Chapter LXIII: repeats the promise of freedom to the English church (8)

+----------------+-----------------------+----------------------------------------------+-----------------------------------
| | Geographical position.| Absolute Values of Elements. | Secular change (mean per annum). |
| Place. +-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+
| | | | | | | | | Interval | | | | |
| | Latitude. | Longitude.| Year. | D. | I. | H. | V. | in years.| D. | I. | H. | V. |
+----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+
| | ° ´ | ° ´ | | ° ´ | ° ´ | | | | ´ | ´ | | |
| Pavlovsk | 59 41N | 30 29E | 1906 | 1 4.2E | 70 36.6N | .16528 | .46963 | 5 | -4.5 | +0.1 | - 6 | -14 |
| Sitka (Alaska) | 57 3N | 135 20W | 1906 |30 3.3E | 74 41.7N | .15502 | .56646 | 4 | -3.0 | -1.6 | +18 | -38 |
| Ekatarinburg | 56 49N | 60 38E | 1906 |10 31.0E | 70 49.5N | .17664 | .50796 | 5 | -4.5 | +1.7 | -23 | +18 |
| Rude Skov | | | | | | | | | | | | |
| (Copenhagen) | 55 51N | 12 27E | 1908 | 9 43.3W | 68 45N | .17406 | .44759 | | | | | |
| Stonyhurst | 53 51N | 2 28W | 1909 |17 28.6W | 68 42.8N | .17424 | .44722 | 5 | -5.9 | -1.1 | + 6 | -25 |
| Hamburg | 53 33N | 9 59E | 1903 |11 10.2W | 67 23.5N | .18126 | .43527 | | | | | |
| Wilhelmshaven | 53 32N | 8 9E | 1909 |11 46.8W | | .18129 | | 5 | -5.2 | | - 7 | |
| Potsdam | 52 23N | 13 4E | 1909 | 9 10.6W | 66 20.0N | .18834 | .42971 | 5 | -5.8 | +0.1 | - 9 | -19 |
| Irkutsk | 52 16N | 104 16E | 1905 | 1 58.1E | 70 25.0N | .20011 | .56250 | 5 | +0.6 | +2.0 | -24 | +39 |
| de Bilt | 52 5N | 5 11E | 1907 |13 19.0W | 66 49.9N | .18559 | .43368 | 5 | -4.7 | -0.6 | + 2 | -16 |
| Valencia | 51 56N | 10 15W | 1909 |20 50.3W | 68 15.1N | .17877 | .44812 | 5 | -5.0 | -1.2 | + 7 | -25 |
| Kew | 51 28N | 0 19W | 1909 |16 10.8W | 66 59.7N | .18506 | .43588 | 5 | -5.4 | -1.1 | + 2 | -35 |
| Greenwich | 51 28N | 0 0 | 1909 |15 47.6W | 66 53.9N | .18526 | .43432 | 5 | -5.5 | -0.7 | + 1 | -20 |
| Uccle | 50 48N | 4 21E | 1908 |13 36.7W | 66 1.6N | .19061 | .42867 | 4 | -5.3 | -0.8 | - 3 | -35 |
| Falmouth | 50 9N | 5 5W | 1909 |17 48.4W | 66 30.6N | .18802 | .43266 | 5 | -4.7 | -1.4 | + 9 | -30 |
| Prague | 50 5N | 14 25E | 1908 | 8 20.9W | | | | 5 | -6.5 | | | |
| Cracow | 50 4N | 19 58E | 1909 | 5 35.1W | 64 18N | | | 3 | -7.3 | | | |
| St Helier | 49 12N | 2 5W | 1907 |16 27.4W | 65 34.5N | | | 5 | -5.3 | -1.2 | | |
| Val Joyeux | 48 49N | 2 1E | 1909 |14 32.9W | 64 43.9N | .19727 | .41792 | 5 | -5.4 | -1.7 | + 1 | -51 |
| Vienna | 48 15N | 16 21E | 1898 | 8 24.1W | | | | | | | | |
| Munich | 48 9N | 11 37E | 1906 | 9 59.5W | 63 10.0N | .20657 | .40835 | 5 | -4.8 | -1.3 | + 4 | -31 |
| O'Gyalla | 47 53N | 18 12E | 1909 | 6 43.9W | | .21094 | | 5 | -5.0 | | -10 | |
| Odessa | 46 26N | 30 46E | 1899 | 4 36.7W | 62 18.2N | .21869 | .41660 | | | | | |
| Pola | 44 52N | 15 51E | 1908 | 8 43.2W | 60 6.8N | .22207 | .38640 | 5 | -5.5 | -0.6 | - 4 | -23 |
| Agincourt | | | | | | | | | | | | |
| (Toronto) | 43 47N | 79 16W | 1906 | 5 45.3W | 74 35.6N | .16397 | .59502 | 4 | +3.4 | +0.9 | -23 | -24 |
| Nice | 43 43N | 7 16E | 1899 |12 4.0W | 60 11.7N | .22390 | .39087 | | | | | |
| Toulouse | 43 37N | 1 28E | 1905 |13 56.3W | 60 49.1N | .22025 | .39439 | 5 | -4.5 | -1.5 | + 2 | - 2 |
| Perpignan | 42 42N | 2 53E | 1907 |13 4.4W | | | | 7 | -4.7 | | | |
| Tiflis | 41 43N | 44 48E | 1905 | 2 41.6E | 56 2.8N | .25451 | .37799 | 7 | -5.2 | +1.7 | -26 | + 2 |
| Capo di Monte | 40 52N | 14 15E | 1906 | 8 40.3W | 56 13.5N | | | 5 | -5.1 | -1.5 | | |
| Madrid | 40 25N | 3 40W | 1901 |15 35.6W | | | | | | | | |
| Coimbra | 40 12N | 8 25W | 1908 |16 46.2W | 58 57.3N | .22946 | .38120 | 5 | -4.6 | -2.9 | +17 | -45 |
| Baldwin | | | | | | | | | | | | |
| (Kansas) | 38 47N | 95 10W | 1906 | 8 30.1E | 68 45.1N | .21807 | .56081 | 4 | -1.7 | +1.8 | -36 | - 8 |
| Cheltenham | | | | | | | | | | | | |
| (Maryland) | 38 44N | 76 50W | 1906 | 5 22.0W | 70 27.3N | .20035 | .56436 | 4 | +3.8 | +1.2 | -38 | -45 |
| Lisbon | 38 43N | 9 9W | 1900 |17 18.0W | 57 54.8N | .23516 | .37484 | | | | | |
| Athens | 37 58N | 21 23E | 1908 | 4 52.9W | 52 11.7N | .26197 | .33613 | 5 | -5.5 | | | |
| San Fernando | 36 28N | 6 12W | 1908 |15 25.6W | 54 48.4N | .24829 | .35206 | 5 | -4.6 | -2.8 | +26 | -24 |
| Tokyo | 35 41N | 139 45E | 1901 | 4 36.1W | 49 0.0N | .29954 | .34459 | | | | | |
| Zi-ka-wei | 31 12N | 121 26E | 1906 | 2 32.0W | 45 35.3N | .33040 | .33726 | 5 | +1.5 | -1.3 | +30 | + 6 |
| Dehra Dun | 30 19N | 78 3E | 1907 | 2 38.3E | 43 36.1N | .33324 | .31736 | 4 | +0.8 | +5.5 | -26 | +77 |
| Helwan | 29 52N | 31 21E | 1909 | 2 49.2W | 40 40.4N | .30031 | .25804 | 5 | -5.7 | +1.2 | - 6 | +13 |
| Havana | 23 8N | 82 25W | 1905 | 2 25.0E | 52 57.4N | .30531 | .40452 | | | | | |
| Barrackpore | 22 46N | 88 22E | 1907 | 1 9.9E | 30 30.2N | .37288 | .21967 | 3 | +4.2 | +3.4 | +21 | +62 |
| Hong-Kong | 22 18N | 114 10E | 1908 | 0 3.9E | 31 2.5N | .37047 | .22292 | 5 | +1.9 | -1.8 | +43 | - 1 |
| Honolulu | 21 19N | 158 4W | 1906 | 9 21.7E | 40 1.8N | .29220 | .24545 | 4 | -0.9 | -3.2 | -19 | -62 |
| Kolaba | 18 54N | 72 49E | 1905 | 0 14.0E | 21 58.5N | .37382 | .15084 | 5 | +2.1 | +7.2 | -11 | +86 |
| Alibagh | 18 39N | 72 52E | 1909 | 1 0.3E | 23 29.0N | .36845 | .16008 | 3 | +1.7 | +6.8 | -10 | +82 |
| Vieques | | | | | | | | | | | | |
| (Porto Rico) | 18 9N | 65 26W | 1906 | 1 33.2W | 49 47.7N | .28927 | .34224 | 2 | +7.2 | +6.8 | -49 | +66 |
| Manila | 14 35N | 120 59E | 1904 | 0 51.4E | 16 0.2N | .38215 | .10960 | 5 | +0.1 | -3.9 | +47 | -34 |
| Kodaikanal | 10 14N | 77 28E | 1907 | 0 40.7W | 3 27.2N | .37431 | .02259 | 4 | +4.3 | +5.5 | +16 | +61 |
| Batavia | 6 11S | 106 49E | 1906 | 0 54.1E | 30 48.5S | .36708 | .21889 | 4 | +2.1 | -7.7 | - 2 | +110|
| Dar es Salaam | 6 49S | 39 18E | 1903 | 7 35.2W | | | | | | | | |
| Mauritius | 20 6S | 57 33E | 1908 | 9 14.3W | 53 44.9S | .23415 | .31932 | 5 | -0.3 | +2.9 | -53 | -131|
| Rio de Janeiro | 22 55S | 43 11W | 1906 | 8 55.5W | 13 57.1S | .24772 | .06164 | 5 | +9.1 | -6.8 | -42 | +44 |
| Santiago | | | | | | | | | | | | |
| (Chile) | 33 27S | 70 42W | 1906 |14 18.7E | 30 11.8S | | | 3 | +6.1 | +9.9 | | |
| Melbourne | 37 50S | 144 58E | 1901 | 8 26.7E | 67 25.0S | .23305 | .56024 | | | | | |
| Christchurch, | | | | | | | | | | | | |
| N.Z. | 43 32S | 172 37E | 1903 |16 18.4E | 67 42.3S | .22657 | .55259 | | | | | |
+----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+

TABLE III.--Declination at London.

+-------+--------------+-------+--------------+-------+--------------+
| Date. | Declination. | Date. | Declination. | Date. | Declination. |
+-------+--------------+-------+--------------+-------+--------------+
| | ° ´ | | ° ´ | | ° ´ |
| 1580 | 11 15E | 1773 | 21 9W | 1860 | 21 38.9W |
| 1622 | 6 0 | 1787 | 23 19 | 1865 | 20 58.7 |
| 1634 | 4 6 | 1795 | 23 57 | 1870 | 20 18.3 |
| 1657 | 0 0 | 1802 | 24 6 | 1875 | 19 35.6 |
| 1665 | 1 22W | 1805 | 24 8 | 1880 | 18 52.1 |
| 1672 | 2 30 | 1817 | 24 36 | 1885 | 18 19.2 |
| 1692 | 6 0 | 1818 | 24 38 | 1890 | 17 50.6 |
| 1723 | 14 17 | 1819 | 24 36 | 1895 | 17 16.8 |
| 1748 | 17 40 | 1820 | 24 34 | 1900 | 16 52.7 |
| | | | | 1905 | 16 32.9 |
+-------+--------------+-------+--------------+-------+--------------+

§ 12. Table VII. gives particulars of the secular change of horizontal
force and northerly inclination at London. Prior to the middle of the
19th century information as to the value of H is of uncertain value.
The earlier inclination data[14] are due to Norman, Gilbert, Bond,
Graham, Heberden and Gilpin. The data from 1857 onwards, both for H
and I, refer to Kew. "London" is rather a vague term, but the
differences between the values of H and I at Kew and Greenwich--in the
extreme west and east--are almost nil. For some time after its
discovery by Robert Norman inclination at London increased. The
earlier observations are not sufficient to admit of the date of the
maximum inclination or its absolute value being determined with
precision. Probably the date was near 1723. This view is supported by
the fact that at Paris the inclination fell from 72° 15´ in 1754 to
71° 48´ in 1780. The earlier observations in London were probably of
no very high accuracy, and the rates of secular change deducible from
them are correspondingly uncertain. It is not improbable that the
average annual change 0´.8 derived from the thirteen years 1773-1786
is too small, and the value 6´.2 derived from the fifteen years
1786-1801 too large. There is, however, other evidence of unusually
rapid secular change of inclination towards the end of the 18th
century in western Europe; for observations in Paris show a fall of
56´ between 1780 and 1791, and of 90´ between 1791 and 1806. Between
1801 and 1901 inclination in London diminished by 3° 26´.5, or on the
average by 2´.1 per annum, while between 1857 and 1900 H increased on
the average by 22[gamma] a year. These values differ but little from
the secular changes given in Table I. as applying at Kew for the epoch
Jan. 1, 1901. Since the beginning, however, of the 20th century a
notable change has set in, which seems shared by the whole of western
Europe. This is shown in a striking fashion by contrasting the data
from European stations in Tables I. and II. There are fifteen of these
stations which give secular change data for H in both tables, while
thirteen give secular data for I. The mean values of the secular
changes derived from these stations are as follows:--

I H

From Table I. -2´.35 +21.0[gamma]
From Table II. -1.12 +1.6[gamma]

The difference in epoch between the two sets of results is only about
5 years, and yet in that short time the mean rate of annual increase
in H fell to a thirteenth of its original value. During 1908-1909 H
diminished throughout all Europe except in the extreme west. Whether
we have to do with merely a temporary phase, or whether a general and
persistent diminution in the value of H is about to set in over Europe
it is yet hardly possible to say.

TABLE IV.--Declination at Kolaba (Bombay).

+-------+----------------+----------------+
| Year. | Declination | Change since |
| | East. | previous year. |
+-------+----------------+----------------+
| | ° ´ ´´ | ´ ´´ |
| 1876 | 0 55 58 | 0 37 E |
| 1877 | 56 39 | 0 41 E |
| 1878 | 57 6 | 0 27 E |
| 1879 | 57 30 | 0 24 E |
| 1880 | 57 9 | 0 21 W |
| 1881 | 0 57 12 | 0 3 E |
| 1882 | 0 56 50 | 0 22 W |
| 1883 | 57 2 | 0 12 E |
| 1884 | 55 39 | 1 23 W |
| 1885 | 55 3 | 0 36 W |
+-------+----------------+----------------+

§ 13. It is often convenient to obtain a formula to express the mean
annual change of an element during a given period throughout an area
of some size. The usual method is to assume that the change at a place
whose latitude is l and longitude [lambda] is given by an expression
of the type c + a(l - l0) + b([lambda] - [lambda]0), where a, b, c are
constants, l0 and [lambda]0, denoting some fixed latitude and
longitude which it is convenient to take as point of departure.
Supposing observational data available from a series of stations
throughout the area, a, b and c can be determined by least squares. As
an example, we may take the following slightly modified formula given
by Ad. Schmidt[15] as applicable to Northern Europe for the period
1890 to 1900. [Delta]D, [Delta]I and [Delta]H represent the mean
annual changes during this period in westerly declination, in
inclination and in horizontal force:--

´ ´ ´
[Delta]D = -5.24 - 0.071(l - 50) + 0.033([lambda] - 10),
[Delta]I = -1.58 + 0.010(l - 50) + 0.036([lambda] - 10),
[Delta]H = +23.5 - 0.59 (l - 50) - 0.35 ([lambda] - 10).

Longitude [lambda] is here counted positive to the east. The central
position assumed here (lat. 50°, long. 10° E.) falls in the north of
Bavaria. In the case of the horizontal force unity represents
1[gamma]. Schmidt found the above formulae to give results in very
close agreement with the data at the eight stations which he had
employed in determining the constants. These stations ranged from
Pavlovsk to Perpignan, and from Stonyhurst to Ekaterinburg in Siberia.
Formulae involving the second as well as the first powers of l - l0
and [lambda] - [lambda]0 have also been used, e.g., by A. Tanakadate
in the Magnetic Survey of Japan.

Table V.--Declination at St Helena and Cape of Good Hope.

+----------------------+----------------------+
| St Helena. | Cape of Good Hope. |
+--------+-------------+--------+-------------+
| Date. | Declination.| Date. | Declination.|
+--------+-------------+--------+-------------+
| | ° ´ | | ° ´ |
| 1610 | 7 13 E | 1605 | 0 30 E |
| 1677 | 0 40 | 1609 | 0 12 W |
| 1691 | 1 0 W | 1675 | 8 14 |
| 1724 | 7 30 | 1691 | 11 0 |
| 1775 | 12 18 | 1775 | 21 14 |
| 1789 | 15 30 | 1792 | 24 31 |
| 1796 | 15 48 | 1818 | 26 31 |
| 1806 | 17 18 | 1839 | 29 9 |
| 1839 | 22 17 | 1842 | 29 6 |
| 1840 | 22 53 | 1846 | 29 9 |
| 1846 | 23 11 | 1850 | 29 19 |
| 1890 | 23 57 | 1857 | 29 34 |
| | | 1874 | 30 4 |
| | | 1890 | 29 32 |
| | | 1903 | 28 44 |
+--------+-------------+--------+-------------+

TABLE VI.--Secular Change of Declination in the United States (+ to
the West).

+---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| Place. |Epoch | 1760 | 70 | 80 | 90 | 1800 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 1900 | 50 |
+---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+
| | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| / Eastport, Maine | | -1.2 | 0.0 | +1.2 | +2.1 | +3.2 | +4.0 | +4.5 | +4.9 | +5.0 | +5.6 | +4.5 | +3.0 | +2.1 | +1.0 | +1.8 | +2.4 |
| | Boston, Mass. | | -2.7 | -1.9 | -1.0 | 0.0 | +1.1 | +1.9 | +2.7 | +3.5 | +4.2 | +4.4 | +4.0 | +3.3 | +3.1 | +3.0 | +3.2 | +3.4 |
| | Albany, New York | | -4.2 | -3.6 | -2.7 | -1.6 | -0.6 | +0.6 | +1.6 | +2.7 | +3.6 | +4.6 | +4.6 | +3.9 | +4.7 | +2.3 | +3.4 | +3.6 |
| | Philadelphia, Penn. | | -4.6 | -4.2 | -3.5 | -2.3 | -1.3 | +0.1 | +1.3 | +2.5 | +3.4 | +4.3 | +4.2 | +4.6 | +4.4 | +3.4 | +3.5 | +3.4 |
| | Baltimore, Maryland | | -3.9 | -3.4 | -2.7 | -2.0 | -0.9 | 0.0 | +0.9 | +2.0 | +2.7 | +3.4 | +3.9 | +4.0 | +3.9 | +3.6 | +3.5 | +3.2 |
| | Richmond, Virginia | | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.1 | +3.6 | +3.9 | +3.8 | +3.7 | +3.4 | +3.2 |
| | Columbia, S. Carolina | | -3.7 | -3.4 | -2.9 | -2.2 | -1.3 | -0.5 | +0.5 | +1.3 | +2.2 | +2.9 | +3.4 | +3.8 | +3.8 | +3.8 | +3.6 | +1.8 |
| | Macon, Georgia | | -3.7 | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.9 | +3.5 | +3.1 | +1.2 |
| \ Tampa, Florida | | -3.0 | -2.5 | -2.0 | -1.1 | -0.4 | +0.4 | +1.1 | +2.0 | +2.5 | +3.0 | +3.2 | +3.5 | +3.7 | +2.8 | +2.9 | +1.6 |
| | | | | | | | | | | | | | | | | | |
| / Marquette, Michigan | | | | | | | | | 0.0 | +1.4 | +2.6 | +3.7 | +4.7 | +5.1 | +4.9 | +3.8 | +2.4 |
| | Columbus, Ohio | | | | | | | -0.9 | 0.0 | +0.9 | +2.0 | +2.9 | +3.4 | +3.6 | +3.7 | +3.9 | +4.0 | +2.4 |
| | Bloomington, Illinois | | | | | | | -2.4 | -1.5 | -0.4 | +0.4 | +1.5 | +2.4 | +2.8 | +4.2 | +3.9 | +2.9 | +1.0 |
| | Lexington, Kentucky | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.8 | +3.8 | +3.4 | +1.8 |
| | Chattanooga, Tennessee | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +4.0 | +3.5 | +3.1 | +1.6 |
| | Little Rock, Arkansas | | | | | | | -2.3 | -1.5 | -0.9 | +0.1 | +0.8 | +1.7 | +2.0 | +3.6 | +3.7 | +2.3 | -1.2 |
| | Montgomery, Alabama | | -3.6 | -3.5 | -3.1 | -2.8 | -2.2 | -1.5 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +2.8 | +3.8 | +3.9 | +2.6 | +0.2 |
| \ Alexandria, Louisiana | | | | | | | -2.1 | -1.6 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +3.6 | +3.3 | +2.0 | -1.4 |
| | | | | | | | | | | | | | | | | | |
| / Northome, Minnesota | | | | | | | | | -1.7 | -0.6 | +0.6 | +1.7 | +2.8 | +4.2 | +4.4 | +3.5 | 0.0 |
| | Jamestown, N. Dakota | | | | | | | | | | | | +1.0 | +1.9 | +3.1 | +4.8 | +1.9 | -2.2 |
| | Des Moines, Iowa | | | | | | | | | -1.5 | -0.6 | +0.6 | +1.5 | +2.5 | +3.8 | +4.5 | +2.7 | -0.6 |
| | Douglas, Wyoming | | | | | | | | | | | | -0.8 | 0.0 | +1.2 | +2.3 | +0.5 | -1.6 |
| | Emporia, Kansas | | | | | | | | | | | | +0.6 | +1.6 | +2.7 | +3.8 | +1.7 | -1.8 |
| | Pueblo, Colorado | | | | | | | | | | | | -0.3 | +0.4 | +1.5 | +3.1 | +0.7 | -2.2 |
| | Okmulgee, Oklahoma | | | | | | | | | | | | +0.9 | +1.5 | +2.7 | +3.9 | +1.4 | -2.4 |
| | Santa Rosa, New Mexico | | | | | | | | | | | | -0.4 | +0.4 | +1.4 | +2.6 | +0.4 | -2.4 |
| \ San Antonio, Texas | | | | | | | | | | -1.1 | -0.5 | -0.5 | +1.1 | +1.8 | +2.7 | +0.9 | -2.4 |
| | | | | | | | | | | | | | | | | | |
| / Seattle, Washington | | | | | -3.3 | -3.5 | -3.7 | -3.7 | -3.5 | -3.3 | -3.0 | -2.6 | -2.1 | -1.3 | -1.9 | -2.0 | -3.2 |
| | Wilson Creek, Washington| | | | | | | | | | | | -2.1 | -1.5 | -0.4 | -1.0 | -1.6 | -3.2 |
| | Detroit, Oregon | | | | | | | -3.8 | -3.9 | -3.9 | -3.7 | -3.4 | -2.9 | -2.5 | -1.8 | -0.8 | -1.8 | -3.8 |
| | Salt Lake, Utah | | | | | | | | | | | | -1.1 | -0.4 | +1.0 | +1.0 | -0.8 | -2.8 |
| | Prescott, Arizona | | | | | | | | | | | | -1.4 | -0.7 | +0.4 | +0.4 | -1.2 | -3.2 |
| | San José, California | | | | | -2.6 | -2.9 | -2.9 | -2.9 | -2.7 | -2.5 | -2.3 | -2.0 | -1.5 | -0.8 | -0.4 | -1.9 | -3.8 |
| \ Los Angeles, " | | | | | -3.4 | -3.4 | -3.5 | -3.2 | -3.0 | -2.7 | -2.1 | -1.6 | -1.1 | -0.9 | -0.3 | -1.6 | -3.6 |
+---------------------------+------+------+------+--------------------+------+------+------+------+------+------+------+------+------+------+------+

Formulae are also wanted to show how the value of an element, or the
rate of change of an element, at a particular place has varied
throughout a long period. For comparatively short periods it is best
to use formulae of the type E = a + bt + ct², where E denotes the
value of an element t years subsequent to some convenient epoch; a, b,
c are constants to be determined from the observational data. For
longer periods formulae of the type E = a + b sin (mt + n), where a,
b, m and n are constants, have been used by Schott[16] and others with
considerable success. The following examples, due to G. W.
Littlehales,[17] for the Cape of Good Hope, will suffice for
illustration:

Declination (West) = 14°.63 + 15°.00 sin {0.61(t - 1850) + 77°.8}
Inclination (South) = 49°.11 + 8°.75 sin {0.8 (t - 1850) + 34°.3}.

Here t denotes the date. It is perhaps hardly necessary to point out
that the extension of any of these empirical formulae--whether to
places outside the surveyed area, or to times not included in the
period of observation--is fraught with danger, which increases rapidly
the further the extrapolation is pushed.

Table VII.--Inclination (northerly) and Horizontal Force at London.

+------+-------+------+---------+------+---------+--------+------+---------+--------+
| Date.| I. | Date.| I. | Date.| I. | H. | Date.| I. | H. |
+------+-------+------+---------+------+---------+--------+------+---------+--------+
| | ° ´ | | ° ´ | | ° ´ | | | ° ´ | |
| 1576 | 71 50 | 1801 | 70 36.0 | 1857 | 68 24.9 | .17474 | 1891 | 67 33.2 | .18193 |
| 1600 | 72 0 | 1821 | 70 3.4 | 1860 | 69 19.8 | .17550 | 1895 | 67 25.4 | .18278 |
| 1676 | 73 30 | 1830 | 69 38.0 | 1865 | 68 8.7 | .17662 | 1900 | 67 11.8 | .18428 |
| 1723 | 74 42 | 1838 | 69 17.3 | 1870 | 67 58.6 | .17791 | 1905 | 67 3.8 | .18510 |
| 1773 | 72 19 | 1854 | 68 31.1 | 1874 | 67 50.0 | .17903 | 1908 | 67 0.9 | .18515 |
| 1786 | 72 9 | | | | | | | | |
+------+-------+------+---------+------+---------+--------+------+---------+--------+

Bauer has employed a convenient graphical method of illustrating
secular change. Radii are drawn from the centre of a sphere parallel
to the direction of the freely dipping needle, and are produced to
intersect the tangent plane drawn at the point which answers to the
mean position of the needle during the epoch under consideration. The
curve formed by the points of intersection shows the character of the
secular change. Fig. 5 (slightly modified from _Nature_, vol. 57, p.
181) applies to London. The curve is being described in the clockwise
direction. This, according to Bauer's[18] own investigation, is the
normal mode of description. Schott and Littlehales have found,
however, a considerable number of cases where it is difficult to say
whether the motion is clockwise or not, while in some stations on both
the east and west shores of the Pacific it was clearly anti-clockwise.
Fritsche[19] dealing with the secular changes from 1600 to 1885--as
given by his calculated values of the magnetic elements--at 204 points
of intersection of equidistant lines of latitude and longitude, found
only sixty-three cases in which the motion was unmistakably clockwise,
while in twenty-one cases it was clearly the opposite.

Diurnal Variations.

§ 14. All the magnetic elements at any ordinary station show a regular
variation in the solar day. To separate this from the irregular
changes, means of the hourly readings must be formed making use of a
number of days. The amplitude of the diurnal change usually varies
considerably with the season of the year. Thus a diurnal inequality
derived from all the days of the year combined, or from a smaller
number of days selected equally from all the months of the year, can
give only the average effect throughout the year. Also unless the
hours of maxima and minima at a given station are but slightly
variable with the season, the result obtained by combining data from
all the months of the year may be a hybrid which does not very closely
resemble the phenomena in the majority of individual months. This
remark applies in particular to the declination at places within the
tropics. One consequence is obviously to make the range of a diurnal
inequality which answers to the year as a whole less than the
arithmetic mean of the twelve ranges obtained for the constituent
months. At stations in temperate latitudes, whilst minor differences
of type do exist between the diurnal inequalities for different months
of the year, the difference is mainly one of amplitude, and the mean
diurnal inequality from all the months of the year gives a very fair
idea of the nature of the phenomena in any individual month.

Table VIII.--Diurnal Inequality of Declination, mean from whole year (+ to West).

+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
| Station. | Jan Mayen. |St Petersburg| Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. | Mauritius.| South Vic- |
| |and Pavlovsk.| | | St Maur. | | | | | toria Land. |
+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
| Latitude.| 71° 0´ N. | 59° 41´ N. | 51° 28´ N.| 51° 28´ N. |48° 49´ N.| 41° 43´ N.| 18° 54´ N.| 6° 11´ S.| 20° 6´ S.| 77° 51´ S. |
|Longitude.| 8° 28´ W. | 30° 29´ E. | 0° 0´. | 0° 19´ W. | 2° 29´ E.| 44° 48´ E.| 72° 49´ E.|106° 49´ E.| 57° 33´ E.| 166° 45´ E. |
+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+
| Period. | 1882-1883. | 1873-1885. | 1890-1900.| 1890-1900. |1883-1897.| 1888-1898.| 1894-1901.| 1883-1894.| 1876-1890.| 1902-1903. |
+----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
| | a. | q. | a. | q. | a. | a. | q. | a. | a. | q. | a. | a. | a. | q. |
+----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
| Hour. | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ |
| 1 | -6.6 | -4.2 | -1.3 | -0.7 | -1.4 | -1.5 | -0.9 | -1.4 | -0.7 | -0.2 | +0.1 | +0.1 | +2.0 | +0.9 |
| 2 | -10.5 | -6.4 | -1.2 | -0.8 | -1.3 | -1.4 | -0.9 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -2.1 | -1.8 |
| 3 | -15.2 | -7.8 | -1.2 | -1.0 | -1.3 | -1.5 | -1.0 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -5.2 | -4.5 |
| 4 | -16.9 | -8.4 | -1.4 | -1.3 | -1.4 | -1.7 | -1.3 | -1.2 | -0.5 | -0.1 | 0.0 | +0.2 | -9.4 | -6.8 |
| 5 | -17.0 | -8.1 | -1.7 | -1.8 | -1.7 | -2.1 | -1.8 | -1.6 | -0.7 | -0.1 | 0.0 | +0.3 | -12.2 | -9.0 |
| 6 | -13.7 | -7.0 | -1.9 | -2.3 | -2.1 | -2.4 | -2.3 | -1.9 | -1.2 | -0.6 | +0.1 | +0.4 | -15.3 | -11.7 |
| 7 | -9.3 | -5.1 | -2.2 | -2.8 | -2.4 | -2.7 | -2.8 | -2.4 | -1.9 | -1.0 | +0.5 | +0.6 | -17.2 | -15.0 |
| 8 | -6.8 | -3.2 | -2.5 | -3.2 | -2.5 | -2.8 | -3.1 | -2.7 | -2.4 | -1.2 | +1.3 | +1.1 | -21.5 | -17.3 |
| 9 | -3.7 | -0.6 | -2.3 | -3.0 | -1.9 | -2.1 | -2.5 | -2.3 | -2.3 | -0.7 | +1.7 | +1.8 | -23.5 | -18.1 |
| 10 | -2.4 | +2.1 | -1.0 | -1.7 | -0.2 | -0.3 | -0.7 | -0.5 | -0.9 | 0.0 | +1.5 | +1.9 | -21.2 | -15.8 |
| 11 | -0.5 | +4.6 | +1.0 | +0.4 | +2.1 | +2.2 | +1.7 | +2.0 | +1.0 | +0.9 | +0.9 | +1.3 | -15.3 | -9.2 |
| Noon | +2.5 | +6.5 | +3.1 | +2.7 | +4.2 | +4.3 | +3.9 | +4.2 | +2.6 | +1.4 | +0.1 | 0.0 | -9.8 | -4.9 |
| 1 | +3.7 | +7.3 | +4.6 | +4.3 | +5.1 | +5.3 | +4.8 | +5.3 | +3.3 | +1.2 | -0.6 | -1.1 | -3.2 | -0.1 |
| 2 | +6.4 | +7.1 | +4.9 | +4.5 | +4.7 | +4.9 | +4.4 | +4.9 | +3.1 | +0.6 | -1.1 | -2.0 | +3.8 | +5.9 |
| 3 | +7.4 | +5.9 | +4.1 | +3.6 | +3.6 | +3.7 | +3.1 | +3.7 | +2.3 | +0.1 | -1.3 | -2.3 | +11.1 | +9.5 |
| 4 | +8.5 | +4.3 | +2.7 | +2.3 | +2.2 | +2.4 | +1.8 | +2.3 | +1.3 | -0.2 | -1.2 | -1.8 | +16.6 | +12.9 |
| 5 | +10.6 | +3.0 | +1.5 | +1.3 | +1.1 | +1.2 | +0.7 | +1.1 | +0.6 | -0.1 | -0.9 | -0.9 | +19.9 | +14.6 |
| 6 | +14.2 | +2.3 | +0.6 | +0.7 | +0.3 | +0.4 | +0.2 | +0.2 | +0.2 | 0.0 | -0.6 | -0.1 | +22.0 | +15.5 |
| 7 | +15.2 | +2.2 | 0.0 | +0.4 | -0.3 | -0.2 | -0.1 | -0.4 | +0.1 | +0.1 | -0.4 | +0.1 | +22.0 | +15.9 |
| 8 | +15.8 | +2.6 | -0.4 | +0.2 | -0.9 | -0.6 | -0.3 | -0.9 | -0.1 | +0.2 | -0.2 | +0.1 | +19.9 | +14.6 |
| 9 | +13.2 | +2.6 | -1.0 | 0.0 | -1.2 | -1.0 | -0.5 | -1.3 | -0.4 | +0.1 | 0.0 | +0.1 | +16.0 | +10.6 |
| 10 | +7.4 | +2.0 | -1.4 | -0.2 | -1.5 | -1.3 | -0.7 | -1.5 | -0.6 | 0.0 | +0.1 | +0.1 | +11.6 | +7.2 |
| 11 | +1.1 | +0.5 | -1.6 | -0.4 | -1.6 | -1.4 | -0.8 | -1.6 | -0.7 | 0.0 | +0.1 | +0.1 | +7.6 | +4.2 |
| 12 | -3.6 | -1.8 | -1.5 | -0.6 | -1.6 | -1.5 | -0.9 | -1.6 | -0.8 | -0.1 | +0.1 | +0.1 | +3.3 | +1.9 |
+----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
| Range | 32.8 | 15.7 | 7.4 | 7.7 | 7.6 | 8.1 | 7.9 | 8.0 | 5.7 | 2.6 | 3.0 | 4.2 | 45.5 | 34.0 |
+----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+

Tables VIII. to XI. give mean diurnal inequalities derived from all
the months of the year combined, the figures representing the
algebraic excess of the hourly value over the mean for the twenty-four
hours. The + sign denotes in Table VIII. that the north end of the
needle is to the west of its mean position for the day; in Tables IX.
to XI. it denotes that the element--the dip being the north or south
as indicated--is numerically in excess of the twenty-four hour mean.
The letter "a" denotes that all days have been included except, as a
rule, those characterized by specially large disturbances. The letter
"q" denotes that the results are derived from a limited number of days
selected as being specially quiet, i.e. free from disturbance. In all
cases the aperiodic or non-cyclic element--indicated by a difference
between the values found for the first and second midnights of the
day--has been eliminated in the usual way, i.e. by treating it as
accumulating at a uniform rate throughout the twenty-four hours. The
years from which the data were derived are indicated. The
algebraically greatest and least of the hourly values are printed in
heavy type; the range thence derived is given at the foot of the
tables.

TABLE IX.--Diurnal Inequality of Horizontal Force, mean from whole
year (Unit 1[gamma] = .00001 C.G.S.)

+--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+
|Station.|Jan Mayen.|St Petersburg|Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. |Mauritius.|S. Victoria|
| | |and Pavlovsk.| | | St Maur. | | | | | Land. |
+--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+
| Period.|1882-1883.| 1873-1885. |1890-1900.|1890-1900.|1883-1897.|1888-1898.|1894-1901.|1883-1894.|1883-1890.| 1902-1903.|
+--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
| | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. |
+--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
| Hour. | | | | | | | | | | | | |
| 1 | -57 |-22 | + 4 | + 5 | + 4 | + 4 | + 5 | + 3 | -10 | -11 | - 3 | -12 |
| 2 | -64 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | -10 | - 1 | -13 |
| 3 | -74 |-25 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | - 8 | + 1 | -14 |
| 4 | -69 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 4 | - 9 | - 7 | + 2 | -15 |
| 5 | -60 |-22 | + 5 | + 4 | + 3 | + 4 | + 6 | + 4 | - 9 | - 5 | + 3 | -15 |
| 6 | -37 |-19 | + 4 | + 4 | + 1 | + 2 | + 4 | + 4 | - 7 | - 1 | + 4 | -12 |
| 7 | -15 |-15 | + 2 | + 2 | - 3 | - 1 | + 1 | + 2 | - 1 | + 5 | + 7 | - 9 |
| 8 | - 1 |-13 | - 3 | - 4 | - 9 | - 7 | - 5 | - 3 | + 8 | +14 | + 9 | - 7 |
| 9 | + 8 |-12 | -10 | -10 | -16 | -13 | -12 | - 8 | -19 | +24 | + 9 | - 3 |
| 10 | +17 |-12 | -16 | -16 | -20 | -18 | -17 | -10 | +26 | +31 | + 9 | + 3 |
| 11 | +32 |-10 | -19 | -20 | -19 | -18 | -16 | - 7 | +30 | +35 | + 9 | + 7 |
| Noon | +49 |- 4 | -17 | -18 | -13 | -12 | -12 | - 1 | +26 | +31 | + 8 | +12 |
| 1 | +65 |+ 8 | -12 | -13 | - 7 | - 7 | - 7 | + 4 | +19 | +22 | + 7 | +18 |
| 2 | +78 |+22 | - 6 | - 6 | - 1 | - 2 | - 4 | + 5 | +10 | +10 | + 2 | +20 |
| 3 | +89 |+37 | 0 | 0 | + 2 | + 1 | - 1 | + 3 | + 2 | - 1 | - 2 | +19 |
| 4 | +83 |+43 | + 3 | + 3 | + 5 | + 3 | 0 | - 1 | - 3 | - 9 | - 6 | +18 |
| 5 | +68 |+49 | + 5 | + 5 | + 7 | + 5 | + 2 | - 4 | - 7 | -13 | - 7 | +15 |
| 6 | +37 |+43 | + 6 | + 6 | + 9 | + 7 | + 4 | - 6 | - 8 | -14 | - 7 | +11 |
| 7 | +13 |+30 | + 7 | + 7 | +10 | + 8 | + 6 | - 4 | - 9 | -15 | - 7 | + 5 |
| 8 | -11 |+15 | + 8 | + 8 | +10 | + 8 | + 7 | - 1 | -10 | -16 | - 8 | + 0 |
| 9 | -33 |+ 1 | + 9 | + 9 | + 8 | + 7 | + 7 | + 1 | -11 | -16 | - 8 | - 4 |
| 10 | -36 |-10 | + 8 | + 9 | + 7 | + 6 | + 6 | + 2 | -11 | -16 | - 8 | - 7 |
| 11 | -40 |-16 | + 7 | + 8 | + 6 | + 6 | + 6 | + 3 | -10 | -15 | - 7 | - 9 |
| 12 | -51 |-20 | + 6 | + 6 | + 5 | + 5 | + 6 | + 3 | -10 | -13 | - 5 | -11 |
+--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
| Range | 163 | 74 | 28 | 29 | 30 | 26 | 24 | 15 | 41 | 51 | 17 | 35 |
+--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+

TABLE X.--Diurnal Inequality of Vertical Force, mean from whole year
(Unit 1[gamma]).

+--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+
| | |St Peters- |Green- | | Parc St| | | |Maur- |South |
|Station.| Jan Mayen.| burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria|
| | | Pavlovsk. | | | | | | | | Land. |
+--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+
| Period.| 1882-1883.| 1873-1885.|1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 |
| | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. |
+--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
| Hour | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. |
+--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
| 1 | +65 | + 3 | - 7 | - 1 | - 3 | + 1 | 0 | + 2 | + 4 | + 7 | + 2 | +13 |
| 2 | +65 | + 2 | - 7 | - 1 | - 4 | + 1 | 0 | + 2 | + 4 | + 5 | + 2 | +12 |
| 3 | +56 | - 1 | - 7 | - 1 | - 4 | 0 | - 1 | + 1 | + 3 | + 4 | + 2 | +10 |
| 4 | +37 | - 5 | - 6 | 0 | - 3 | 0 | 0 | + 1 | + 3 | + 3 | + 2 | + 8 |
| 5 | +16 | - 7 | - 5 | 0 | - 2 | + 1 | 0 | + 2 | + 5 | + 2 | + 2 | + 3 |
| 6 | - 7 | - 8 | - 4 | 0 | - 1 | + 1 | + 1 | + 3 | + 7 | + 1 | + 2 | 0 |
| 7 | -17 | - 6 | - 3 | 0 | 0 | 0 | + 1 | + 3 | + 6 | 0 | + 3 | 0 |
| 8 | -14 | - 4 | - 2 | 0 | 0 | - 1 | 0 | + 3 | 0 | - 3 | + 4 | - 2 |
| 9 | - 9 | 0 | - 3 | - 1 | - 3 | - 4 | - 4 | - 1 | - 8 | -11 | + 5 | - 6 |
| 10 | - 6 | + 5 | - 2 | - 2 | - 6 | - 8 | - 8 | - 7 | -14 | -20 | + 3 | -13 |
| 11 | - 6 | +10 | - 3 | - 4 | - 9 | -11 | -12 | -11 | -15 | -26 | 0 | -17 |
| Noon | -10 | +16 | - 3 | - 5 | -10 | -11 | -12 | -11 | -10 | -27 | - 4 | -20 |
| 1 | -13 | +21 | - 1 | - 4 | - 6 | - 8 | - 9 | - 9 | - 3 | -21 | - 7 | -20 |
| 2 | -24 | +23 | + 2 | - 1 | 0 | - 3 | - 3 | - 5 | + 1 | -13 | - 9 | -16 |
| 3 | -31 | +20 | + 8 | + 2 | + 5 | + 2 | + 2 | - 1 | + 4 | - 4 | - 8 | -12 |
| 4 | -40 | +13 | + 9 | + 3 | + 8 | + 5 | + 6 | + 1 | + 3 | + 4 | - 5 | - 6 |
| 5 | -48 | + 2 | +10 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +10 | - 3 | - 1 |
| 6 | -53 | - 9 | +10 | + 3 | +10 | + 7 | + 8 | + 4 | 0 | +13 | 0 | + 3 |
| 7 | -47 | -18 | + 9 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +14 | 0 | + 6 |
| 8 | -36 | -20 | + 8 | + 3 | + 7 | + 5 | + 6 | + 3 | + 1 | +14 | + 1 | + 9 |
| 9 | - 7 | -19 | + 6 | + 2 | + 5 | + 5 | + 5 | + 3 | + 2 | +14 | + 2 | +11 |
| 10 | +18 | -13 | + 3 | + 2 | + 3 | + 4 | + 3 | + 3 | + 3 | +13 | + 2 | +12 |
| 11 | +42 | - 5 | - 2 | 0 | 0 | + 3 | + 2 | + 3 | + 3 | +11 | + 2 | +12 |
| 12 | +54 | 0 | - 5 | - 1 | - 2 | + 2 | + 1 | + 2 | + 3 | + 9 | + 2 | +13 |
+--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
| Range | 118 | 43 | 17 | 8 | 20 | 18 | 20 | 15 | 22 | 41 | 14 | 33 |
+--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+

When comparing results from different stations, it must be remembered
that the disturbing forces required to cause a change of 1´ in
declination and in dip vary directly, the former as the horizontal
force, the latter as the total force. Near a magnetic pole the
horizontal force is relatively very small, and this accounts, at least
partly, for the difference between the declination phenomena at Jan
Mayen and South Victoria Land on the one hand and at Kolaba, Batavia
and Mauritius on the other. There is, however, another cause, already
alluded to, viz. the variability in the type of the diurnal inequality
in tropical stations. With a view to illustrating this point Table
XII. gives diurnal inequalities of declination for June and December
for a number of stations lying between 45° N. and 45° S. latitude.
Some of the results are represented graphically in fig. 6, plus
ordinates representing westerly deflection. At the northmost station,
Toronto, the difference between the two months is mainly a matter of
amplitude, the range being much larger at midsummer than at midwinter.
The conspicuous phenomenon at both seasons is the rapid swing to the
west from 8 or 9 a.m. to 1 or 2 p.m. At the extreme southern station,
Hobart--at nearly equal latitude--the rapid diurnal movement is to the
east, and so in the opposite direction to that in the northern
hemisphere, but it again takes place at nearly the same hours in June
(midwinter) as in December. If, however, we take a tropical station
such as Trivandrum or Kolaba, the phenomena in June and December are
widely different in type. At Trivandrum--situated near the magnetic
equator in India--we have in June the conspicuous forenoon swing to
the west seen at Toronto, occurring it is true slightly earlier in the
day; but in December at the corresponding hours the needle is actually
swinging to the east, just as it is doing at Hobart. In June the
diurnal inequality of declination at tropical stations--whether to the
north of the equator like Trivandrum, or to the south of it like
Batavia--is on the whole of the general type characteristic of
temperate regions in the northern hemisphere; whereas in December the
inequality at these stations resembles that of temperate regions in
the southern hemisphere. Comparing the inequalities for June in Table
XII. amongst themselves, and those for December amongst themselves,
one can trace a gradual transformation from the phenomena seen at
Toronto to those seen at Hobart. At a tropical station the change from
the June to the December type is probably in all cases more or less
gradual, but at some stations the transition seems pretty rapid.

TABLE XI.--Diurnal Inequality of Inclination mean from whole year.