+---------------------------------+-----+-----+-----+-----+-----+-----+----+----+-----+-----+-----+-----+
| Place and Period. | Jan.| Feb.|March|April| May | June|July|Aug.|Sept.| Oct.| Nov.| Dec.|
+---------------------------------+-----+-----+-----+-----+-----+-----+----+----+-----+-----+-----+-----+
| Karasjok (10), 1903-1904 | 143 | 150 | 137 | 94 | 74 | 65 | 70 | 67 | 67 | 87 | 120 | 126 |
| Sodankyla (31), 1882-1883 | 94 | 133 | 148 | 155 | 186 | 93 | 53 | 77 | 47 | 72 | 71 | 71 |
| Potsdam (9), 1904 | 167 | 95 | 118 | 88 | 93 | 72 | 73 | 65 | 97 | 101 | 108 | 123 |
| Kew (12), 1898-1904 | 127 | 141 | 113 | 87 | 77 | 70 | 61 | 72 | 76 | 96 | 126 | 153 |
| Greenwich (13), 1893-1894, 1896 | 110 | 112 | 127 | 107 | 83 | 71 | 76 | 84 | 83 | 104 | 104 | 139 |
| Florence (14), 1883-1886 | 132 | 110 | 98 | 84 | 86 | 81 | 77 | 90 | 89 | 99 | 129 | 125 |
| Perpignan (15), 1886-1888 | 121 | 112 | 108 | 89 | 91 | 92 | 89 | 82 | 74 | 99 | 122 | 121 |
| Lisbon (16), 1884-1886 | 104 | 105 | 104 | 92 | 91 | 93 | 87 | 92 | 100 | 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 |
| " (7.8 m.) 1890-1895 | 100 | 89 | 103 | 120 | 98 | 103 | 85 | 99 | 73 | 101 | 117 | 112 |
+---------------------------------+-----+-----+-----+-----+-----+-----+----+----+-----+-----+-----+-----+
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 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 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 not
infrequently the criterion by reference to which days are rejected or
are accepted as normal.
4. The potential gradient near the ground varies with the season of
the year and the hour of the day, and is largely dependent on the
weather conditions. It is thus difficult to form even a rough estimate
of the mean value at any place unless hourly readings exist, extending
over the whole or the greater part of a year. It is even somewhat
precipitate to assume that a mean value deduced from a single year is
fairly representative of average conditions. At Potsdam, G. Ludeling
(9) found for the mean value for 1904 in volts per metre 242. At
Karasjok in the extreme north of Norway G.C. Simpson (10) in 1903-1904
obtained 139. At 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
Kremsmunster, as compared to the comparative similarity between the
results for Kew and Karasjok, suggests that the mean value of the
potential gradient may be much more dependent on local conditions than
on difference of latitude.
At any single station potential gradient has a wide range of values.
The largest positive and negative values recorded are met with during
disturbed weather. During thunderstorms the record from an
electrograph shows large sudden excursions, the trace usually going
off the sheet with every flash of lightning when the thunder is near.
Exactly what the potential changes amount to under such circumstances
it is impossible to say; what the trace shows depends largely on the
type of electrometer. Large rapid changes are also met with in the
absence of thunder during heavy rain or snow fall. In England the
largest values of a sufficiently steady character to be shown
correctly by an ordinary electrograph occur during winter fogs. At
such times gradients of +400 or +500 volts per metre are by no means
unusual at Kew, and voltages of 700 or 800 are occasionally met with.
5. Annual Variation.--Table I. gives the annual variation of the
potential gradient at a number of stations arranged according to
latitude, the mean value for the whole year being taken in each case
as 100. Karasjok as already mentioned is in the extreme north of
Norway (69 deg. 17' N.); Sodankyla was the Finnish station of the
international polar year 1882-1883. At Batavia, which is near the
equator (6 deg. 11' 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
stalions the difference between summer and winter months is
conspicuous. From the European data one would be disposed to conclude
that 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.
TABLE II.--_Diurnal Variation Potential Gradient_.
+-------+--------+---------+-------------+---------+--------+---------+--------+-------+-------------+---------+
|Station|Karasjok|Sodankyla| Kew(19, 12).|Greenwich|Florence|Perpignan| Lisbon.| Tokyo.| Batavia. | Cape |
| | | | | | | | | | |Horn(20).|
+-------+--------+---------+------+------+---------+--------+---------+--------+-------+------+------+---------+
|Period | 1903-4.| 1882-83 | 1862-| 1898-| 1893-96.|1883-85.| 1886-88.|1884-86.|1897-98| 1887-| 1890-| 1882-83.|
| | | | 1864.| 1904.| | | | |1900-1.| 1890.| 1895.| |
+-------+--------+---------+------+------+---------+--------+---------+--------+-------+------+------+---------+
| Days. | | All. | All. |Quiet.| All. | All. | Fine. | All. | All. | Dry. | Dry. | Pos. |
+-------+--------+---------+------+------+---------+--------+---------+--------+-------+------+------+---------+
| h | 5.5 | 3.0 | 3.5 | 3.35 | 3.0 | | 8.4 | 3.0 | 1.7 | 2 | 7.8 | 3.5 |
| l | | 2.5 | 1.0 | 1.3 | 1.8 | | 1.5 | 0.5 | 2.0 | | 7.8 | 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 | 109 | 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 | 117 | 95 |
| 7 | 81 | 97 | 92 | 103 | 100 | 100 | 107 | 101 | 167 | 158 | 147 | 106 |
| 8 | 87 | 100 | 106 | 112 | 102 | 112 | 114 | 105 | 149 | 104 | 119 | 118 |
| 9 | 94 | 98 | 107 | 115 | 100 | 113 | 111 | 104 | 117 | 67 | 82 | 119 |
| 10 | 101 | 102 | 100 | 112 | 101 | 107 | 100 | 104 | 87 | 42 | 55 | 123 |
| 11 | 99 | 98 | 90 | 101 | 96 | 100 | 96 | 102 | 70 | 35 | 46 | 123 |
| Noon. | 103 | 102 | 92 | 94 | 97 | 95 | 99 | 108 | 61 | 30 | 43 | 115 |
| 1 | 106 | 105 | 90 | 89 | 96 | 92 | 99 | 111 | 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 | 110 | 108 | 108 | 99 | 102 | 94 | 113 | 108 | 76 | 67 | 73 | 84 |
| 6 | 119 | 110 | 121 | 108 | 108 | 113 | 126 | 111 | 95 | 91 | 108 | 110 |
| 7 | 129 | 102 | 134 | 115 | 111 | 121 | 131 | 116 | 107 | 120 | 145 | 107 |
| 8 | 136 | 111 | 139 | 118 | 115 | 129 | 129 | 114 | 114 | 137 | 155 | 123 |
| 9 | 139 | 111 | 138 | 119 | 117 | 132 | 120 | 109 | 119 | 146 | 155 | 112 |
| 10 | 133 | 104 | 128 | 115 | 117 | 127 | 109 | 102 | 120 | 148 | 147 | 99 |
| 11 | 121 | 108 | 113 | 108 | 111 | 114 | 97 | 92 | 119 | 151 | 143 | 85 |
| 12 | 102 | 93 | 99 | 99 | 104 | 100 | 86 | 85 | 112 | 147 | 130 | 98 |
+-------+--------+---------+------+------+---------+--------+---------+--------+-------+------+------+---------+
TABLE III.--_Diurnal Variation Potential Gradient_.
+--------+-----------+-----------+-----------------+-----------+-----------+---------+-----------+-----------+
|Station.| Karasjok. | Sodankyla.| Kew. | Greenwich.| Bureau | Eiffel | Perpignan | Batavia |
| | | | | |Central(21)|Tower(21)| (21). | (2 m.) |
+--------+-----------+-----------+-----------------+-----------+-----------+---------+-----------+-----------+
| Period.| 1903-4. | 1882-83. | 1898-1904. |1894, 1896.| 1894-99. | 1896-98.| 1885-95. | 1887-90. |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---------+-----+-----+-----+-----+
| | Win-| Sum-| Win-| Sum-| Win-|Equi-| Sum-| Win-| Sum-| Win-| Sum-| Summer. | Win-| Sum-| Win | Sum-|
| | ter.| mer.| ter.| mer.| ter.| nox.| mer.| ter.| mer.| ter.| mer.| | ter.| mer.| ter.| mer.|
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---------+-----+-----+-----+-----+
| Hour. | | | | | | | | | | | | | | | | |
| 1 | 76 | 104 | 90 | 99 | 91 | 93 | 96 | 87 | 110 | 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 | 111 | 82 | 87 | 90 | 78 | 94 | 75 | 94 | 78 | 72 | 92 | 132 | 123 |
| 6 | 61 | 83 | 80 | 114 | 86 | 97 | 101 | 82 | 101 | 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 | 82 | 93 | 95 | 122 | 104 | 118 | 120 | 97 | 111 | 111 | 120 | 103 | 122 | 108 | 118 | 92 |
| 9 | 90 | 93 | 91 | 109 | 111 | 119 | 119 | 98 | 102 | 113 | 106 | 110 | 126 | 100 | 74 | 64 |
| 10 | 104 | 93 | 106 | 101 | 114 | 110 | 110 | 102 | 98 | 111 | 94 | 109 | 114 | 93 | 43 | 40 |
| 11 | 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 |
| 1 | 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 | 110 | 94 | 90 | 28 | 32 |
| 3 | 119 | 100 | 121 | 93 | 99 | 82 | 76 | 111 | 78 | 111 | 78 | 107 | 95 | 88 | 24 | 41 |
| 4 | 115 | 99 | 111 | 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 | 111 | 109 | 98 | 114 | 98 | 124 | 97 | 109 | 128 | 110 | 88 | 94 |
| 7 | 136 | 110 | 118 | 102 | 114 | 120 | 111 | 117 | 99 | 124 | 123 | 113 | 133 | 122 | 119 | 122 |
| 8 | 134 | 113 | 117 | 106 | 112 | 124 | 123 | 113 | 108 | 116 | 134 | 110 | 131 | 127 | 138 | 135 |
| 9 | 137 | 125 | 115 | 90 | 111 | 123 | 129 | 111 | 118 | 104 | 130 | 109 | 124 | 125 | 145 | 147 |
| 10 | 125 | 135 | 112 | 90 | 108 | 118 | 125 | 110 | 124 | 97 | 122 | 105 | 111 | 117 | 148 | 148 |
| 11 | 114 | 126 | 113 | 103 | 103 | 109 | 116 | 102 | 120 | 90 | 115 | 101 | 96 | 108 | 149 | 152 |
| 12 | 96 | 111 | 95 | 85 | 96 | 99 | 105 | 93 | 116 | 83 | 108 | 94 | 83 | 95 | 148 | 146 |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---------+-----+-----+-----+-----+
At the temperate stations the maximum occurs near midwinter; 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 100. The
data are some from "all" days, some from "quiet," "fine" or "dry"
days. The height, h, and the distance from the wall, l, were 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 10 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 mu ch more conspicuous than the morning minimum.
[Illustration: FIG. 1.]
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 September at Sodankyla,
Greenwich and Batavia; May to August at Kew, Bureau Central (Paris),
Eiffel Tower and Perpignan; and May to July at Karasjok. "Winter"
includes October to March at Sodankyla, Greenwich and Batavia;
November to February at Kew and Bureau Central; November to January at
Karasjok, and December and January at Perpignan. Mean results from
March, April, September and October at Kew are assigned to "Equinox."
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.