Chapter LXIII: repeats the promise of freedom to the English church (11)

+-----+--------------------------------------+-------------------------------------+
| | Forenoon. | Afternoon. |
|Hour.+------------+-----------+-------------+-----------+-----------+-------------+
| | Kew | Greenwich |Parc St Maur | Kew | Greenwich |Parc St Maur |
| | 1890-1900. | 1890-1894.| 1883-1897. | 1890-1900.| 1890-1894.| 1893-1897. |
+-----+------------+-----------+-------------+-----------+-----------+-------------+
| | ´ | ´ | ´ | ´ | ´ | ´ |
| 1 | -0.58 | -0.59 | -0.63 | +0.42 | +0.44 | +0.40 |
| 2 | -0.54 | -0.47 | -0.47 | +0.52 | +0.45 | +0.50 |
| 3 | -0.51 | -0.31 | -0.32 | +0.57 | +0.52 | +0.59 |
| 4 | -0.41 | -0.23 | -0.16 | +0.60 | +0.51 | +0.55 |
| 5 | -0.28 | -0.10 | -0.01 | +0.46 | +0.34 | +0.38 |
| 6 | -0.08 | +0.12 | +0.18 | +0.21 | +0.04 | +0.07 |
| 7 | +0.13 | +0.30 | +0.34 | -0.06 | -0.24 | -0.25 |
| 8 | +0.29 | +0.48 | +0.47 | -0.27 | -0.50 | -0.54 |
| 9 | +0.40 | +0.56 | +0.53 | -0.47 | -0.68 | -0.74 |
| 10 | +0.44 | +0.58 | +0.51 | -0.61 | -0.78 | -0.79 |
| 11 | +0.48 | +0.50 | +0.44 | -0.62 | -0.77 | -0.79 |
| 12 | +0.45 | +0.44 | +0.38 | -0.54 | -0.61 | -0.67 |
+-----+------------+-----------+-------------+-----------+-----------+-------------+

Magnetic Disturbances.

§ 31. A satisfactory definition of magnetic disturbance is about as
difficult to lay down as one of heterodoxy. The idea in its generality
seems to present no difficulty, but it is a very different matter when
one comes to details. Amongst the chief disturbances recorded since
1890 are those of February 13-14 and August 12, 1892; July 20 and
August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903;
February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On
such days as these the oscillations shown by the magnetic curves are
large and rapid, aurora is nearly always visible in temperate
latitudes, earth currents are prominent, and there is
interruption--sometimes very serious--in the transmission of telegraph
messages both in overhead and underground wires. At the other end of
the scale are days on which the magnetic curves show practically no
movement beyond the slow regular progression of the regular diurnal
inequality. But between these two extremes there are an infinite
variety of intermediate cases. The first serious attempt at a precise
definition of disturbance seems due to General Sabine[35a]. His method
had once an extensive vogue, and still continues to be applied at some
important observatories. Sabine regarded a particular observation as
disturbed when it differed from the mean of the observations at that
hour for the whole month by not less than a certain limiting value.
His definition takes account only of the extent of the departure from
the mean, whether the curve is smooth at the time or violently
oscillating makes no difference. In dealing with a particular station
Sabine laid down separate limiting values for each element. These
limits were the same, irrespective of the season of the year or of the
sun-spot frequency. A departure, for example, of 3´.3 at Kew from the
mean value of declination for the hour constituted a disturbance,
whether it occurred in December in a year of sun-spot minimum, or in
June in a year of sun-spot maximum, though the regular diurnal
inequality range might be four times as large in the second case as in
the first. The limiting values varied from station to station, the
size depending apparently on several considerations not very clearly
defined. Sabine subdivided the disturbances in each element into two
classes: the one tending to increase the element, the other tending to
diminish it. He investigated how the numbers of the two classes varied
throughout the day and from month to month. He also took account of
the aggregate value of the disturbances of one sign, and traced the
diurnal and annual variations in these aggregate values. He thus got
two sets of diurnal variations and two sets of annual variations of
disturbance, the one set depending only on the number of the disturbed
hours, the other set considering only the aggregate value of the
disturbances. Generally the two species of disturbance variations were
on the whole fairly similar. The aggregates of the + and -
disturbances for a particular hour of the day were seldom equal, and
thus after the removal of the disturbed values the mean value of the
element for that hour was generally altered. Sabine's complete scheme
supposed that after the criterion was first applied, the hourly means
would be recalculated from the undisturbed values and the criterion
applied again, and that this process would be repeated until the
disturbed observations all differed by not less than the accepted
limiting value from the final mean based on undisturbed values alone.
If the disturbance limit were so small that the disturbed readings
formed a considerable fraction of the whole number, the complete
execution of Sabine's scheme would be exceedingly laborious. As a
matter of fact, his disturbed readings were usually of the order of 5%
of the total number, and unless in the case of exceptionally large
magnetic storms it is of little consequence whether the first choice
of disturbed readings is accepted as final or is reconsidered in the
light of the recalculated hourly means.

Sabine applied his method to the data obtained during the decade 1840
to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to
data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C.
Chambers[36] applied it to data from Bombay. The yearly publication of
the Batavia observatory gives corresponding results for that station,
and Th. Moureaux [33] has published similar data for Parc St Maur.
Tables XXX. to XXXII. are based on a selection of these data. Tables
XXX. and XXXI. show the annual variation in Sabine's disturbances, the
monthly values being expressed as percentages of the arithmetic mean
value for the 12 months. The Parc St Maur and Batavia data, owing to
the long periods included, are especially noteworthy. Table XXX. deals
with the east (E) and west (W) disturbances of declination separately.
Table XXXI., dealing with disturbances in horizontal and vertical
force, combines the + and - disturbances, treated numerically. At Parc
St Maur the limits required to qualify for disturbance were 3´.0 in D,
20[gamma] in H, and 12[gamma] in V; the corresponding limits for
Batavia were 1´.3, 11[gamma] and 11[gamma]. The limits for D at
Toronto, Bombay and Hobart were respectively 3´.6, 1´.4 and 2´.4.

At Parc St Maur the disturbance data from all three elements give
distinct maxima near the equinoxes; a minimum at midwinter is clearly
shown, and also one at midsummer, at least in D and H. A decline in
disturbance at midwinter is visible at all the stations, but at
Batavia the equinoctial values for D and V are inferior to those at
midsummer.

TABLE XXX.--Annual Variation of Disturbances (Sabine's numbers).

+-----------+-------------+-------------+-------------+-------------+-------------+
| | Parc St Maur| Toronto | Bombay | Batavia | Hobart |
| | 1883-97. | 1841-48. | 1859-65. | 1883-99. | 1843-48. |
+-----------+------+------+------+------+------+------+------+------+------+------+
| Month. | E. | W. | E. | W. | E. | W. | E. | W. | E. | W. |
+-----------+------+------+------+------+------+------+------+------+------+------+
| January | 78 | 60 | 55 | 66 | 89 | 89 | 180 | 223 | 165 | 182 |
| February | 116 | 92 | 75 | 86 | 94 | 67 | 138 | 144 | 121 | 116 |
| March | 126 | 107 | 92 | 94 | 129 | 97 | 102 | 87 | 114 | 104 |
| April | 105 | 113 | 115 | 114 | 106 | 129 | 67 | 73 | 110 | 102 |
| May | 101 | 118 | 101 | 101 | 63 | 99 | 72 | 71 | 62 | 53 |
| June | 77 | 89 | 95 | 72 | 78 | 81 | 45 | 27 | 32 | 37 |
| July | 82 | 104 | 140 | 126 | 121 | 173 | 62 | 46 | 50 | 49 |
| August | 88 | 113 | 137 | 133 | 154 | 131 | 69 | 69 | 86 | 78 |
| September | 134 | 137 | 163 | 139 | 111 | 108 | 135 | 144 | 135 | 114 |
| October | 119 | 115 | 101 | 111 | 140 | 128 | 95 | 88 | 124 | 123 |
| November | 99 | 94 | 73 | 85 | 43 | 43 | 106 | 91 | 79 | 111 |
| December | 75 | 58 | 51 | 72 | 72 | 55 | 124 | 137 | 123 | 130 |
+-----------+------+------+------+------+------+------+------+------+------+------+

Table XXXII. shows in some cases a most conspicuous diurnal variation
in Sabine's disturbances. The data are percentages of the totals for
the whole 24 hours. But whilst at Batavia the easterly and westerly
disturbances in D vary similarly, at Parc St Maur they follow opposite
laws, the easterly showing a prominent maximum near noon, the westerly
a still more prominent maximum near midnight. The figures in the
second last line of the table, if divided by 0.24, will give the
percentage of hours which show the species of disturbance indicated.
For instance, at Parc St Maur, out of 100 hours, 3 show disturbances
to the west and 3.7 to the east; or in all 6.7 show disturbances of
declination. The last line gives the average size of a disturbance of
each type, the unit being 1´ in D and 1[gamma] in H and V.

TABLE XXXI.--Annual Variation of Disturbances.

+-----------+-------------+-------------+---------------------------+
| |Parc St Maur.| Toronto. | Batavia. |
+-----------+-------------+-------------+-------------+-------------+
| Month. | Numbers. | Aggregates. | Numbers. | Aggregates. |
+-----------+------+------+------+------+------+------+------+------+
| | H. | V. | H. | V. | H. | V. | H. | V. |
| +------+------+------+------+------+------+------+------+
| January | 81 | 51 | 58 | 56 | 96 | 151 | 89 | 154 |
| February | 96 | 133 | 94 | 74 | 105 | 123 | 110 | 125 |
| March | 126 | 118 | 94 | 108 | 116 | 105 | 117 | 103 |
| April | 94 | 111 | 150 | 149 | 104 | 76 | 105 | 73 |
| May | 108 | 133 | 90 | 112 | 101 | 92 | 105 | 95 |
| June | 90 | 85 | 36 | 50 | 82 | 69 | 79 | 66 |
| July | 99 | 128 | 61 | 71 | 90 | 83 | 95 | 81 |
| August | 113 | 92 | 75 | 108 | 91 | 91 | 98 | 91 |
| September | 119 | 122 | 171 | 160 | 113 | 111 | 114 | 115 |
| October | 101 | 94 | 148 | 129 | 114 | 89 | 104 | 86 |
| November | 104 | 81 | 98 | 75 | 99 | 102 | 100 | 101 |
| December | 70 | 51 | 128 | 100 | 89 | 108 | 84 | 110 |
+-----------+------+------+------+------+------+------+------+------+

At Batavia disturbances increasing and decreasing the element are
about equally numerous, but this is exceptional. Easterly disturbances
of declination predominated at Toronto, Point Barrow, Fort Kennedy,
Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse
was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and
Parc St Maur the ratios borne by the eastern to the western
disturbances were 1.19 and 1.23 respectively, and so not much in
excess of unity; but the preponderance of easterly disturbances at the
North American[37] stations was considerably larger than this.

TABLE XXXII.--Diurnal Variation of Disturbances (Sabine's numbers).

+-------------+-----------------------------------------+-----------------------------------------+
| | Parc St Maur. | Batavia. |
| +-------------+-------------+-------------+-------------+-------------+-------------+
| Hour. | D. | H. | V. | D. | H. | V. |
| +------+------+------+------+------+------+------+------+------+------+------+------+
| | E. | W. | + | - | + | - | E. | W. | + | - | + | - |
+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
| 0-3 | 10.1 | 20.3 | 9.0 | 8.3 | 5.7 | |9.2 | 1.1 | 5.8 | 13.1 | 6.6 | 4.0 | 7.4 |
| 3-6 | 12.3 | 8.2 | 8.4 | 8.0 | 6.4 | 10.4 | 7.6 | 7.3 | 14.2 | 4.8 | 6.3 | 10.0 |
| 6-9 | 15.7 | 3.8 | 14.1 | 12.5 | 7.2 | 9.0 | 24.9 | 16.8 | 12.1 | 9.9 | 21.2 | 21.7 |
| 9-noon | 16.2 | 5.1 | 18.0 | 15.6 | 12.9 | 15.4 | 38.5 | 33.0 | 8.6 | 15.8 | 19.8 | 16.4 |
| noon-3 | 19.3 | 6.7 | 15.3 | 16.5 | 18.2 | 18.3 | 18.8 | 24.7 | 16.8 | 21.1 | 23.5 | 22.1 |
| 3-6 | 14.8 | 9.7 | 12.5 | 15.4 | 22.9 | 21.8 | 6.4 | 5.4 | 13.3 | 16.9 | 12.6 | 12.7 |
| 6-9 | 5.7 | 21.2 | 11.4 | 13.2 | 18.9 | 11.2 | 2.3 | 3.4 | 9.9 | 13.6 | 7.1 | 4.1 |
| 9-12 | 5.9 | 25.0 | 11.2 | 10.5 | 7.8 | 4.7 | 0.4 | 3.8 | 12.0 | 11.1 | 5.6 | 5.4 |
+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
| Mean number | | | | | | | | | | | | |
| per day | 0.88| 0.72| 1.15| 1.56| 1.04| 0.96| 0.46| 0.44| 1.62| 1.61| 1.19| 1.13|
| Mean size | .. | .. | .. | .. | .. | .. | 1.72| 1.69| 18.0| 19.5 | 16.7 | 15.5 |
+-------------+------+------+------+------+------+------+------+------+------+------+------+------+

§ 32. From the point of view of the surveyor there is a good deal to
be said for Sabine's definition of disturbance, but it is less
satisfactory from other standpoints. One objection has been already
indicated, viz. the arbitrariness of applying the same limiting value
at a station irrespective of the size of the normal diurnal range at
the time. Similarly it is arbitrary to apply the same limit between 10
a.m. and noon, when the regular diurnal variation is most rapid, as
between 10 p.m. and midnight, when it is hardly appreciable. There
seems a distinct difference of phase between the diurnal inequalities
on different types of days at the same season; also the phase angles
in the Fourier terms vary continuously throughout the year, and much
more rapidly at some stations and at some seasons than at others. Thus
there may be a variety of phenomena which one would hesitate to regard
as disturbances which contribute to the annual and diurnal variations
in Tables XXX. to XXXII.

Sabine, as we have seen, confined his attention to the departure of
the hourly reading from the mean for that hour. Another and equally
natural criterion is the apparent character of the magnetograph curve.
At Potsdam curves are regarded as "1" quiet, "2" moderately disturbed,
or "3" highly disturbed. Any hourly value to which the numeral 3 is
attached is treated as disturbed, and the annual Potsdam publication
contains tables giving the annual and diurnal variations in the number
of such disturbed hours for D, H and V. According to this point of
view, the extent to which the hourly value departs from the mean for
that hour is immaterial to the results. It is the greater or less
sinuosity and irregularity of the curve that counts. Tables XXXIII.
and XXXIV. give an abstract of the mean Potsdam results from 1892 to
1901. The data are percentages: in Table XXXIII. of the mean monthly
total, in Table XXXIV. of the total for the day. So far as the annual
variation is concerned, the results in Table XXXIII. are fairly
similar to those in Table XXX. for Parc St Maur. There are pronounced
maxima near the equinoxes, especially the spring equinox. The diurnal
variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus
in the case of H the largest disturbance numbers at Parc St Maur
occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur
between 4 p.m. and midnight. Considering the comparative proximity of
Parc St Maur and Potsdam, one must conclude that the apparent
differences between the results for these two stations are due almost
entirely to the difference in the definition of disturbance.

TABLE XXXIII.--Annual Variation of Potsdam Disturbances.

+---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
| Element.| Jan.| Feb.| Mar.| April.| May.| June.| July.| Aug.| Sept.| Oct.| Nov.| Dec.|
+---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
| D | 129 | 170 | 149 | 90 | 86 | 57 | 62 | 64 | 59 | 118 | 94 | 82 |
| H | 109 | 133 | 131 | 102 | 109 | 82 | 94 | 91 | 89 | 101 | 75 | 84 |
| V | 106 | 171 | 170 | 108 | 121 | 56 | 64 | 74 | 93 | 87 | 78 | 70 |
+---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
| Mean | 115 | 158 | 150 | 100 | 105 | 65 | 73 | 76 | 94 | 102 | 82 | 79 |
+---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+

TABLE XXXIV.--Diurnal Variation of Potsdam Disturbances.

+--------+------+------+-----+---------+------+------+------+-------+
| Hours. | 1-3. | 4-6. | 7-9.| 10-noon.| 1-3. | 4-6. | 7-9. | 10-12.|
+--------+------+------+-----+---------+------+------+------+-------+
| D | 14.9 | 11.1 | 8.0 | 5.2 | 5.7 | 13.1 | 22.5 | 19.5 |
| H | 10.5 | 8.4 | 8.0 | 8.5 | 11.3 | 17.6 | 19.2 | 16.5 |
| V | 13.5 | 9.7 | 5.7 | 4.7 | 8.5 | 17.2 | 21.5 | 19.2 |
+--------+------+------+-----+---------+------+------+------+-------+
| Mean | 13.0 | 9.7 | 7.2 | 6.1 | 8.5 | 16.0 | 21.1 | 18.4 |
+--------+------+------+-----+---------+------+------+------+-------+

TABLE XXXV.--Disturbed Day less ordinary Day Inequality (Unit 1´, + to West).

+------+------+------+------+------+------+------+------+------+------+------+------+------+
| Hour.| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+
| a.m. | -3.4 | -2.6 | -2.0 | -0.3 | +1.6 | +1.9 | +2.3 | +2.0 | +2.1 | +2.0 | +1.6 | +1.8 |
| p.m. | +1.8 | +2.2 | +2.1 | +1.7 | +1.4 | 0.0 | -1.3 | -2.8 | -3.5 | -2.6 | -3.5 | -2.4 |
+------+------+------+------+------+------+------+------+------+------+------+------+------+

One difficulty in the Potsdam procedure is the maintenance of a
uniform standard. Unless very frequent reference is made to the curves
of some standard year there must be a tendency to enter under "3" in
quiet years a number of hours which would be entered under "2" in a
highly disturbed year. Still, such a source of uncertainty is unlikely
to have much influence on the diurnal, or even on the annual,
variation.

§ 33. A third method of investigating a diurnal period in disturbances
is to form a diurnal inequality from disturbed days alone, and compare
it with the corresponding inequalities from ordinary or from quiet
days. Table XXXV. gives some declination data for Kew, the quantity
tabulated being the algebraic excess of the disturbed day hourly value
over that for the ordinary day in the mean diurnal inequality for the
year, as based on the 11 years 1890 to 1900.

The disturbed day inequality was corrected for non-cyclic change in
the usual way. Fig. 11 shows the results of Table XXXV. graphically.
The irregularities are presumably due to the limited number, 209, of
disturbed days employed; to get a smooth curve would require probably
a considerably longer period of years. The differences between
disturbed and ordinary days at Kew are of the same general character
as those between ordinary and quiet days in Table XXIX.; they are,
however, very much larger, the range in Table XXXV. being fully 5½
times that in Table XXIX. If quiet days had replaced ordinary days in
Table XXXV., the algebraic excess of the disturbed day would have
varied from +2´.7 at 2 p.m. to -4´.1 at 11 p.m., or a range of 6´.8.

§ 34. When the mean diurnal inequality in declination for the year at
Kew is analysed into Fourier waves, the chief difference, it will be
remembered, between ordinary and quiet days was that the amplitude of
the 24-hour term was enhanced in the ordinary days, whilst its phase
angle indicated an earlier occurrence of the maximum. Similarly, the
chief difference between the Fourier waves for the disturbed and
ordinary day inequalities at Kew is the increase in the amplitude of
the 24-hour term in the former by over 70%, and the earlier occurrence
of its maximum by about 1 hour 50 minutes. It is clear from these
results for Kew, and it is also a necessary inference from the
differences obtained by Sabine's method between east and west or + and
- disturbances, that there is present during disturbances some
influence which affects the diurnal inequality in a regular systematic
way, tending to make the value of the element higher during some hours
and lower during others than it is on days relatively free from
disturbance. At Kew the consequence is a notable increase in the range
of the regular diurnal inequality on disturbed days; but whether this
is the general rule or merely a local peculiarity is a subject for
further research.

§ 35. There are still other ways of attacking the problem of
disturbances. W. Ellis[27] made a complete list of disturbed days at
Greenwich from 1848 onwards, arranging them in classes according to
the amplitude of the disturbance shown on the curves. Of the 18,000
days which he considered, Ellis regarded 2,119, or only about 12%, as
undisturbed. On 11,898 days, or 66%, the disturbance movement in
declination was under 10´; on 3614, or 20%, the disturbance, though
exceeding 10´, was under 30´; on 294 days it lay between 30´ and 60´;
while on 75 days it exceeded 60´. Taking each class of disturbances
separately, Ellis found, except in the case of his "minor"
disturbances--those under 10´--a distinct double annual period, with
maxima towards the equinoxes. Subsequently C. W. Maunder,[38] making
use of these same data, and of subsequent data up to 1902, put at his
disposal by Ellis, came to similar conclusions. Taking all the days
with disturbances of declination over 10´, and dealing with 15-day
periods, he found the maxima of frequency to occur the one a little
before the spring equinox, the other apparently after the autumnal
equinox; the two minima were found to occur early in June and in
January. When the year is divided into three seasons--winter (November
to February), summer (May to August), and equinox--Maunder's figures
lead to the results assigned to Greenwich disturbed days in Table
XXXVI. The frequency in winter, it will be noticed, though less than
at equinox, is considerably greater than in summer. This greater
frequency in winter is only slightly apparent in the disturbances over
60´, but their number is so small that this may be accidental. The
next figures in Table XXXVI. relate to highly disturbed days at Kew.
The larger relative frequency at Kew in winter as compared to summer
probably indicates no real difference from Greenwich, but is simply a
matter of definition. The chief criterion at Kew for classifying the
days was not so much the mere amplitude of the largest movement, as
the general character of the day's curve and its departure from the
normal form. The data in Table XXXVI. as to magnetic storms at
Greenwich are based on the lists given by Maunder[39] in the _Monthly
Notices_, R.A.S. A storm may last for any time from a few hours to
several days, and during part of its duration the disturbance may not
be very large; thus it does not necessarily follow that the
frequencies of magnetic storms and of disturbed days will follow the
same laws. The table shows, however, that so far as Greenwich is
concerned the annual variations in the two cases are closely alike. In
addition to mean data for the whole 56 years, 1848 to 1903, Table
XXXVI. contains separate data for the 14 years of that period which
represented the highest sun-spot frequency, and the 15 years which
represented lowest sun-spot frequency. It will be seen that relatively
considered the seasonal frequencies of disturbance are more nearly
equal in the years of many than in those of few sun-spots. Storms are
more numerous as a whole in the years of many sun-spots, and this
preponderance is especially true of storms of the largest size. This
requires to be borne in mind in any comparisons between larger and
smaller storms selected promiscuously from a long period. An unduly
large proportion of the larger storms will probably come from years of
large sun-spot frequency, and there is thus a risk of assigning to
differences between the laws obeyed by large and small storms
phenomena that are due in whole or in part to differences between the
laws followed in years of many and of few sun-spots. The last data in
Table XXXVI. are based on statistics for Batavia given by W. van
Bemmelen,[40] who considers separately the storms which commence
suddenly and those which do not. These sudden movements are recorded
over large areas, sometimes probably all over the earth, if not
absolutely simultaneously, at least too nearly so for differences in
the time of occurrence to be shown by ordinary magnetographs. It is
ordinarily supposed that these sudden movements, and the storms to
which they serve as precursors, arise from some source extraneous to
the earth, and that the commencement of the movement intimates the
arrival, probably in the upper atmosphere, of some form of energy
transmitted through space. In the storms which commence gradually the
existence of a source external to the earth is not so prominently
suggested, and it has been sometimes supposed that there is a
fundamental difference between the two classes of storms. Table XXXVI.
shows, however, no certain difference in the annual variation at
Batavia. At the same time, this possesses much less significance than
it would have if Batavia were a station like Greenwich, where the
annual variation in magnetic storms is conspicuous.

Besides the annual period, there seems to be also a well-marked
diurnal period in magnetic disturbances. This is apparent in Tables
XXXVII. and XXXVIII., which contain some statistics for Batavia due to
van Bemmelen, and some for Greenwich derived from the data in
Maunder's papers referred to above. Table XXXVII. gives the relative
frequency of occurrence for two hour intervals, starting with
midnight, treating separately the storms of gradual (g) and sudden (s)
commencement. In Table XXXVIII. the day is subdivided into three equal
parts. Batavia and Greenwich agree in showing maximum frequency of
beginnings about the time of minimum frequency of endings and
conversely; but the hours at which the respective maxima and minima
occur at the two places differ rather notably.

§ 36. There are peculiarities in the sudden movements ushering in
magnetic storms which deserve fuller mention. According to van
Bemmelen the impulse consists usually at some stations of a sudden
slight jerk of the magnet in one direction, followed by a larger
decided movement in the opposite direction, the former being often
indistinctly shown. Often we have at the very commencement but a faint
outline, and thereafter a continuous movement which is only sometimes
distinctly indicated, resulting after some minutes in the displacement
of the trace by a finite amount from the position it occupied on the
paper before the disturbance began. This may mean, as van Bemmelen
supposes, a small preliminary movement in the opposite direction to
the clearly shown displacement; but it may only mean that the magnet
is initially set in vibration, swinging on both sides of the position
of equilibrium, the real displacement of the equilibrium position
being all the time in the direction of the displacement apparent after
a few minutes. To prevent misconception, the direction of the
displacement apparent after a few minutes has been termed the
direction of the first _decided_ movement in Table XXXIX., which
contains some data as to the direction given by Ellis[41] and van
Bemmelen.[40] The + sign means an increase, the - sign a decrease of
the element. The sign is not invariably the same, it will be
understood, but there are in all cases a marked preponderance of
changes in the direction shown in the table. The fact that all the
stations indicated an increase in horizontal force is of special
significance.

TABLE XXXVI.--Disturbances, and their Annual Distribution.

+-------------------------------+-------+---------------------------+
| | Total | Percentages. |
| |Number.+--------+---------+--------+
| | | Winter.| Equinox.| Summer.|
+-------------------------------+-------+--------+---------+--------+
| Greenwich disturbed days, | | | | |
| all, 1848-1902 | 4,214 | 33.9 | 39.2 | 26.9 |
| Greenwich disturbed days, | | | | |
| range 10´ to 30´, 1848-1902 | 3,830 | 33.9 | 39.0 | 27.1 |
| Greenwich disturbed days, | | | | |
| range 30´ to 60´, 1848-1902 | 307 | 34.5 | 41.0 | 24.4 |
| Greenwich disturbed days, | | | | |
| range over 60´, 1848-1902 | 77 | 29.9 | 41.6 | 28.6 |
| Kew highly disturbed days, | | | | |
| 1890-1900 | 209 | 38.3 | 41.6 | 20.1 |
| Greenwich magnetic storms, | | | | |
| all, 1848-1903 | 726 | 32.1 | 42.3 | 25.6 |
| Greenwich magnetic storms, | | | | |
| range 20´ to 30´, 1848-1903 | 392 | 30.1 | 43.6 | 26.3 |
| Greenwich magnetic storms, | | | | |
| range over 30´, 1848-1903 | 334 | 34.4 | 40.7 | 24.9 |
| Greenwich magnetic storms, | | | | |
| all, 14 years of S. max. | 258 | 35.3 | 38.0 | 26.7 |
| Greenwich magnetic storms, | | | | |
| all, 15 years of S. min. | 127 | 28.4 | 48.0 | 23.6 |
| Batavia magnetic storms, | | | | |
| all, 1883-1899 | 1,008 | 32.9 | 34.9 | 32.2 |
| Batavia magnetic storms of | | | | |
| gradual commencement | 679 | 32.4 | 34.8 | 32.8 |
| Batavia magnetic storms of | | | | |
| sudden commencement | 329 | 33.7 | 35.3 | 31.0 |
+-------------------------------+-------+--------+---------+--------+

TABLE XXXVII.--Batavia Magnetic Storms, Diurnal Distribution
(percentages).

+--------------+----+----+----+----+----+----+----+----+----+----+----+----+
| Hour. | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |
+--------------+----+----+----+----+----+----+----+----+----+----+----+----+
| Beginning /g | 5 | 5 | 5 | 6 | 20 | 16 | 7 | 5 | 6 | 9 | 8 | 8 |
| \s | 7 | 5 | 7 | 10 | 10 | 11 | 10 | 8 | 8 | 9 | 8 | 7 |
| Maximum /g | 12 | 10 | 6 | 5 | 4 | 9 | 9 | 6 | 6 | 6 | 12 | 15 |
| \s | 14 | 7 | 5 | 2 | 2 | 9 | 9 | 5 | 8 | 10 | 13 | 16 |
| End all | 15 | 16 | 19 | 13 | 5 | 3 | 6 | 5 | 4 | 5 | 4 | 5 |
+--------------+----+----+----+----+----+----+----+----+----+----+----+----+

TABLE XXXVIII.--Greenwich Magnetic Storms, Diurnal Distribution.

+------------------------+--------+-------+-----------------------------+
| | | | Percentages. |
| Epoch. | Class. | Total +---------+---------+---------+
| | |Number.| 1-8 p.m.| 9 p.m.- | 5 a.m.- |
| | | | | 4 a.m. | noon. |
+------------------------+--------+-------+---------+---------+---------+
| / 1848-1903 | all | 721 | 60.1 | 21.9 | 18.0 |
| Beginning < 1882-1903 | " | 276 | 58.0 | 18.8 | 23.2 |
| \ " " | sudden | 77 | 45.4 | 27.3 | 27.3 |
| | | | | | |
| / 1848-1903 | all | 720 | 9.4 | 44.6 | 46.0 |
| End < 1882-1903 | " | 276 | 7.2 | 41.7 | 51.1 |
| \ " " | sudden | 77 | 11.7 | 35.1 | 53.2 |
+------------------------+--------+-------+---------+---------+---------+

§ 37. That large magnetic disturbances occur simultaneously over large
areas was known in the time of Gauss, on whose initiative observations
were taken at 5-minute intervals at a number of stations on
prearranged _term days_. During March 1879 and August 1880 some large
magnetic storms occurred, and the magnetic curves showing these at a
number of stations fitted with Kew pattern magnetographs were compared
by W. G. Adams.[42] He found the more characteristic movements to be,
so far as could be judged, simultaneous at all the stations. At
comparatively near stations such as Stonyhurst and Kew, or Coimbra and
Lisbon, the curves were in general almost duplicates. At Kew and St
Petersburg there were usually considerable differences in detail, and
the movements were occasionally in opposite directions. The
differences between Toronto, Melbourne or Zi-ka-wei and the European
stations were still more pronounced. In 1896, on the initiative of M.
Eschenhagen,[43] eye observations of declination and horizontal force
were taken at 5-second intervals during prearranged hours at Batavia,
Manila, Melbourne and nine European stations. The data from one of
these occasions when appreciable disturbance prevailed were published
by Eschenhagen, and were subsequently analysed by Ad. Schmidt.[44]
Taking the stations in western Europe, Schmidt drew several series of
lines, each series representing the disturbing forces at one instant
of time as deduced from the departure of the elements at the several
stations from their undisturbed value. The lines answering to any one
instant had a general sameness of direction with more or less
divergence or convergence, but their general trend varied in a way
which suggested to Schmidt the passage of a species of vortex with
large but finite velocity.

TABLE XXXIX.--Direction of First Decided Movement.

+-----------+-------------+------------------+----------------+
| Place. | Declination.| Horizontal Force.| Vertical Force.|
+-----------+-------------+------------------+----------------+
| Pavlovsk | West | + | + |
| Potsdam | West | + | - |
| Greenwich | West | + | + |
| Zi-ka-wei | East | + | - |
| Kolaba | East | + | - |
| Batavia | West | + | - |
| Mauritius | East | + | + |
| Cape Horn | West | + | - |
+-----------+-------------+------------------+----------------+

The conclusion that magnetic disturbances tend to follow one another
at nearly equal intervals of time has been reached by several
independent observers. J. A. Broun[45] pronounced for a period of
about 26 days, and expressed a belief that a certain zone, or zones,
of the sun's surface might exert a prepotent influence on the earth's
magnetism during several solar rotations. Very similar views were
advanced in 1904 by E. W. Maunder,[39] who was wholly unaware of
Broun's work. Maunder concluded that the period was 27.28 days,
coinciding with the sun's rotation period relative to an observer on
the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he
found the interval between the commencement of successive storms to
approach closely to the above period in a considerably larger number
of instances than one would have expected from mere chance. He found
several successions of three or four storms, and in one instance of as
many as six storms, showing his interval. In a later paper Maunder
reached similar results for magnetic storms at Greenwich from 1848 to
1881. Somewhat earlier than Maunder, Arthur Harvey[46] deduced a
period of 27.246 days from a consideration of magnetic disturbances at
Toronto. A. Schuster,[47] examining Maunder's data mathematically,
concluded that they afforded rather strong evidence of a period of
about ½ (27.28) or 13.6 days. Maunder regarded his results as
_demonstrating_ that magnetic disturbances originate in the sun. He
regarded the solar action as arising from active areas of limited
extent on the sun's surface, and as propagated along narrow, well
defined streams. The active areas he believed to be also the seats of
the formation of sun-spots, but believed that their activity might
precede and outlive the visible existence of the sun-spot.

Maunder did not discuss the physical nature of the phenomenon, but his
views are at least analogous to those propounded somewhat earlier by
Svante Arrhenius,[48] who suggested that small negatively charged
particles are driven from the sun by the repulsion of light and reach
the earth's atmosphere, setting up electrical currents, manifest in
aurora and magnetic disturbances. Arrhenius's calculations, for the
size of particle which he regarded as most probable, make the time of
transmission to the earth slightly under two days. Amongst other
theories which ascribe magnetic storms to direct solar action may be
mentioned that of Kr. Birkeland,[49] who believes the vehicle to be
cathode rays. Ch. Nordmann[50] similarly has suggested Röntgen rays.
Supposing the sun the ultimate source, it would be easier to
discriminate between the theories if the exact time of the originating
occurrence could be fixed. For instance, a disturbance that is
propagated with the velocity of light may be due to Röntgen rays, but
not to Arrhenius's particles. In support of his theory, Nordmann
mentions several cases when conspicuous visual phenomena on the sun
have synchronized with magnetic movements on the earth--the best known
instance being the apparent coincidence in time of a magnetic
disturbance at Kew on the 1st of September 1859 with a remarkable
solar outburst seen by R. C. Carrington. Presumably any electrical
phenomenon on the sun will set up waves in the aether, so transmission
of electric and magnetic disturbances from the sun to the earth with
the velocity of light is a certainty rather than a hypothesis; but it
by no means follows that the energy thus transmitted can give rise to
sensible magnetic disturbances. Also, when considering Nordmann's
coincidences, it must be remembered that magnetic movements are so
numerous that it would be singular if no apparent coincidences had
been noticed. Another consideration is that the movements shown by
ordinary magnetographs are seldom very rapid. During some storms,
especially those accompanied by unusually bright and rapidly varying
auroral displays, large to and fro movements follow one another in
close succession, the changes being sometimes too quick to be
registered distinctly on the photographic paper. This, however, is
exceptional, even in polar regions where disturbances are largest and
most numerous. As a rule, even when the change in the direction of
movement in the declination needle seems quite sudden, the movement in
one direction usually lasts for several minutes, often for 10, 15 or
30 minutes. Thus the cause to which magnetic disturbances are due
seems in many cases to be persistent in one direction for a
considerable time.

§ 38. Attempts have been made to discriminate between the theories as
to magnetic storms by a critical examination of the phenomena. A
general connexion between sun-spot frequency and the amplitude of
magnetic movements, regular and irregular, is generally admitted. If
it is a case of cause and effect, and the interval between the solar
and terrestrial phenomena does not exceed a few hours, then there
should be a sensible connexion between corresponding daily values of
the sun-spot frequency and the magnetic range. Even if only some
sun-spots are effective, we should expect when we select from a series
of years two groups of days, the one containing the days of most
sun-spots, the other the days of least, that a prominent difference
will exist between the mean values of the absolute daily magnetic
ranges for the two groups. Conversely, if we take out the days of
small and the days of large magnetic range, or the days that are
conspicuously quiet and those that are highly disturbed, we should
expect a prominent difference between the corresponding mean sun-spot
areas. An application of this principle was made by Chree[23] to the
five quiet days a month selected by the astronomer royal between 1890
and 1900. These days are very quiet relative to the average day and
possess a much smaller absolute range. One would thus have expected on
Birkeland's or Nordmann's theory the mean sun-spot frequency derived
from Wolfer's provisional values for these days to be much below his
mean value, 41.22, for the eleven years. It proved, however, to be
41.28. This practical identity was as visible in 1892 to 1895, the
years of sun-spot maximum, as it was in the years of sun-spot minimum.
Use was next made of the Greenwich _projected_ sun-spot areas, which
are the result of exact measurement. The days of each month were
divided into three groups, the first and third--each normally of ten
days--containing respectively the days of largest and the days of
least sun-spot area. The mean sun-spot area from group 1 was on the
average about five times that for group 3. It was then investigated
how the astronomer royal's quiet days from 1890 to 1900, and how the
most disturbed days of the period selected from the Kew[24] magnetic
records, distributed themselves among the three groups of days.
Nineteen months were excluded, as containing more than ten days with
no sun-spots. The remaining 113 months contained 565 quiet and 191
highly disturbed days, whose distribution was as follows:

+----------------+---------+---------+---------+
| | Group 1.| Group 2.| Group 3.|
| +---------+---------+---------+
| Quiet days | 179 | 195 | 191 |
| Disturbed days | 68 | 65 | 58 |
+----------------+---------+---------+---------+

The group of days of largest sun-spot area thus contained slightly
under their share of quiet days and slightly over their share of
disturbed days. The differences, however, are not large, and in three
years, viz. 1895, 1897 and 1899, the largest number of disturbed days
actually occurred in group 3, while in 1895, 1896 and 1899 there were
fewer quiet days in group 3 than in group 1. Taking the same
distribution of days, the mean value of the absolute daily range of
declination at Kew was calculated for the group 1 and the group 3 days
of each month. The mean range from the group 1 days was the larger in
57% of the individual months as against 43% in which it was the
smaller. When the days of each month were divided into groups
according to the absolute declination range at Kew, the mean sun-spot
area for the group 1 days (those of largest range) exceeded that for
the group 3 days (those of least range) in 55% of the individual
months, as against 45% of cases in which it was the smaller.

Taking next the five days of largest and the five days of least range
in each month, sun-spot areas were got out not merely for these days
themselves, but also for the next subsequent day and the four
immediately preceding days in each case. On Arrhenius's theory we
should expect the magnetic range to vary with the sun-spot area, not
on the actual day but two days previously. The following figures give
the percentage excess or deficiency of the mean sun-spot area for the
respective groups of days, relative to the average value for the whole
epoch dealt with. n denotes the day to which the magnetic range
belongs, n + 1 the day after, n - 1 the day before, and so on.
Results are given for 1894 and 1895, the years which were on the whole
the most favourable and the least favourable for Arrhenius's
hypothesis, as well as for the whole eleven years.

TABLE XL.

+-------------------------+-------+-------+-------+-------+--------+-------+
| Day. | n - 4 | n - 3 | n - 2 | n - 1 | n | n + 1 |
+-------------------------+-------+-------+-------+-------+--------+-------+
| Five days of \ 1894 | +12 | + 9 | +11 | +12 | +11 | + 6 |
| largest range > 1895 | -16 | -17 | -15 | -12 | -11 | -10 |
| / 11 yrs. | + 9 | + 8 | + 8 | + 7 | + 5 | + 0.5|
| Five days of \ 1894 | -15 | -17 | -19 | -21 | -21 | -19 |
| least range > 1895 | +17 | +10 | + 1 | - 2 | - 2 | - 4 |
| / 11 yrs. | - 4 | - 4 | - 7 | - 7 | - 7 | - 6 |
+-------------------------+-------+-------+-------+-------+--------+-------+

Taking the 11-year-means we have the sun-spot area practically normal
on the day subsequent to the representative day of large magnetic
range, but sensibly above its mean on that day and still more so on
the four previous days. This suggests an emission from the sun taking
a highly variable time to travel to the earth. The 11-year mean data
for the five days of least range seem at first sight to point to the
same conclusion, but the fact that the deficiency in sun-spot area is
practically as prominent on the day after the representative day of
small magnetic range as on that day itself, or the previous days,
shows that the phenomenon is probably a secondary one. On the whole,
taking into account the extraordinary differences between the results
from individual years, we seem unable to come to any very positive
conclusion, except that in the present state of our knowledge little
if any clue is afforded by the extent of the sun's spotted area on any
particular day as to the magnetic conditions on the earth on that or
any individual subsequent day. Possibly some more definite information
might be extracted by considering the extent of spotted area on
different zones of the sun. On theories such as those of Arrhenius or
Maunder, effective bombardment of the earth would be more or less
confined to spotted areas in the zones nearest the centre of the
visible hemisphere, whilst all spots on this hemisphere contribute to
the total spotted area. Still the _projected_ area of a spot rapidly
diminishes as it approaches the edge of the visible hemisphere, i.e.
as it recedes from the most effective position, so that the method
employed above gives a preponderating weight to the central zones. One
rather noteworthy feature in Table XL. is the tendency to a sequence
in the figures in any one row. This seems to be due, at least in large
part, to the fact that days of large and days of small sun-spot area
tend to occur in groups. The same is true to a certain extent of days
of large and days of small magnetic range, but it is unusual for the
range to be much above the average for more than 3 or 4 successive
days.

Pulsations.

§ 39. The records from ordinary magnetographs, even when run at the
usual rate and with normal sensitiveness, not infrequently show a
repetition of regular or nearly regular small rhythmic movements,
lasting sometimes for hours. The amplitude and period on different
occasions both vary widely. Periods of 2 to 4 minutes are the most
common. W. van Bemmelen[51] has made a minute examination of these
movements from several years' traces at Batavia, comparing the results
with corresponding statistics sent him from Zi-ka-wei and Kew. Table
XLI. shows the diurnal variation in the frequency of occurrence of
these small movements--called _pulsations_ by van Bemmelen--at these
three stations. The Batavia results are from the years 1885 and 1892
to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the
years 1897, 1898 and 1900, as given by van Bemmelen, while (ii)
answers to the period 1900-1905, as given in the Zi-ka-wei _Bulletin_
for 1905. The Kew data are for 1897. The results are expressed as
percentages of the total for the 24 hours. There is a remarkable
contrast between Batavia and Zi-ka-wei on the one hand and Kew on the
other, pulsations being much more numerous by night than by day at the
two former stations, whereas at Kew the exact reverse holds. Van
Bemmelen decided that almost all the occasions of pulsation at
Zi-ka-wei were also occasions of pulsations at Batavia. The hours of
commencement at the two places usually differed a little, occasionally
by as much as 20 minutes; but this he ascribed to the fact that the
earliest oscillations were too small at one or other of the stations
to be visible on the trace. Remarkable coincidence between pulsations
at Potsdam and in the north of Norway has been noted by Kr.
Birkeland.[49]

With magnetographs of greater sensitiveness and more open time scales,
waves of shorter period become visible. In 1882 F. Kohlrausch[52]
detected waves with a period of about 12 seconds. Eschenhagen[53]
observed a great variety of short period waves, 30 seconds being
amongst the most common. Some of the records he obtained suggest the
superposition of regular sine waves of different periods. Employing a
very sensitive galvanometer to record changes of magnetic induction
through a coil traversed by the earth's lines of force, H. Ebert[54]
has observed vibrations whose periods are but a small fraction of a
second. The observations of Kohlrausch and Eschenhagen preceded the
recent great development of applications of electrical power, while
longer period waves are shown in the Kew curves of 50 years ago, so
that the existence of natural waves with periods of from a few seconds
up to several minutes can hardly be doubted. Whether the much shorter
period waves of Ebert are also natural is more open to doubt, as it is
becoming exceedingly difficult in civilized countries to escape
artificial disturbances.

TABLE XLI.--Diurnal Distribution of Pulsations.

+---------------+-----+-----+-----+--------+--------+-----+-----+------+
| Hours. | 0-3.| 3-6.| 6-9.| 9-Noon.| Noon-3.| 3-6.| 6-9.| 9-12.|
+---------------+-----+-----+-----+--------+--------+-----+-----+------+
| Batavia | 28 | 9 | 2 | 6 | 8 | 6 | 13 | 28 |
| Zi-ka-wei (i) | 33 | 5 | 2 | 7 | 4 | 4 | 10 | 35 |
| " (ii) | 23 | 6 | 8 | 11 | 7 | 5 | 14 | 26 |
| Kew | 4 | 8 | 19 | 14 | 22 | 18 | 11 | 4 |
+---------------+-----+-----+-----+--------+--------+-----+-----+------+

Lunar Influence.

§ 40. The fact that the moon exerts a small but sensible effect on the
earth's magnetism seems to have been first discovered in 1841 by C.
Kreil. Subsequently Sabine[55] investigated the nature of the lunar
diurnal variation in declination at Kew, Toronto, Pekin, St Helena,
Cape of Good Hope and Hobart. The data in Table XLII. are mostly due
to Sabine. They represent the mean lunar diurnal inequality in
declination for the whole year. The unit employed is 0´.001, and as in
our previous tables + denotes movement to the _west_. By "mean
departure" is meant the arithmetic mean of the 24 hourly departures
from the mean value for the lunar day; the range is the difference
between the algebraically greatest and least of the hourly values. Not
infrequently the mean departure gives the better idea of the
importance of an inequality, especially when as in the present case
two maxima and minima occur in the day. This double daily period is
unusually prominent in the case of the lunar diurnal inequality, and
is seen in the other elements as well as in the declination.

TABLE XLII.--Lunar Diurnal Inequality of Declination (unit 0´.001).