | 0.65 | 1.08 | 1.85 | 2.92 | 3.83 |
| 2 " 3 | .. | .. | 2.70 | 3.88 | 5.33 |
+----------+--------------+----------+----------+----------+----------+

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.

TABLE IX.--_Potential, Dissipation, Ionization._

+------------+----------------------------+----------------------------------+
| Potential | q | Karasjok (Simpson (10)). |
| gradients | | |
| volts per +----------+--------+--------+------+------+------+------+------+
| metre. | Kremsmun-| Freibu-| Rothho-| a+ | a- | I+ | I- | Q |
| | ster(41).|rg (43).| rn(43).| | | | | |
+------------+----------+--------+--------+------+------+------+------+------+
| 0 to 50 | .. | 1.12 | .. | .. | .. | .. | .. | .. |
| 50 " 100 | 1.14 | 1.31 | .. | 4.29 | 4.67 | 0.43 | 0.39 | 1.11 |
| 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 | 1.58 | 0.26 | 0.19 | 1.42 |
| 300 " 400 | .. | .. | 4.33 | 0.60 | 0.85 | .. | .. | .. |
| 400 " 500 | .. | .. | 5.46 | .. | .. | .. | .. | .. |
| 500 " 700 | .. | .. | 8.75 | .. | .. | .. | .. | .. |
+------------+----------+--------+--------+------+------+------+------+------+

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 Kremsmunster Zolss (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 relationship 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 100 and 150
the mean value of a- was 1.27 times greater than when A lay between 0
and 50; while when A lay between 120 and 150 the mean value of I+ was
1.53 times larger than when A lay between 0 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, [rho] 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^(-2)(d/dr)(r^2 dV/dr) + 4[pi][rho] = 0.

For practical purposes we may treat r^2 as constant, and replace d/dr
by d/dh, where h is height in centimetres above the ground.

We thus find [rho] = -(1/4[pi]) (d^2)V/d(h^2).

If we take a tube of force 1 sq. cm. in section, and suppose it cut by
equipotential surfaces at heights h1 and h2 above the ground, we have
for the total charge M included in the specified portion of the tube

4[pi]M = (dV/dh)h1 - (dV/dh)h2.

Taking Linke's (28) figures as given in S 10, and supposing h1 = 0, h2
= 15 X 10^4, 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 = (1/(4[pi])) (125.25)/100. Taking 1 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 [sigma] = - (1/(4[pi])) X 125 volts per metre, = 0.000331 in e
ectrostatic units. Thus, on the view now generally current, in the
circumstances answering to Linke's experiments we have on the ground a
charge of -331 X 10^(-6) C.G.S. units per sq. cm. Of the corresponding
positive charge, 265 X 10^(-6) lies below the 1500 metres level, 40 X
10^(-6) between this and the 4000 metres level, and only 26 X 10^(-6)
above 4000 metres.

There is 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 (d^2)V/d(h^2) is - (1/10) volt/(metre)^2. From
this we deduce for the charge [rho] per cubic centimetre (1/(4[pi])) X
10^(-5) (volt/cm^2), or 2.7 X 10^(-9) electrostatic units. But taking,
for example, Simpson's mean values at Karasjok, we have observed

[rho] [equivalent] I+ - I1 = 0.05 X (cm./metre)^3 = 5 X 10^(-8),

and thus (calculated [rho])/(observed [rho]) = 0.05 approximately.
Gerdien himself makes I+ - I- considerably larger than Simpson, and
concludes that the observed value of [rho] is from 30 to 50 times that
calculated. The presumption is either that (d^2)V/d(h^2) 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 100 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 X
300 for the positive, and 1.6 X 300 for the negative. The positive and
negative ions travel in opposite directions, so the total current is
(1/300)(0.25 X 10^(-6))(1.3 X 300 + 1.6 X 300), or 73 X 10^(-8) in
electrostatic measure, otherwise 2.4 X 10^(-16) amperes per sq. cm. As
to the convection current, Gerdien supposes--as in S 25--[rho] = 2.7 X
10^(-9) electrostatic units, and on fine days puts the average
velocity of rising air currents at 10 cm. per second. This gives a
convection current of 2.7 X 10^(-8) electrostatic units, or about 1/27
of the conduction current. For the total current we have approximately
2.5 X 10^(-16) amperes per sq. cm. This is insignificant compared to
the size of the currents which several authorities have calculated
from considerations as to 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.