Chapter LXIII: repeats the promise of freedom to the English church (9)

+--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
| | | St Peters- |Green- | | Parc St| | | |Maur- |South |
|Station.| Jan Mayen. | burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria|
| | | Pavlovsk. | | | | | | | | Land. |
+--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
| End | North. | North. | North.| North.| North. | North.| North.| South. | South.| South. |
|Dipping | | | | | | | | | | |
+--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+
| Period.| 1882-1883. | 1873-1885. |1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 |
| | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. |
+--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
| | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. |
+--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
| Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| 1 | +4.6 | +1.5 | -0.5 | -0.3 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +0.9 | +0.3 | +0.6 |
| 2 | +5.0 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.6 | +0.8 | +0.2 | +0.7 |
| 3 | +5.6 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.5 | +0.6 | 0.0 | +0.7 |
| 4 | +5.0 | +1.5 | -0.4 | -0.3 | -0.3 | -0.2 | -0.4 | -0.2 | +0.5 | +0.5 | -0.0 | +0.7 |
| 5 | +4.2 | +1.4 | -0.5 | -0.3 | -0.2 | -0.2 | -0.4 | -0.2 | +0.7 | +0.3 | -0.1 | +0.7 |
| 6 | +2.4 | +1.2 | -0.4 | -0.3 | -0.1 | -0.1 | -0.3 | -0.1 | +0.8 | +0.1 | -0.2 | +0.5 |
| 7 | +0.7 | +0.9 | -0.2 | -0.1 | +0.2 | +0.1 | 0.0 | 0.0 | +0.5 | -0.2 | -0.3 | +0.4 |
| 8 | -0.1 | +0.8 | +0.1 | +0.3 | +0.6 | +0.4 | +0.4 | +0.3 | -0.2 | -0.8 | -0.4 | +0.3 |
| 9 | -0.7 | +0.8 | +0.6 | +0.6 | +1.0 | +0.8 | +0.7 | +0.5 | -1.2 | -1.7 | -0.4 | +0.1 |
| 10 | -1.2 | +0.9 | +1.0 | +1.0 | +1.1 | +1.0 | +0.9 | +0.3 | -1.9 | -2.7 | -0.5 | -0.2 |
| 11 | -2.2 | +0.8 | +1.2 | +1.2 | +1.0 | +0.9 | +0.7 | 0.0 | -2.1 | -3.3 | -0.6 | -0.4 |
| Noon | -3.4 | +0.4 | +1.1 | +1.1 | +0.6 | +0.6 | +0.4 | -0.5 | -1.6 | -3.1 | -0.7 | -0.7 |
| 1 | -4.5 | -0.2 | +0.7 | +0.7 | +0.3 | +0.2 | +0.2 | -0.6 | -0.8 | -2.4 | -0.8 | -0.9 |
| 2 | -5.6 | -1.2 | +0.4 | +0.4 | +0.1 | +0.1 | +0.2 | -0.5 | -0.2 | -1.3 | -0.6 | -1.0 |
| 3 | -6.3 | -2.2 | +0.2 | +0.1 | 0.0 | 0.0 | +0.2 | -0.3 | +0.3 | -0.2 | -0.3 | -1.0 |
| 4 | -6.1 | -2.9 | 0.0 | -0.1 | -0.1 | -0.1 | +0.2 | +0.1 | +0.3 | +0.7 | +0.1 | -0.9 |
| 5 | -5.1 | -3.2 | -0.1 | -0.3 | -0.2 | -0.2 | +0.1 | +0.4 | +0.2 | +1.3 | +0.4 | -0.7 |
| 6 | -3.1 | -2.9 | -0.2 | -0.3 | -0.3 | -0.3 | 0.0 | +0.5 | +0.2 | +1.5 | +0.5 | -0.5 |
| 7 | -1.7 | -2.2 | -0.3 | -0.4 | -0.4 | -0.4 | -0.2 | +0.4 | +0.3 | +1.6 | +0.5 | -0.2 |
| 8 | +0.3 | -1.3 | -0.3 | -0.5 | -0.4 | -0.4 | -0.3 | +0.2 | +0.4 | +1.6 | +0.6 | 0.0 |
| 9 | +2.0 | -0.3 | -0.4 | -0.6 | -0.4 | -0.4 | -0.3 | +0.1 | +0.5 | +1.6 | +0.6 | +0.2 |
| 10 | +2.5 | +0.5 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.5 | +0.6 | +0.4 |
| 11 | +3.0 | +1.0 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.4 | +0.5 | +0.5 |
| 12 | +4.0 | +1.3 | -0.5 | -0.4 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +1.2 | +0.4 | +0.6 |
+--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
| Range | 11.9 | 4.8 | 1.7 | 1.8 | 1.5 | 1.4 | 1.3 | 1.1 | 2.9 | 4.9 | 1.4 | 1.7 |
+--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+

TABLE XII.--Diurnal Inequality of Declination (+ to West).

+--------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
|Station.| Toronto. | Kolaba. |Trivandrum.| Batavia. | St Helena.| Mauritius.| Cape. | Hobart. |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Month. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| 1 |-0.4 |-0.1 |-0.3 | 0.0 |-0.3 |-0.1 |+0.1 |+0.1 |-0.1 |-0.4 | 0.0 |+0.1 |-0.4 |-0.7 |+0.8 |+1.1 |
| 2 |-0.2 |+0.4 |-0.3 |+0.1 |-0.4 |+0.1 |-0.1 |+0.1 |-0.2 |-0.1 |-0.2 |+0.2 |-0.5 |-0.4 |+0.3 |+1.1 |
| 3 |-0.2 |-0.1 |-0.3 |+0.1 |-0.4 |+0.3 |-0.2 |+0.2 |-0.2 |+0.1 |-0.2 |+0.4 |-0.7 |-0.1 |-0.1 |+1.0 |
| 4 |-1.2 |-0.4 |-0.3 |+0.3 |-0.5 |+0.5 |-0.3 |+0.3 |-0.3 |+0.3 |-0.2 |+0.7 |-0.6 |+0.3 |-0.1 |+1.1 |
| 5 |-2.9 |-0.6 |-0.7 |+0.4 |-0.7 |+0.7 |-0.3 |+0.5 |-0.5 |+0.6 |-0.3 |+1.0 |-0.7 |+1.0 | 0.0 |+1.7 |
| 6 |-5.2 |-0.6 |-1.6 |+0.5 |-1.6 |+1.1 |-0.5 |+1.2 |-1.0 |+0.9 |-0.4 |+1.7 |-1.0 |+2.2 | 0.0 |+2.7 |
| 7 |-6.2 |-0.9 |-2.2 |+0.7 |-1.7 |+1.4 |-1.1 |+2.0 |-2.2 |+1.9 |-1.1 |+2.6 |-1.6 |+3.3 |-0.1 |+4.4 |
| 8 |-6.0 |-1.2 |-2.1 |+0.2 |-1.1 |+0.9 |-0.4 |+2.3 |-1.5 |+2.2 |-1.0 |+2.4 |-0.8 |+3.6 |+0.1 |+5.6 |
| 9 |-4.4 |-1.8 |-1.1 |-0.1 |-0.2 |+0.5 |+0.5 |+2.0 |-0.3 |+1.3 |+0.2 |+2.0 |+0.7 |+3.1 |+0.6 |+5.6 |
| 10 |-1.5 |-1.1 | 0.0 |-0.2 |+0.6 |+0.3 |+0.9 |+1.3 |+0.3 |+0.2 |+1.2 |+1.1 |+1.6 |+1.6 |+1.2 |+3.6 |
| 11 |+2.1 |+0.6 |+1.2 | 0.0 |+1.2 |+0.1 |+1.0 |+0.4 |+0.5 |-1.0 |+1.4 | 0.0 |+1.5 |+0.1 |+1.0 |+0.7 |
| Noon |+4.8 |+2.2 |+2.1 | 0.0 |+1.4 |-0.4 |+0.7 |-0.6 |+0.3 |-1.4 |+1.0 |-1.4 |+0.8 |-1.0 |-0.1 |-2.6 |
| 1 |+6.1 |+3.2 |+2.0 |-0.2 |+1.1 |-0.8 |+0.3 |-1.4 |+0.3 |-1.2 |+0.1 |-2.2 |+0.3 |-1.8 |-1.4 |-5.1 |
| 2 |+6.1 |+3.2 |+1.6 |-0.3 |+0.7 |-0.9 |-0.2 |-1.8 |+0.2 |-0.4 |-0.9 |-2.5 |-0.3 |-1.9 |-2.2 |-6.2 |
| 3 |+5.2 |+2.4 |+0.9 |-0.3 |+0.3 |-0.9 |-0.7 |-1.9 |+0.2 |+0.4 |-1.5 |-2.2 |-0.3 |-1.4 |-2.4 |-5.8 |
| 4 |+3.6 |+1.5 |+0.2 |-0.3 |+0.1 |-0.8 |-0.8 |-1.6 |+0.7 |+0.6 |-1.3 |-1.6 |+0.2 |-0.8 |-1.6 |-4.8 |
| 5 |+1.8 |+0.5 | 0.0 |-0.2 | 0.0 |-0.4 |-0.5 |-1.2 |+1.1 |+0.4 |-0.3 |-1.0 |+0.5 |-0.8 |-0.7 |-3.3 |
| 6 |+0.7 |-0.1 |+0.1 |-0.2 |+0.2 |-0.4 |-0.1 |-0.7 |+1.0 |+0.1 |+0.5 |-0.5 |+0.5 |-0.6 |-0.4 |-1.9 |
| 7 | 0.0 |-0.8 |+0.3 |-0.2 |+0.5 |-0.4 |+0.1 |-0.6 |+0.6 |-0.4 |+0.7 |-0.3 |+0.4 |-0.8 | 0.0 |-1.0 |
| 8 | 0.0 |-1.2 |+0.4 |-0.1 |+0.5 |-0.3 |+0.2 |-0.5 |+0.5 |-0.7 |+0.7 |-0.3 |+0.3 |-0.9 |+0.5 |-0.3 |
| 9 |-0.5 |-1.4 |+0.3 |-0.1 |+0.4 |-0.2 |+0.4 |-0.3 |+0.4 |-0.9 |+0.6 |-0.2 |+0.2 |-0.9 |+1.1 | 0.0 |
| 10 |-0.5 |-1.7 |+0.1 | 0.0 |+0.2 |-0.1 |+0.4 |-0.1 |+0.2 |-1.0 |+0.4 |-0.1 |+0.1 |-1.0 |+1.3 |+0.6 |
| 11 |-0.7 |-1.1 |-0.1 |-0.1 | 0.0 |-0.1 |+0.3 | 0.0 |+0.1 |-0.8 |+0.3 | 0.0 | 0.0 |-1.0 |+1.3 |+0.9 |
| 12 |-0.6 |-0.7 |-0.2 |-0.1 |-0.2 |-0.1 |+0.2 |+0.1 |-0.1 |-0.6 |+0.1 |+0.1 |-0.2 |-1.0 |+1.1 |+1.2 |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Range |12.3 | 5.0 | 4.3 | 1.0 | 3.1 | 2.3 | 2.1 | 4.2 | 3.3 | 3.6 | 2.9 | 5.1 | 3.2 | 5.5 | 3.7 |11.8 |
+--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

§ 15. In the case of the horizontal force there are, as Table IX.
shows, two markedly different types of diurnal inequality. In the one
type, exemplified by Pavlovsk or Greenwich, the force is below its
mean value in the middle of the day; it has a principal minimum about
10 or 11 a.m., and morning and evening maxima, the latter usually the
largest. In the other type, exemplified by Kolaba or Batavia, the
horizontal force is above its mean in the middle of the day, and has
a maximum about 11 a.m. The second type may be regarded as the
tropical type. At tropical stations, such as Kolaba, Batavia, Manila
and St Helena, the type is practically the same in summer as in
winter, and is the same whether the station is north or south of the
equator. Similarly, what we may call the temperate type is seen--with
comparatively slight modifications--both in summer and winter at
stations such as Greenwich or Pavlovsk. In winter, it is true, the
pronounced daily minimum is a little later and the early morning
maximum is relatively more important than in summer. There is not, as
in the case of the declination, any essential difference between the
phenomena at temperate stations in the northern and southern
hemispheres.

With diminishing latitude, there is a gradual transition from the
temperate to the tropical type of horizontal force diurnal variation,
and at stations whose latitude is under 45° there is a very
appreciable variation in type with the season. The mean diurnal
variation for the year at Tiflis in Table IX. really represents a
struggle between the two types, in which on the whole the temperate
type prevails. If we take the diurnal variations at Tiflis for
midsummer and midwinter, we find the former essentially of the
temperate, the latter essentially of the tropical type. A similar
conflict may be seen in the mean diurnal inequality for the year at
the Cape of Good Hope, but there the tropical type on the whole
predominates, and it prevails more at midwinter than at midsummer.
Toronto and Hobart, though similar in latitude to Tiflis, show a
closer approach to the temperate type. Still at both stations the
hours during which the force is below its mean value tend to extend
back towards midnight, especially at midsummer. The amplitude of the
horizontal force range appears less at intermediate stations, such as
Tiflis, than at stations in either higher or lower latitudes. There
is a very great difference in this respect between the north and the
south of India.

§ 16. In the case of the vertical force in higher temperate
latitudes--at Pavlovsk for instance--the diurnal inequalities from
"all" and from "quiet" days differ somewhat widely in amplitude and
slightly even in type. In mean latitudes, e.g. at Tiflis, there is
often a well marked double period in the mean diurnal inequality for
the whole year; but even at Tiflis this is hardly, if at all, apparent
in the winter months. In the summer months the double period is
distinctly seen at Kew and Greenwich, though the evening maximum is
always pre-eminent. Speaking generally, the time of the minimum, or
principal minimum, varies much less with the season than that of the
maximum. At Kew, for instance, on quiet days the minimum falls between
11 a.m. and noon in almost all the months of the year, but the time of
the maximum varies from about 4 p.m. in December to 7 p.m. in June. At
Kolaba the time of the minimum is nearly independent of the season;
but the changes from positive to negative in the forenoon and from
negative to positive in the afternoon are some hours later in winter
than in summer. At Batavia the diurnal inequality varies very little
in type with the season, and there is little evidence of more than one
maximum and minimum in the day. At Batavia, as at Kolaba, negative
values occur near noon; but it must be remembered that while at Kolaba
and more northern stations vertical force urges the north pole of a
magnet downwards, the reverse is true of Batavia, as the dip is
southerly. At St Helena vertical force is below its mean value in the
forenoon, but the change from - to + occurs at noon, or but little
later, both in winter and summer. At the Cape of Good Hope the
phenomena at midsummer are similar to those at Kolaba, the force being
below its mean value from about 9 a.m. to 3 p.m. and above it
throughout the rest of the day; but at midwinter there is a
conspicuous double period, the force being below its mean from 1 a.m.
to 7 a.m. as well as from 11 a.m. to 3 p.m., and thus resembling the
all-day annual results at Greenwich. At Hobart vertical force is below
its mean value from 1 a.m. to 9 a.m. at midsummer, and from 4 a.m. to
noon at midwinter; while the force is above its mean persistently
throughout the afternoon both in summer and winter, there is at
midwinter a well marked secondary minimum about 6 p.m., almost the
same hour as that at which the maximum for the day is observed in
summer.

TABLE XIII.--Range of the Diurnal Inequality of Declination.

+-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
| Place. | Period. | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
+-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
| | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| Pavlovsk | 1890-1900 a | 4.93 | 6.15 | 8.58 |10.93 |12.18 |12.27 |11.82 |11.38 | 8.70 | 6.87 | 5.54 | 4.63 |
| " | " q | 2.96 | 4.20 | 8.73 |11.28 |12.89 |13.28 |12.31 |11.70 | 9.37 | 6.91 | 3.95 | 2.66 |
| Ekatarinburg| 1890-1900 a | 3.33 | 4.32 | 7.63 |11.19 |11.82 |11.58 |11.09 |10.45 | 8.13 | 5.60 | 3.73 | 3.14 |
| Greenwich | 1865-1896 a | 5.87 | 7.07 | 9.40 |11.42 |10.55 |10.90 |10.82 |10.93 | 9.66 | 8.15 | 6.41 | 5.15 |
| Kew | 1890-1900 a | 4.92 | 6.06 | 9.08 |10.95 |10.66 |10.92 |10.59 |11.01 | 9.49 | 7.73 | 5.37 | 4.46 |
| " | " q | 4.07 | 4.76 | 8.82 |10.57 |10.92 |10.62 |10.18 |11.01 | 9.76 | 7.51 | 4.75 | 3.34 |
| Toronto | 1842-1848 a | 5.96 | 6.05 | 9.18 | 9.94 |11.55 |12.34 |12.21 |13.14 |10.76 | 6.96 | 6.32 | 4.97 |
| Manila | 1890-1900 a | 1.79 | 1.09 | 2.13 | 3.02 | 3.84 | 3.94 | 4.21 | 4.89 | 4.53 | 1.83 | 0.85 | 1.33 |
| Trivandrum | 1853-1864 a | 2.06 | 1.48 | 0.79 | 1.67 | 2.90 | 3.06 | 3.06 | 3.64 | 3.31 | 1.27 | 2.14 | 2.33 |
| Batavia | 1884-1899 a | 4.18 | 4.64 | 3.57 | 2.93 | 2.38 | 2.03 | 2.31 | 3.16 | 3.80 | 4.51 | 4.50 | 4.19 |
| St Helena | 1842-1847 a | 3.72 | 5.19 | 4.93 | 3.30 | 2.64 | 3.24 | 3.42 | 3.59 | 2.40 | 4.43 | 4.05 | 3.54 |
| Mauritius | 1876-1890 a | 5.2 | 6.1 | 6.3 | 4.7 | 4.1 | 2.9 | 3.4 | 4.9 | 5.0 | 5.5 | 5.6 | 5.1 |
| Cape | 1841-1846 a | 5.14 | 8.21 | 7.27 | 5.00 | 3.91 | 3.21 | 3.54 | 4.98 | 4.33 | 5.96 | 6.36 | 5.47 |
| Hobart | 1841-1848 a |11.66 |11.80 | 9.50 | 7.26 | 4.56 | 3.70 | 4.61 | 5.89 | 8.24 |11.01 |12.05 |11.81 |
+-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+

§ 17. Variations of inclination are connected with those of horizontal
and vertical force by the relation

[delta]I = ½ sin 2I {V^-1 [delta]V - H^-1 [delta]H}.

Thus in temperate latitudes where V is considerably in excess of H,
whilst diurnal changes in V are usually less than those in H, it is
the latter which chiefly dominate the diurnal changes in inclination.
When the H influence prevails, I has its highest values at hours when
H is least. This explains why the dip is above its mean value near
midday at stations in Table XI. from Pavlovsk to Parc St Maur. Near
the magnetic equator the vertical force has the greater influence.
This alone would tend to make a minimum dip in the late forenoon, and
this minimum is accentuated owing to the altered type of the
horizontal force diurnal variation, whose maximum now coincides
closely with the minimum in the vertical force. This accounts for the
prominence of the minimum in the diurnal variation of the inclination
at Kolaba and Batavia, and the large amplitude of the range. Tiflis
shows an intermediate type of diurnal variation; there is a minimum
near noon, as in tropical stations, but inclination is also below its
mean for some hours near midnight. The type really varies at Tiflis
according to the season of the year. In June--as in the mean equality
from the whole year--there is a well marked double period; there is a
principal minimum at 2 p.m. and a secondary one about 4 a.m.; a
principal maximum about 9 a.m. and a secondary one about 6 p.m. In
December, however, only a single period is recognizable, with a
minimum about 8 a.m. and a maximum about 7 p.m. The type of diurnal
inequality seen at the Cape of Good Hope does not differ much from
that seen at Batavia. Only a single period is clearly shown. The
maximum occurs about 8 or 9 p.m. throughout the year. The time of the
minimum is more variable; at midsummer it occurs about 11 a.m., but at
midwinter three or four hours later. At Hobart the type varies
considerably with the season. In June (midwinter) a double period is
visible. The principal minimum occurs about 8 a.m., as at the Cape.
But, corresponding to the evening maximum seen at the Cape, there is
now only a secondary maximum, the principal maximum occurring about 1
p.m. At midsummer the principal maximum is found--as at Kew or
Greenwich--about 10 or 11 a.m., the principal minimum about 4 p.m.

§ 18. Even at tropical stations a considerable seasonal change is
usually seen in the amplitude of the diurnal inequality in at least
one of the magnetic elements. At stations in Europe, and generally in
temperate latitudes, the amplitude varies notably in all the elements.
Table XIII. gives particulars of the inequality range of declination
derived from hourly readings at selected stations, arranged in order
of latitude from north to south. The letters "a" and "q" are used in
the same sense as before. At temperate stations in either
hemisphere--e.g. Pavlovsk, Greenwich or Hobart--the range is
conspicuously larger in summer than in winter. In northern temperate
stations a decided minimum is usually apparent in December. There is,
on the other hand, comparatively little variation in the range from
April to August. Sometimes, as at Kew and Greenwich, there is at least
a suggestion of a secondary minimum at midsummer. Manila and
Trivandrum show a transition from the December minimum, characteristic
of the northern stations, to the June minimum characteristic of the
southern, there being two conspicuous minima in February or March and
in November or October. At St Helena there are two similar minima in
May and September, while a third apparently exists in December. It
will be noticed that at both Pavlovsk and Kew the annual variation in
the range is specially prominent in the quiet day results.

Table XIV. gives a smaller number of data analogous to those of Table
XIII., comprising inequality ranges for horizontal force, vertical
force and inclination. In some cases the number of years from which
the data were derived seems hardly sufficient to give a smooth annual
variation. It should also be noticed that unless the same group of
years is employed the data from two stations are not strictly
comparable. The difference between the all and quiet day vertical
force data at Pavlovsk is remarkably pronounced. The general tendency
in all the elements is to show a reduced range at midwinter; but in
some cases there is also a distinct reduction in the range at
midsummer. This double annual period is particularly well marked at
Batavia.

TABLE XIV.--Ranges in the Diurnal Inequalities.

+-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+
| | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
+-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+
| H (unit 1[gamma]) | | | | | | | | | | | | |
| Pavlovsk 1890-1900 a | 12 | 20 | 32 | 46 | 47 | 49 | 49 | 44 | 39 | 32 | 17 | 11 |
| " " q | 12 | 17 | 31 | 42 | 45 | 45 | 42 | 40 | 37 | 31 | 17 | 10 |
| Ekatarinburg " a | 11 | 15 | 29 | 37 | 40 | 40 | 39 | 36 | 33 | 27 | 13 | 9 |
| Kew " q | 15 | 17 | 26 | 36 | 38 | 39 | 38 | 38 | 35 | 27 | 20 | 11 |
| Toronto 1843-1848 a | 23 | 21 | 24 | 28 | 29 | 29 | 26 | 28 | 41 | 25 | 21 | 20 |
| Batavia 1883-1898 a | 49 | 47 | 54 | 60 | 51 | 48 | 50 | 53 | 58 | 52 | 43 | 40 |
| St Helena 1843-1847 a | 43 | 41 | 48 | 53 | 46 | 40 | 40 | 45 | 41 | 40 | 40 | 32 |
| Mauritius 1883-1890 a | 21 | 15 | 21 | 23 | 20 | 21 | 20 | 22 | 20 | 21 | 21 | 20 |
| Cape of Good Hope 1841-1846 a | 13 | 10 | 13 | 13 | 15 | 16 | 14 | 18 | 21 | 14 | 17 | 20 |
| Hobart 1842-1848 a | 42 | 43 | 34 | 28 | 19 | 17 | 22 | 23 | 23 | 35 | 39 | 42 |
| | | | | | | | | | | | | |
| V (unit 1[gamma]) | | | | | | | | | | | | |
| Pavlovsk 1890-1900 a | 15 | 27 | 29 | 24 | 26 | 20 | 23 | 19 | 23 | 20 | 18 | 14 |
| " " q | 4 | 5 | 9 | 13 | 13 | 12 | 13 | 10 | 9 | 7 | 5 | 4 |
| Ekatarinburg " a | 10 | 15 | 17 | 21 | 22 | 19 | 20 | 16 | 14 | 13 | 11 | 9 |
| Kew 1891-1900 q | 7 | 10 | 20 | 25 | 31 | 27 | 28 | 23 | 20 | 15 | 9 | 6 |
| Toronto 1843-1848 a | 12 | 14 | 17 | 23 | 26 | 14 | 27 | 32 | 34 | 25 | 19 | 18 |
| Batavia 1883-1898 a | 42 | 48 | 48 | 45 | 31 | 31 | 32 | 29 | 41 | 50 | 40 | 33 |
| St Helena 1843-1847 a | 16 | 13 | 12 | 14 | 13 | 11 | 17 | 11 | 17 | 11 | 15 | 18 |
| Mauritius 1884-1890 a | 12 | 16 | 18 | 15 | 14 | 13 | 15 | 21 | 20 | 16 | 13 | 11 |
| Cape of Good Hope 1841-1846 a | 29 | 47 | 41 | 38 | 21 | 12 | 14 | 19 | 19 | 35 | 33 | 28 |
| Hobart 1842-1848 a | 25 | 27 | 22 | 23 | 24 | 21 | 22 | 28 | 26 | 22 | 23 | 27 |
| | | | | | | | | | | | | |
| _Inclination_ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| Pavlovsk 1890-1900 a | 0.97 | 1.24 | 2.07 | 2.79 | 2.72 | 2.88 | 2.85 | 2.64 | 2.52 | 2.18 | 1.20 | 0.89 |
| Ekatarinburg " a | 0.79 | 0.94 | 1.70 | 2.08 | 2.25 | 2.19 | 2.18 | 2.08 | 2.00 | 1.70 | 0.88 | 0.69 |
| Kew " q | 0.98 | 1.01 | 1.38 | 1.86 | 2.05 | 2.02 | 2.05 | 2.15 | 1.98 | 1.57 | 1.27 | 0.63 |
| Toronto 1843-1848 a | 1.15 | 0.94 | 1.19 | 1.23 | 1.31 | 1.37 | 1.13 | 1.26 | 1.87 | 1.16 | 1.09 | 1.05 |
| Batavia 1883-1898 a | 4.88 | 5.22 | 5.56 | 5.62 | 4.21 | 4.05 | 4.24 | 4.17 | 5.13 | 5.58 | 4.51 | 3.85 |
| Cape of Good Hope 1842-1846 a | 1.55 | 2.29 | 2.23 | 2.23 | 1.60 | 1.41 | 1.54 | 1.70 | 1.86 | 2.03 | 1.55 | 2.04 |
| Hobart 1842-1848 a | 1.95 | 2.16 | 1.72 | 1.62 | 1.23 | 1.16 | 1.28 | 1.42 | 1.39 | 1.75 | 2.04 | 2.10 |
+-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+

§ 19. When discussing diurnal inequalities it is sometimes convenient
to consider the components of the horizontal force in and
perpendicular to the astronomical meridian, rather than the horizontal
force and declination. If N and W be the components of H to
astronomical north and west, and D the westerly declination, N = H
cos D, W = H sin D. Thus corresponding small variations in N, W, H and
D are connected by the relations:--

[delta]N = cos D[delta]H - H sin D[delta]D,
[delta]W = sin D[delta]H + H cos D[delta]D.

If [delta]H and [delta]D denote the departures of H and D at any hour
of the day from their mean values, then [delta]N and [delta]W
represent the corresponding departures of N and W from their mean
values. In this way diurnal inequalities may be calculated for N and W
when those for H and D are known. The formulae suppose [delta]D to be
expressed in absolute measure, i.e. 1´ of arc has to be replaced by
0.0002909. If we take as an example a station at which H is .185 then
H[delta]D = .0000538 (number of minutes in [delta]D). In other words,
employing 1[gamma] as unit of force, one replaces H[delta]D by
5.38[delta]D, where [delta]D represents declination change expressed
as usual in minutes of arc. In calculating diurnal inequalities for N
and W, one ought, strictly speaking, to assign to H and D the exact
mean values belonging to these elements for the month or the year
being dealt with. For practical purposes, however, a slight departure
from the true mean values is immaterial, and one can make use of a
constant value for several successive years without sensible error. As
an example, Table XV. gives the mean diurnal inequality for the whole
year in N and W at Falmouth, as calculated from the 12 years 1891 to
1902. The unit employed is 1[gamma].

The data in Table XV. are closely similar to corresponding Kew data,
and are presumably fairly applicable to the whole south of England for
the epoch considered. At Falmouth there is comparatively little
seasonal variation in the type of the diurnal variation in either N or
W. The amplitude of the diurnal range varies, however, largely with
the season, as will appear from Table XVI., which is based on the same
12 years as Table XV.

Diurnal inequalities in N and W lend themselves readily to the
construction of what are known as _vector diagrams_. These are curves
showing the direction and intensity at each hour of the day of the
horizontal component of the disturbing force to which the diurnal
inequality may be regarded as due. Figs. 7 and 8, taken from the
_Phil. Trans._ vol. 204A, will serve as examples. They refer to the
mean diurnal inequalities for the months stated at Kew (1890 to 1900)
and Falmouth (1891 to 1902), thick lines relating to Kew, thin to
Falmouth. NS and EW represent the geographical north-south and
east-west directions; their intersection answers to the origin (thick
lines for Kew, thin for Falmouth). The line from the origin to M
represents the magnetic meridian. The line from the origin to any
cross--the number indicating the corresponding hour counted from
midnight as 0--represents the magnitude and direction at that hour of
the horizontal component of the disturbing force to which the diurnal
inequality may be assigned. The cross marks the point whose
rectangular co-ordinates are the values of [delta]N and [delta]W
derived from the diurnal inequalities of these elements. In figs. 7
and 8 the distances of the points N, E, S, W from their corresponding
origin represents 10[gamma]. The tendency to form a loop near
midnight, seen in the November and December curves, is
characteristic of the winter months at Kew and Falmouth. The shape is
less variable in summer than in winter; but even in summer the portion
answering to the hours 6 p.m. to 6 a.m. varies a good deal. The object
of presenting the Kew and Falmouth curves side by side is to emphasize
the close resemblance between the magnetic phenomena at places in
similar latitudes, though over 200 miles apart and exhibiting widely
different ranges for their meteorological elements. With considerable
change of latitude however the shape of vector diagrams changes
largely.

TABLE XV.--Diurnal Inequalities in N. and W. at Falmouth (unit
1[gamma]).

+---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Hour. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|N. /a.m. | + 6 | + 5 | + 5 | + 5 | + 6 | + 6 | + 5 | + 1 | - 6 | -14 | -20 | -20 |
| \p.m. | -17 | -12 | - 6 | - 1 | + 3 | + 6 | + 9 | + 9 | + 9 | + 8 | + 7 | + 7 |
|W. /a.m. | - 2 | - 2 | - 3 | - 4 | - 6 | - 9 | -13 | -17 | -19 | -13 | - 3 | +11 |
| \p.m. | +20 | +22 | +17 | +11 | + 6 | + 4 | + 2 | + 1 | 0 | - 1 | - 2 | - 2 |
+---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

Fourier Series.

§ 20. Any diurnal inequality can be analysed into a series of harmonic
terms whose periods are 24 hours and submultiples thereof. The series
may be expressed in either of the equivalent forms:--

a1 cos t + b1 sin t + a2 cos 2t + b2 sin 2t + ... (i)

c1 sin (t + [alpha]1) + c2 sin (2t + [alpha]2) + .... (ii)

TABLE XVI.--Ranges in Diurnal Inequalities at Falmouth (unit
1[gamma]).

+----+------+------+------+------+------+------+------+------+------+------+------+------+
| | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. |
+----+------+------+------+------+------+------+------+------+------+------+------+------+
| N. | 21 | 23 | 30 | 39 | 39 | 37 | 37 | 39 | 36 | 32 | 24 | 15 |
| W. | 20 | 24 | 46 | 54 | 55 | 55 | 54 | 56 | 51 | 39 | 24 | 15 |
+----+------+------+------+------+------+------+------+------+------+------+------+------+

In both forms t denotes time, counted usually from midnight, one hour
of time being interpreted as 15° of angle. Form (i) is that utilized
in actually calculating the constants a, b, ... Once the a, b, ...
constants are known, the c, [alpha], ... constants are at once
derivable from the formulae:--

tan [alpha]_n = a_n/b_n;
c_n = a_n/sin [alpha]_n = b_n/cos [alpha]_n = [root](a_n² + b_n²).

The a, b, c, [alpha] constants are called sometimes Fourier, sometimes
Bessel coefficients.

FIG. 7.]

By taking a sufficient number of terms a series can always be obtained
which will represent any set of diurnal inequality figures; but unless
one can obtain a close approach to the observational figures from the
terms possessing the periods 24, 12, 8 and 6 hours the physical
significance and general utility of the analysis is somewhat
problematical. In the case of the magnetic elements, the 24 and 12
hour terms are usually much the more important; the 24-hour term is
generally, but by no means always, the larger of the two. The c
constants give the amplitudes of the harmonic terms or waves, the
[alpha] constants the phase angles. An advance of 1 hour in the time
of occurrence of the first (and subsequent, if any) maximum and
minimum answers to an _increase_ of 15° in [alpha]1 of 30° in
[alpha]2, of 45° in [alpha]3, of 60° in [alpha]4 and so on. In the
case of magnetic elements the phase angles not infrequently possess a
somewhat large annual variation. It is thus essential for a minute
study of the phenomena at any station to carry out the analysis for
the different seasons of the year, and preferably for the individual
months. If the a and b constants are known for all the individual
months of one year, or for all the Januarys of a series of years, we
have only to take their arithmetic means to obtain the corresponding
constants for the mean diurnal inequality of the year, or for the
diurnal inequality of the average January of the series of years.
This, however, is obviously not true of the c or [alpha] constants,
unless the phase angle is absolutely unchanged throughout the
contributory months or years. This is a point requiring careful
attention, because when giving values of c and [alpha] for the whole
year some authorities give the arithmetic mean of the c's and
[alpha]'s calculated from the diurnal inequalities of the individual
months of the year, others give the values obtained for c and [alpha]
from the mean diurnal inequality of the whole year. The former method
inevitably supplies a larger value for c than the latter, supposing
[alpha] to vary with the season. At some observatories, e.g. Greenwich
and Batavia, it has long been customary to publish every year values
of the Fourier coefficients for each month, and to include other
elements besides the declination. For a thoroughly satisfactory
comparison of different stations, it is necessary to have data from
one and the same epoch; and preferably that epoch should include at
least one 11-year period. There are, however, few stations which can
supply the data required for such a comparison and we have to make the
best of what is available. Information is naturally most copious for
the declination. For this element E. Engelenburg[20] gives values of
C1, C2, C3, C4, and of [alpha]1, [alpha]2, [alpha]3, [alpha]4 for each
month of the year for about 50 stations, ranging from Fort Rae (62° 6´
N. lat.) to Cape Horn (55° 5´ S. lat.). From the results for
individual stations, Engelenburg derives a series of means which he
regards as representative of 11 different zones of latitude. His data
for individual stations refer to different epochs, and some are based
on only one year's observations. The original observations also differ
in reliability; thus the results are of somewhat unequal value. The
mean results for Engelenburg's zones must naturally have some of the
sources of uncertainty reduced; but then the fundamental idea
represented by the arrangement in zones is open to question. The
majority of the data in Table XVII. are taken from Engelenburg, but
the phase angles have been altered so as to apply to westerly
declination. The stations are arranged in order of latitude from north
to south; in a few instances results are given for quiet days. The
figures represent in all cases arithmetic means derived from the 12
monthly values. In the table, so far as is known, the local mean time
of the observatory has been employed. This is a point requiring
attention, because most observatories employ Greenwich time, or time
based on Greenwich or some other national observatory, and any
departure from local time enters into the values of the constants. The
data for Victoria Land refer to the "Discovery's" 1902-1903 winter
quarters, where the declination, taken westerly, was about 207°.5.

As an example of the significance of the phase angles in Table XVII.,
take the ordinary day data for Kew. The times of occurrence of the
maxima are given by t + 234° = 450° for the 24-hour term, 2t + 39°.7 =
90° or = 450° for the 12-hour term, and so on, taking an hour in t as
equivalent to 15°.

Thus the times of the maxima are:--

24-hour term, 2 h. 24 m. p.m.; 12-hour term, 1 h. 41 m. a.m. and p.m.

8-hour term, 4 h. 41 m. a.m., 0 h. 41 m. p.m., and 8 h. 41 m. p.m.

6-hour term, 0 h. 33 m. a.m. and p.m., and 6 h. 33 m. a.m. and p.m.

The minima, or extreme easterly positions in the waves, lie midway
between successive maxima. All four terms, it will be seen, have
maxima at some hour between 0h. 30m. and 2h. 30m. p.m. They thus
reinforce one another strongly from 1 to 2 p.m., accounting for the
prominence of the maximum in the early afternoon.

FIG. 8.]

The utility of a Fourier analysis depends largely on whether the
several terms have a definite physical significance. If the 24-hour
and 12-hour terms, for instance, represent the action of forces whose
distribution over the earth or whose seasonal variation is essentially
different, then the analysis helps to distinguish these forces, and
may assist in their being tracked to their ultimate source. Suppose,
for example, one had reason to think the magnetic diurnal variation
due to some meteorological phenomenon, e.g. heating of the earth's
atmosphere, then a comparison of Fourier coefficients, if such
existed, for the two sets of phenomena would be a powerful method of
investigation.

TABLE XVII.--Amplitudes and Phase Angles for Diurnal Inequality of
Declination.

+---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| Place. | Epoch. | c1. | c2. | c3. | c4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
+---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| | | ´ | ´ | ´ | ´ | ° | ° | ° | ° |
| Fort Rae (all) | 1882-1883 | 18.49 | 8.22 | 1.99 | 2.07 | 156.5 | 41.9 | 308 | 104 |
| " (quiet) | " | 9.09 | 4.51 | 1.32 | 0.73 | 166.5 | 37.5 | 225 | 350 |
| Ekatarinburg | 1841-1862 | 2.57 | 1.81 | 0.73 | 0.22 | 223.3 | 7.4 | 204 | 351 |
| Potsdam | 1890-1899 | 2.81 | 1.90 | 0.83 | 0.31 | 239.9 | 32.6 | 237 | 49 |
| Kew (ordinary) | 1890-1900 | 2.91 | 1.79 | 0.79 | 0.27 | 234.0 | 39.7 | 239 | 57 |
| Kew (quiet) | " | 2.37 | 1.82 | 0.90 | 0.30 | 227.3 | 42.1 | 240 | 55 |
| Falmouth (quiet) | 1891-1902 | 2.18 | 1.82 | 0.91 | 0.29 | 226.2 | 40.5 | 238 | 56 |
| Parc St Maur | 1883-1899 | 2.70 | 1.87 | 0.85 | 0.30 | 238.6 | 32.5 | 235 | 95 |
| Toronto | 1842-1848 | 2.65 | 2.34 | 1.00 | 0.33 | 213.7 | 34.9 | 238 | 350 |
| Washington | 1840-1842 | 2.38 | 1.86 | 0.65 | 0.33 | 223.0 | 26.6 | 223 | 53 |
| Manila | 1890-1900 | 0.53 | 0.58 | 0.43 | 0.17 | 266.3 | 50.7 | 226 | 89 |
| Trivandrum | 1853-1864 | 0.54 | 0.46 | 0.29 | 0.10 | 289.0 | 49.6 | | 114 |
| Batavia | 1883-1899 | 0.80 | 0.88 | 0.43 | 0.13 | 332.0 | 163.2 | 5 | 236 |
| St. Helena | 1842-1847 | 0.68 | 0.61 | 0.63 | 0.34 | 275.8 | 171.4 | 27 | 244 |
| Mauritius | 1876-1890 | 0.86 | 1.11 | 0.76 | 0.22 | 21.6 | 172.7 | 350 | 161 |
| C. of G. Hope | 1841-1846 | 1.15 | 1.13 | 0.80 | 0.35 | 287.7 | 156.0 | 351 | 193 |
| Melbourne | 1858-1863 | 2.52 | 2.45 | 1.23 | 0.35 | 27.4 | 176.7 | 9 | 193 |
| Hobart | 1841-1848 | 2.29 | 2.15 | 0.87 | 0.32 | 33.6 | 170.8 | 349 | 185 |
| S. Georgia | 1882-1883 | 2.13 | 1.28 | 0.76 | 0.31 | 30.3 | 185.3 | 7 | 180 |
| Victoria Land (all) | 1902-1903 | 20.51 | 4.81 | 1.21 | 1.32 | 158.7 | 306.9 | 292 | 303 |
| " (quieter) | " | 15.34 | 4.05 | 1.24 | 1.18 | 163.8 | 312.9 | 261 | |
+---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+

§ 21. Fourier coefficients of course often vary much with the season
of the year. In the case of the declination this is especially true of
the phase angles at tropical stations. To enter on details for a
number of stations would unduly occupy space. A fair idea of the
variability in the case of declination in temperate latitudes may be
derived from Table XVIII., which gives monthly values for Kew derived
from ordinary days of an 11-year period 1890-1900.

Fourier analysis has been applied to the diurnal inequalities of the
other magnetic elements, but more sparingly. Such results are
illustrated by Table XIX., which contains data derived from quiet days
at Kew from 1890 to 1900. _Winter_ includes November to February,
_Summer_ May to August, and _Equinox_ the remaining four months. In
this case the data are derived from mean diurnal inequalities for the
season specified. In the case of the c or amplitude coefficients the
unit is 1´ for I (inclination), and 1[gamma] for H and V (horizontal
and vertical force). At Kew the seasonal variation in the amplitude is
fairly similar for all the elements. The 24-hour and 12-hour terms
tend to be largest near midsummer, and least near midwinter; but the
8-hour and 6-hour terms have two well-marked maxima near the
equinoxes, and a clearly marked minimum near midsummer, in addition
to one near midwinter. On the other hand, the phase angle phenomena
vary much for the different elements. The 24-hour term, for instance,
has its maximum earlier in winter than in summer in the case of the
declination and vertical force, but the exact reverse holds for the
inclination and the horizontal force.

TABLE XVIII.--Kew Declination: Amplitudes and Phase Angles (local mean
time).

+----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
+----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| | ´ | ´ | ´ | ´ | ° | ° | ° | ° |
| January | 1.79 | 0.86 | 0.41 | 0.27 | 251.2 | 29.8 | 254 | 64 |
| February | 2.41 | 1.11 | 0.57 | 0.30 | 242.0 | 27.7 | 235 | 39 |
| March | 3.05 | 1.98 | 1.11 | 0.45 | 233.2 | 36.1 | 223 | 49 |
| April | 3.35 | 2.48 | 1.17 | 0.39 | 224.8 | 39.2 | 228 | 61 |
| May | 3.57 | 2.38 | 0.87 | 0.17 | 221.3 | 50.8 | 245 | 89 |
| June | 3.83 | 2.39 | 0.74 | 0.05 | 212.6 | 46.7 | 239 | 72 |
| July | 3.72 | 2.30 | 0.77 | 0.11 | 214.6 | 48.1 | 233 | 8 |
| August | 3.64 | 2.43 | 1.05 | 0.18 | 228.2 | 57.2 | 244 | 51 |
| September| 3.35 | 2.02 | 1.04 | 0.35 | 236.9 | 55.3 | 245 | 70 |
| October | 2.69 | 1.69 | 0.92 | 0.48 | 240.1 | 35.6 | 235 | 65 |
| November | 1.94 | 1.06 | 0.51 | 0.32 | 248.3 | 28.3 | 247 | 61 |
| December | 1.61 | 0.81 | 0.35 | 0.20 | 255.1 | 22.0 | 243 | 56 |
+----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+

Annual Inequality.

§ 22. If secular change proceeded uniformly throughout the year, the
value E_n of any element at the middle of the nth month of the year
would be connected with E, the mean value for the whole year, by the
formula E_n = E + (2n - 13)s/24, where s is the secular change per
annum. For the present purpose, difference in the lengths of the
months may be neglected. If one applies to E_n - E the correction -(2n
- 13)s/24 one eliminates a regularly progressive secular change; what
remains is known as the _annual inequality_. If only a short period of
years is dealt with, irregularities in the secular change from year to
year, or errors of observation, may obviously simulate the effect of a
real annual inequality. Even when a long series of years is included,
there is always a possibility of a spurious inequality arising from
annual variation in the instruments, or from annual change in the
conditions of observation. J. Liznar,[21] from a study of data from a
number of stations, arrived at certain mean results for the annual
inequalities in declination and inclination in the northern and
southern hemispheres, and J. Hann[22] has more recently dealt with
Liznar's and newer results. Table XX. gives a variety of data,
including the mean results given by Liznar and Hann. In the case of
declination + denotes westerly position; in the case of inclination it
denotes a larger dip (whether the inclination be north or south).
According to Liznar declination in summer is to the west of the normal
position in both hemispheres. The phenomena, however, at Parc St Maur
are, it will be seen, the exact opposite of what Liznar regards as
normal; and whilst the Potsdam results resemble his mean in type, the
range of the inequality there, as at Parc St Maur, is relatively
small. Of the three sets of data given for Kew the first two are
derived in a similar way to those for other stations; the first set
are based on quiet days only, the second on all but highly disturbed
days. Both these sets of results are fairly similar in type to the
Parc St Maur results, but give larger ranges; they are thus even more
opposed to Liznar's normal type. The last set of data for Kew is of a
special kind. During the 11 years 1890 to 1900 the Kew declination
magnetograph showed to within 1´ the exact secular change as derived
from the absolute observations; also, if any annual variation existed
in the position of the base lines of the curves it was exceedingly
small. Thus the accumulation of the daily non-cyclic changes shown by
the curves should closely represent the combined effects of secular
change and annual inequality. Eliminating the secular change, we
arrive at an annual inequality, based on all days of the year
including the highly disturbed. It is this annual inequality which
appears under the heading s. It is certainly very unlike the annual
inequality derived in the usual way. Whether the difference is to be
wholly assigned to the fact that highly disturbed days contribute in
the one case, but not in the other, is a question for future research.

TABLE XIX.--Kew Diurnal Inequality: Amplitudes and Phase Angles (local
mean time).

+-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. |
+-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
| | ´ | ´ | ´ | ´ | ° | ° | ° | ° |
| /Winter | 0.240 | 0.222 | 0.104 | 0.076 | 250.0 | 91.8 | 344 | 194 |
| I < Equinox | 0.601 | 0.290 | 0.213 | 0.127 | 290.3 | 135.5 | 4 | 207 |
| \Summer | 0.801 | 0.322 | 0.172 | 0.070 | 312.5 | 155.5 | 39 | 238 |
| | | | | | | | | |
| /Winter | 3.62 | 3.86 | 1.81 | 1.13 | 82.9 | 277.3 | 154 | 6 |
| H < Equinox | 10.97 | 5.87 | 3.32 | 1.84 | 109.6 | 303.5 | 167 | 16 |
| \Summer | 14.85 | 6.23 | 2.35 | 0.95 | 130.3 | 316.5 | 199 | 41 |
| | | | | | | | | |
| /Winter | 2.46 | 1.67 | 0.86 | 0.42 | 153.9 | 300.8 | 108 | 280 |
| V < Equinox | 6.15 | 4.70 | 2.51 | 0.94 | 117.2 | 272.3 | 99 | 289 |
| \Summer | 8.63 | 6.45 | 2.24 | 0.55 | 122.0 | 272.4 | 100 | 285 |
+-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+

In the case of the inclination, Liznar found that in both hemispheres
the dip (north in the northern, south in the southern hemisphere) was
larger than the normal when the sun was in perihelion, corresponding
to an enhanced value of the horizontal force in summer in the northern
hemisphere.

In the case of annual inequalities, at least that of the declination,
it is a somewhat suggestive fact that the range seems to become less
as we pass from older to more recent results, or from shorter to
longer periods of years. Thus for Paris from 1821 to 1830 Arago
deduced a range of 2´ 9´´. Quiet days at Kew from 1890 to 1894 gave a
range of 1´.2, while at Potsdam Lüdeling got a range 30% larger than
that in Table XX. when considering the shorter period 1891-1899. Up to
the present, few individual results, if any, can claim a very high
degree of certainty. With improved instruments and methods it may be
different in the future.

TABLE XX.--Annual Inequality.