+------------+----------------------------+----------------------------------+
| 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.
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 = [alpha] n^2, where q is the number
of ions of one sign made in 1 cc. of air per second by the emanation,
[alpha] 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 q = 4 as
a mean value. Taking for [alpha] Townsend's value 1.2 X 10^(-6), Mache
finds n = 1800. The charge on an ion being 3.4 X 10^(-10) Mache
deduces for the ionic charge, I+ or I-, per cubic metre 1800 X 3.4 X
10^(-10) X 10^6, or 0.6. 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 [alpha] 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 = [root](q/[alpha]),
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 the average
annual number of thunderstorm days to be respectively 6.4 and 10.7;
while at Paris (1873-1893) E. Renou (66) found 27.3 such days. In some
tropical stations, at certain seasons of the year, thunder is almost a
daily occurrence. At Batavia (18) during the epoch 1867-1895, there
were on the average 120 days of thunder in the year.
As an example of a large area throughout which thunder frequency
appears 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 100th 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."