See also:

• MAGNETISM
• MAGNETISM, TERRESTRIAL

Hellmann 6 * considers it almost certain that the departure of the needle from the true north was known in Europe before the See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

It was not until midsummer 1634 that Gellibrand felt sure of his facts, and yet the change of declination since 158o exceeded 7° The delay probably arose from the strength of the preconceived idea, apparently universally held, that the declination was absolutely fixed. This idea, it would appear, derived some of its strength from the See also:

• POSITIVE (or PORTABLE) ORGAN

He also found that the See also:

• AMPLITUDE (from Lat. amplus, large)

Measurements of the intensity of the magnetic force were somewhat crude until See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Rucker and Sir T. E. See also:

• THORPE [or TnoRP], JOHN (/l. 1570-1618)
• THORPE, BENJAMIN (1782-1870)

The unifilar magnetometer (q.v.), for tionat instance, gives the absolute values of the declination and Methods and horizontal force, whilst the See also:

• INCLINOMETER (Dip CIRCLE)

A very See also:

• COMMON

A useful and not unusual addition to this is a statement of the absolutely largest and smallest values of each element recorded during each day, with the precise times of their occurrence. On days of large disturbance even hourly readings give but a very imperfect idea of the phenomena, and it is customary at some observatories, e.g. See also:

• GREENWICH

Instead of See also:

• DRAWING

His selected quiet days for St See also:

• PETERSBURG

The declination is sometimes counted from o° to 36o°, o° answering to the case when the so-called north pole (or north seeking pole) is directed towards geographical north, 9o° to the case when it is directed to the east, and so on. It is more usual, however, to reckon declination only from o° to 18o°, characterizing it as easterly or westerly according as the north pole points to the east or to the west of the geographical meridian. The force is also completely defined by H or V, together with D the declination, and I the inclination to the See also:

• HORIZON (Gr. 6pfTwv, dividing)

A very stout suspension must be avoided at all cost, but the fibre must not be so thin as to have a considerable See also:

• RISK

The information being of special use to sailors, the preparation of magnetic charts has been largely the work of See also:

• NAVAL

The former part is clearly on the isogonal where the declination is 0°, the latter on the isogonal where it is 18o°. Isogonals will thus radiate out from the north geographical pole (and similarly of course from the See also:

• SOUTH
• SOUTH, ROBERT (1634–1716)

3.4 fr4ty TLv pe.tron .n.,b. IhttLD T.In wd Yr nc~ Ls. See also:

• LEON
• LEON, LUIS PONCE DE (1527-1591)
• LEON, MOSES BEN SI
• LEON, or LEON DE LAS ALDAMAS

Thus, during our course round the circle the needle will have pointed in all possible directions. In other words, isogonals answering to all possible values of the declination have their origin in the north magnetic pole. The same remark applies of course to the south magnetic pole. Now, suppose ourselves at the north geographical pole of the earth. Neglecting as before diurnal variation and similar temporary changes, and assuming no abnormal local disturbance, the compass needle at and very See also:

• CLOSE
• CLOSE (from Lat. clausum, shut)
• CLOSE, MAXWELL HENRY (1822-1903)

2 is a reduced copy of the admiralty chart of inclination or dip for the epoch 1907. The places where the dip has the same value See also:

• LIE, JONAS LAURITZ EDEMIL (1833—1908)
• LIE, MARIUS SOPHUS (1842–1899)

The curves, called isomagnelics, connect the places where so-called foci is in Canada, the other in the north-east of See also:

• SIBERIA

4) and total force. The isomagnetic of zero vertical force coincides necessarily with that of zero dip, and there is in general considerable resemblance between the forms of lines of equal vertical force and those of equal dip. The highest values of the vertical force occur in areas surrounding the magnetic poles, and are fully 50% larger than the largest values of the horizontalformer having the higher value of the force. There are, however, higher values of the total force than at either of these foci throughout a considerable area to the south of Australia. In the northern hemisphere the lines of equal total force—called isodynamic lines—form two sets more or less distinct, consisting of closed ovals, one set surrounding the See also:

• CANADIAN

um: 1/ 0 Amummmmilmmizoilote.m......mcii.. -3° 110r't . N) 4'7 See also:

• URI

:2u° W. 1o6 W. 86W. a«L.wa fr.. . .4.:9.99 N9...1e..9 w• 1,9.1. C...nu.ium... 0.. wan.;..~ir See also:

• EMERY (Ger. Smirgel)

Table I. gives the mean values of the declination, inclination and horizontal force for See also:

• JANUARY

S ,y /ma y " a! e' ~2 , . a //~ i•g O ~L~/PJ.! ~i~~1 `b / / a •. // ?Asia "j////// ~,Ej'y%y y ~a j/~~~ ////j / ~ ~/%%%/'/' q ~ )4/ • f//~. %//.r///// ^ . ................. /o 4014rivims,zavi,rzArif/A or ~~ i ' „` =~Jl//~//. -~~j ~~'y///~~i-v e/ar0/////'~~ gym- .h` ./ rr .. r' ' JO' - .. .~ ~~ Qi• mG lI Y eo° ` 6_._ homaahon.al p..o.i..See also:

• LOO (formerly called " Lanterloo," Fr. lanturlu, the refrain of a popular 17th-century song)

Table II. is similar to Table I., but includes vertical force results; it is more extensive and contains more recent data. In it the number of years is specified from which the mean secular change is derived; in all cases the last year of the period employed was that to which the absolute values assigned to the element belong. The great See also:

• MAJORITY (Fr. majorite; Med. Lat. majoritas; Lat. major, greater)

This possibility should always be See also:

• BORNE, KARL LUDWIG (1786–1837)

After getting well to the north of Iceland it doubled again to the south, passing to the east of the Baltic. The second agonic line which now lies to the west of St Petersburg appears in 1600 to have continued, after traversing Australia, in a nearly northerly direction through the extreme east of China. The nature of the changes in declination in western Europe will be under-stood from Table III., the data from which, though derived from a variety of places in the south-east of England,10 may be regarded as approximately true of London. The earliest result is that obtained by Borough at Limehouse. Those made in the 16th century are due to Gunter, Gellibrand, Henry See also:

• BOND
• BOND, SIR EDWARD AUGUSTUS (1815-1898)

Absolute Secular change. values. D. I. H. D. I. H. , , Pavlovsk . 0 39.8E 70 36.8N .16553 - 4.1 -0.8 Y + 7 Ekatarinburg 10 6.3E 70 40.5N .17783 - 4.6 +0.5 -13 See also:

• COPENHAGEN (Danish Kjobenhavn)

9 54.2W 66 24.5N .18852 - 4.2 -1.6 +16 See also:

• IRKUTSK

. 15 13.7W 65 o•oN •1967o - 4'0 -2.2 +23 See also:

• MUNICH (Ger. Munchen)

. . 17 15.7W 57 53'oN .23548 See also:

• ATHENS
• ATHENS ['AN vat, Athenae, modem colloquial Greek `Ath va]

0 52.2E 16 13.5N .38064 + 0•I -5.3 +47 See also:

• BATAVIA

§ to. At Paris there seems to have been a maximum of easterly declination (about 9°) about 1580; the needle pointed to true north about 1662, and reached its extreme westerly position between 1812 and 1814. The phenomena at See also:

• ROME
• ROME (Roma)

Thus, in this case the rate of secular change has increased fairly steadily since the turning point was reached. Table V. contains some data for St Helena and the Cape of Good Hope,12 both places having a long magnetic history. The remarkable feature at St Helena is the uniformity in the rate of secular change. The figures for the Cape show a reversal in the direction of the secular change about 1840, but after a few years the arrested movement to the west again became visible. According, however, to J. C. See also:

• BEATTIE, JAMES (1735—1803)

At present the See also:

• MOTION (Lat. motio, from movere, to move)
• MOTION, LAWS OF

Bauer, 1908. The values seem, in most cases, based to some extent on calculation, and very probably the secular change was not in reality quite so regular as the figures suggest. For the Western States the earliest data are comparatively recent, but for some of the eastern states data earlier than any in the table appear in the Report of the Coast and Geodetic Survey for 1902. These data indicate that the easterly movement of the magnet, visible in all the earlier figures for the Eastern States in Table VI., existed in all of them at least as far back as 1700. There is not very much evidence as to the secular change between 1700 and 1650, the earliest date to which the Coast and Geodetic Survey's figures refer. The figures show a maximum of westerly declination about 167o in New See also:

• JERSEY
• JERSEY, EARLS OF

But in a few years a complete change took place. The movement to the east, which had become exceedingly small, if existent, in the Pacific states, began to accelerate; the movement to the west continued in the central, as in the eastern states, but perceptibly slackened. In 1905 the area throughout which the movement to the west still continued had greatly contracted and See also:

• LAY

H. V. See also:

• INTERVAL

. 53 33N 9 59E 1903 II I0.2W 67 23.5N .18126 .43527 Wilhelmshaven. 53 32N 8 9E 1909 II 46.8W .18129 5 -5.2 - 7 Potsd2m. 52 23N 13 4E 1909 9 Io•6W 66 20•0N .18834 .42971 5 -5.8 +0•I - 9 -19 Irkutsk . . 52 16N 104 16E 1905 158.1E 70 25•oN •20011 .56250 5 +o•6 +2.0 -24 +39 de Bilt . . 52 5N 5 IIE 1907 13 19•0W 66 49.9N '18559 .43368 5 -4.7 -o•6 + 2 -16 See also:

• VALENCIA
• VALENCIA, or VALENTIA

. 50 9N 5 5W 1909 17 48.4W 66 30•6N •188o2 •43266 5 -4.7 -1.4 + 9 -30 Prague . . . 50 5N 14 25E 1908 8 20.9W 5 -6.5 See also:

• CRACOW (Pol. Krakov; Ger. Krakau)

43 43N 7 16E 1899 12 4•oW 6o 11.7N .22390 .39087 Toulouse . . 43 37N 128E 1905 13 56.3W 6o 49•1N .22025 '39439 5 -4'5 -I.5 + 2 - 2 Perpignan . . 42 42N 2 53E 1907 13 4.4W 7 -4.7 See also:

• TIFLIS

37 58N 21 23E 1908 452.9W 52II.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 o•oN .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 See also:

• DEHRA

. . 18 54N 72 49E 1905 0 14.0E 21 58.5N '37382 .15084 5 +2.1 +7.2 -II +86 Alibagh . . i8 39N 72 52E 1909 1 0•3E 23 29•oN •36845 •16008 3 +I.7 +6.8 -To +82 Vieques (See also:

• PORTO

At See also:

• PUEBLO

Probably the date was near 1723. This view is supported by the fact that at Paris the inclination fell from 720 15' in 1754 to 71° 48' in 1780. The Date. Declination. Date. Declination. Date. Declination. ° / 0 / 0 / 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 o 0 1802 24 6 1875 19 35'6 1665 I 22W 1805 24 8 188o 18 52.1 1672 2 30 1817 24 36 1885 18 19.2 1692 6 o 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 i6 32'9 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 o'•8 derived from the thirteen years 1773-1786 is too small, and the value 6'•2 derived from the fifteen years 1786-18o1 too large. There is, however, other evidence of unusually Year. Declina- Change since Year.

Declina- Change since tion East. previous year. tion East. previous year. O / Y / p O / N / M '1876 0 55 58 0 37 E 1881 0 57 12 0 3 E 1877 56 39 0 41 E 1882 0 56 5o 0 22 W 1878 57 6 0 27 E 1883 57 2 0 12 E 1879 57 30 0 24 E 1884 55 39 123 W 188o 57 9 0 21 W 1885 55 3 0 36 W 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 178o and 1791, and of 90' between 1791 and 1806. Between 18oI and 1901 inclination in London diminished by 3° 26'•5, or on the average by 2'•I per annum, while between 1857 and 1900 H increased on the average by 22y a 'year. These values differ but little from the secular changes given in Table I. as applying at Kew for the epoch ,See also:

• JAN

During 1908-19o9 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. § 13. It is often convenient to obtain a See also:

• FORMULA
• FORMULA (Lat. diminutive of forma, shape, pattern, &c., especially used of rules of judicial procedure)

Cape of Good Hope. Date. Declination. Date. Declination. 16,o 7 13 E 16o5 0 30 E 1677 0 40 1609 0 12 W 1691 I o W 1675 8 14 1724 7 30 1691 II o 1775 12 18 1775 2I 14 1789 15 30 1792 24 31 1796 15 48 1818 26 31 1806 17 i8 1839 29 9 1839 22 17 1842 29 6 184o 22 53 1846 29 9 1846 23 II 1850 29 19 1890 23 57 1857 29 34 1874 30 4 1890 29 32 1903 28 44 See also:

• BAVARIA (Ger. Bayern)

Epoch 176o 70 8o 90 1800 lo 20 30 40 50 6o 70 8o 90 1900 50 Eastport, Maine -P2 0.0 +P2 +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, See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

-2.4 -1.5 -0.4 +0.4 +P5 +2.4 +2.8 +4'2 +3'9 +2.9 +I'o 1 See also:

• LEXINGTON
• LEXINGTON, BARON

. See also:

• DETROIT

o o o o i 1576 71 50 1801 70 36.0 1857 68 24.9 '17474 1891 67 33.2 .18193 1600 72 O 1821 70 3.4 186o 69 19.8 .17550 1895 67 25.4 .18278 1676 73 30 1830 69 38.0 1865 68 8.7 •17662 190067 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 Formulae are also wanted to show how the value of an element, described in the clockwise direction. This, according to Bauer's 18 or the rate of change of an element, at a particular place has own investigation, is the normal mode of description. Schott varied throughout a long period. For comparatively short periods and Littlehales have found, however, a considerable number it is best to use formulae of the type E_¢~ bt I ct2, where E of cases where it is difficult to say whether the motion is clockwise denotes the value of an element t years subsequent to some or not, while in some stations on both the east and west shores of convenient epoch; ¢, b, care constants to be determined from the Pacific it was clearly See also:

• ANTI, or CAMPA

The ampl tude of the diurnal change usually varies considerably with the Damao Diurnal out that the See also:

• EXTENSION (Lat. ex, out ; tendere, to stretch)

The curve i s being from a limited number of days selected as being specially quiet, Table VIII.-Diurnal Inequality of Declination, mean from whole year (+ to West). is mainly one of amplitude, and the mean diurnal inequality from all the months of the year gives a very See also:

• FAIR

Batavia. Mauritius. South Vic- Tiflis. and Pavlovsk. See also:

• LAND

77° 51' S. Longitude. 8° 28' W. 3o° 29' E. 0° o'. 0° 19'W. 2° 29' E.44° 48'E. 72° 49' E. Io6° 49'E. 57° 33' E. 166° 45' E. Period.

1882-1883. 1873-1885. 1890-1900. 1890-1900. 1883-1897.1888-1898 .1894-1901.1883-1894.1876-189o. 1902-1903. a. q. a. q. a. a. q. a. a. q. a. a. a. q. Hour. r r r r r r r r -6.6 -4.2 -1.3 -0.7 -1'4 -1.5 -0.9 -P4 -0.7 -0.2 +0.1 +0.1 +2.0 +0.9 2 -10.5 -6.4 -P2 -o•8 -P3 -1.4 -0.9 -1.2 -0.6 -o•i -o•i -{-O•I -2•I -I.8 3 -15.2 -7.8 -1.2 -I.0 -P3 -1.5 -1.0 -P2 -0.6 -o I -0.1 +o.1 -5.2 -4.5 4 -16.9 -8.4 -P4 -1.3 -i•4 -1.7 -1.3 -1.2 -0.5 0.0 +0.2 -9.4 -6.8 5 -17.0 -8.1 -1.7 -I.8 -I.7 -2•I -1.8 -I.6 -O.7 -o•I 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 -o•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 -P9 -1•o +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 +I•I -2P5 -17.3 9 -3.7. -o•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 +P5 +1'9 -2P2 -15.8 11 -0.5 +4.6 +1.0 +0.4 +2.1 +2.2 +P7 +2.0 +1•o +0.9 +0.9 +P3 -15.3 -9.2 See also:

• NOON

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•I -0.4 +o•1 +22.0 +15.9 8 +15.8 +2.6 -0.4 +0.2 -o.9 -o.6 -0.3 -0.9 -0.1 +0.2 -O.2 +0.1 +19.9 +14.6 9 +13.2 +2.6 -1•o 0.0 -1.2• -1.0 -0.5 -1'3 -0.4 +o•I o•o +o•I +,6•o +Io•6 10 +7.4 +2.0 -I.4 -O.2 -I.5 -I.3 -0'7 -1.5 -0.6 0.0 +0.1 +O.1 +1I.6 +7.2 II +1•i +0.5 -i.6 -0.4 -i.6 -1.4 -o•8 -I.6 -0.7 0.0 +0.1 +0.1 +7.6 +4.2 12 -3.6 -1.8 -P5 -o•6 -P6 -1.5 -0.9 -I.6 -o•8 -0•I +0.1 +0.1 +3'3 +P9 Range 32.8 15.7 7.4 7.7 . 7'6 8•I 7.9 8.0 5'7 2.6 3'0 4'2 45'5 34'0 St Petersburg Parc S. See also:

• VICTORIA
• VICTORIA (or VITTORIA), TOMMASSO LUDOVICO DA (C. I540-C. 1613)
• VICTORIA [ALEXANDRINA VICTORIA]

(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. I -57 -22 + 4 + 5 + 4 + 4 + 5 + 3 -to -II - 3 -I2 2 -64 -24 + 4 + 4 + 3 + 4 + 5 + 3 — 9 —to — t -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 — I + 4 -12 7 -15 -15 + 2 + 2 — 3 — I + 1 + 2 — I + 5 + 7 — 9 8 -1 -13 -3 -4 -9 -7 -5 3 +8 +14 +9 -7 9 + 8 -12 -I0 -I0 -16 -13 -12 - 8 +19 +24 + 9 — 3 10 +17 -I2 -16 -16 -20 -18 -17 -10 +26 +31 + 9 + 3 I I +32 -10 -19 -20 -19 -18 -16 — 7 +30 +35 + 9 + 7 Noon +49 — 4 -17 -18 -13 -12 -12 — I +26 +31 + 8 +12 t +65 + 8 -12 -13 — 7 — 7 — 7 + 4 +19 +22 + 7 +18 2 +78 +22 -6 -6 — I -2 -4 + 5 +to +to + 2 +20 3 +89 +37 0 0 + 2 + I - I + 3 + 2 — 1 — 2 +19 4 +83 +43 + 3 + 3 + 5 + 3 0 — I — 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 +t5 '+ 8 + 8 +10 + 8 + 7 - I -I0 -16 - 8 + 0 9 -33 +1 + 9 + 9 + 8 + 7 + 7 +1 -11 -16 -8 -4 to -36 —to + 8 + 9 + 7 + 6 + 6 + 2 -tt -16 - 8 - 7 II -40 -16 + 7 + 8 + 6 + 6 + 6 + 3 —to -15 — 7 — 9 12 -51 -20 + 6 + 6 + 5 + 5 + 6 + 3 -10 -13 — 5 —II Range 163 74 28 29 30 26 24 15 41 51 17 35 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 See also:

• UNIFORM

The conspicuous phenomenon at both seasons is the rapid See also:

• SWING, DAVID (1830-1894)

1890—1900. 1891—1900. 1883—1897. 1888—1898. 1894—1901. 1883—1894. 1884—189o. 1902—1903. a. q. a. q. a. q. a. a. q. a. a. a. Hour I +65 +3 — 7 — 1 — 3 + 1 0 +2 +4 +7 +2 +13 2 +65 +2 — 7 — I — 4 + 1 0 +2 +4 +5 +2 +12 3 +56 — 1 -7 — I 4 0 — I +1 +3 +4 +2 +to 4 +37 -5 -6 0 -3 O o +1 +3 +3 +2 +8 5 +16 — 7 — 5 0 — 2 +1 0 +2 +5 +2 +2 +3 6 — 7— 8 — 4 0 — I + 1 + 1 + 3 + 7 + 1 + 2 0 7 -17 -6 -3 o 0 0 + 1 +3 +6 0 +3 0 8 -14 -4 -2 0 0 — I 0 +3 0 -3 +4 -2 9 -9 0 -3 — 1 -3 -4 -4 — t -8 —II +5 -6 to -6 +5 -2 -2 -6 -8 -8 -7 -14 -20 +3 -13 II - 6 +to — 3 — 4 — 9 —II -12 —It -15 -26 0 -17 Noon —to +16 — 3 — 5 -10 -11 -12 -11 —to -27 — 4 -20 t -13 +21 — I -4 -6 -8 —,9 -9 -3 -21 -7 -20 2 -24 +23 +2 — I o -3 3 -5 +1 -13 -9 -16 3 -31 +20 +8 +2 +5 +2 +2 — I +4 -4 — 8 -12 4 -40 +13 +9 +3 +8 +5 +6 +1 +3 +4 — 5 -6 5 + 2 +10 + 3 + 9 + 6 + 7 + 3 O +10 - 3 - I 6 48 -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 +II to +18 -13 +3 +2 +3 +4 +3 +3 +3 +13 +2 +12 II +42 — 5 — 2 0 0 +3 +2 +3 +3 +11 +•2 +12 12 +54 0 — 5 — I — 2 +2 + 1 +2 +3 +9 +2 +13 Range 118 43 17 8 20 18 20 15 22 41 14 33 . St. Petersburg Pare South Vic- Station.

Jan Mayen. and Pavlovsk. Greenwich. Kew. St Maur. Tiflis. Kolaba. Batavia. Mauritius. toria Land. End Dipping. North. North. North.

North. North. North. North. South. South. South. Period. 1882-1883. 1873-1885. 1890-1900. 1891-1900.1883-1897.

1888-1898. 1894-1901. 1883-1894. 1884-1890. 1902-1903. a. q. a. q. a. q. a. a. q. a. a. a. - Hour / / / / / / / / / / / / i +4.6 +1.5 -0.5 -0.3 -0.4 -0.3 -0.3 -0.1 +0.6 +°•9 +0.3 +0.6 2 +5.0 +1.6 -0.5 -0.3 -0.3 -0.2 -O.3. -O.1 +0.6 +0.8 +0.2 +0.7 3 +5.6 +1.6 -o.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 o•0 +0.7 5 +4.2 +1.4 -0.5 -0.3 -0.2 -0.2 •-°•4 -0.2 +0.7 +0.3 -0•I +0.7 6 +2.4 +1.2 -0.4 -0.3 -0.1 -0•I -0.3 -0.I +0.8 +0.1 -0'2 +0.5 7 +0.7 +0.9 -0.2 -0•I +0.2 +0•I 0•o 0.0 +0.5 -0.2 -0.3 +0.4 8 -0.1 +o•8 +0.1 +°•3 +0.6 +o•4 +0.4 +0.3 -0.2 -o•8 -0.4 +0.3 9 -0.7 +0.8 +0.6 +o•6 +1•o +0.8 +0.7 +0.5 -I.2 -I.7 -0.4 +O•I lo -1.2 +0.9 +1.0 +I.0 +1.1 +1.0 +0.9 +0.3 -1.9 -2.7 -0.5 -0.2 II -2.2 +0.8 +1.2 +1.2 +J•0 +0.9 +0.7 0.0 -2.1 -3.3 -o•6 -0.4 Noon -3.4 +0.4 +I•I +1.1 +o•6 +o•6 +0.4 -0.5 -1.6 -3.1 -0.7 -0.7 -4.5 -0.2 +01 +01 +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•I +0•I +0.2 -0.5 -0.2 -1.3 -o•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•I -O•I -0•I +O.2 +0.1 +0.3 +0.7 +0•I -0.9 5 -5'I -3.2 -0.1 -0.3 -0.2 +0.1 +0.4 +0.2 +P3 +O.4 -0.7 6 -3.1 -2.9 -0.2 -0.3 -0.3 -0'3 0.0 +0.5 +0.2 +P5 +°•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 -0.3 -0.5 -0.4 -0.4 -0.3 +0.2 +0.4 +1.6 +o•6 0.0 9 +2.0 -0.3 -0.4 -o.6 -0.4 -0.4 -0'3 +0.1 +0.5 +1.6 +0.6 +0.2 to +2.5 +0.5 -0.5 -0.6 -0.4 -0.3 -0.3 0.0 +0.6 +1.5 +o•6 +0.4 II +3.0 +1.0 -0.5 -0.6 -0.4 -0.3 -0.3 0.O +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 +o•6 +1.2 +0.4 +o•6 Range 11.9 4.8 1.7 1.8 I.5 P4 1.3 1.1 2.9 4'9 1.4 1.7 I or 2 p.m. At the extreme See also:

• SOUTHERN

Comparing the inequalities for June in Table XII. amongst them-selves, and those for December amongst themselves, one can trace a See also:

• GRADUAL (Med. Lat. gradualis, of or belonging to steps or degrees; gradus, step)

Cape. Hobart. Month. June. Dec. June. Dec. June. Dec. June. Dec. June.

Dec. June. Dec. June. Dec. June. Dec. Hour -O.4 -0• I -0.3 0.0 -0.3 -0.1 +0• I +0• I -O• I -O.4 O.0 +0• I -O.4 -O.7 +0.8 +1.1 I 2 -0'2 +0.4 -O'3 +0.1 -0.4 +o•1 -0.1 +O•I -0.2 -0.1 -O.2 +0.2 -O.5 -O'4 +O'3 +I•I 3 -0.2 -O•I -0.3 +0•I -0.4 +0.3 -0.2 +O.2 -O.2 +0•I -0.2 +0.4 -0.7 -0'1 -O.1 +1.0 4 -1.2 -0.4 -0.3 +0.3 -0.5 +0.5 -0.3 +°'3 -0 3 +0.3 -0.2 +0.7 -o•6 +0.3 -0.1 +I•I 5 -2.9 -o•6 -O'7 +0.4 -0.7 +01 -0.3 +0.5 -0.5 +0.6 -0.3 +PO -0.7 +1.0 0.0 +11 6 -5.2 -o•6 -1.6 +0.5 -1.6 +I.I -O.5 +1.2 -I.O +0.9 -0.4 +I.7 -PO +2.2 O.0 +21 7 -6.2 -0.9 -2.2 +0.7 -1.7 +1.4 -1.1 +2•o -2.2 +I.9 -I I +2.6 -1.6 +3'3 -0'1 +4'4 8 -6•o -1.2 -2.1 +0.2 -I•I +0.9 -0.4 +2.3 -1.5 +2.2 -1•o +2.4 -o•8 +3.6 +o•1 +5.6 9 -4.4- -1.8 -1.1 -0.1 -0.2 +°-5 +0.5 +2.0 -0.3 +1.3 +0.2 +2.0 +01 +3'1 +o•6 +5.6 10 -I.5 -1•I 0.0 -0.2 +o•6 +0.3 +0.9 +1.3 +0.3 +0.2 +1.2 +I•I +1.6 +1.6 +1.2 +3'6 II +2•I +0.6 +I.2 0.0 +I.2 +0•I +1.0 +0.4 +0.5 -I.O +1.4 O.O +P5 +0•I +I.0 +01 Noon +4.8 +2.2 +2.1 0.0 +1.4 -0.4 +01 -o•6 +0.3 -1.4 +I•o -1.4 +0.8 -I.0 -0•I -2.6 +6•I +3.2 +2.0 -0.2 +I•I -0.8 +0.3 -1.4 +0.3 -1.2 +0.1 -2.2 +0.3 -1.8 -I.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 +O•I -0.8 -0.8 -I.6 +0.7 +o•6 -1.3 -1.6 +0.2 -o•8 -1.6 -4.8 5 +1.8 +0.5 0'O -O.2 0.O -O.4 -O.5 -1'2 +1.1 +0.4 -0.3 -1.O +0.5 -O.8 -0.7 -3'3 6 +0 7 -0.1 +0.1 -O.2 +0.2 -0.4 -0.1 -0.7 +I.O +0.1 +0.5 -0.5 +0.5 -o•6 -0.4 -P9 7 0.0 -o•8 +0.3 -0.2 +0.5 -0.4 +0.1 - 0.6 +o•6 -0.4 +01 -0'3 +0.4 -o'8 0.0 - I•o 8 0.0 - I.2 +0.4 -0.1 +0.5 -0.3 +0.2 -0.5 +0.5 -O.7 +0.7 -O.3 +0.3 -0.9 +°•5 -- O'3 9 -0.5 -1.4 +0.3 -0.1 +0.4 -0'2 +°•4 -O'3 +0.4 -0.9 +O.6 -0.2 +O.2 -0.9 +1.1 0.0 10 -0.5 -1.7 +0•I 0.0 +0.2 -0.1 +0'4 -O•I +0.2 -PO +0.4 -0•I +0•I -I.0 +I.3 +0.6 II -O.7 -1.1 -0'I -0•I O.0 -0•I +0.3 0.O +O•I -O.8 +0'3 0.O 0.O -I.0 +1.3 +0.9 12 -0.6 -0.7 -0.2 -0•I -O.2 -0.1 +0.2 +0•I -0.1 -O.6 +O•I +O.1 -0'2 -PO +I•I +P2 Range 12.3 5.0 4.3 1.0 ~ 3.1 2.3 I 2.1 4.2 3.3 3.6 2.9 5.1 3.2 5.5 3.7 11.8 day, and has a maximum about II 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. +6 +4 +2 0 +2 0 +2 0 +2' 0 0 +4 +2 0 Midt. 6 Noon 6 .MIdt. Midt...6 Noon 6 Midt. 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 See also:

• VARIATIONS
• VARIATIONS, CALCULUS
• VARIATIONS, CALCULUS OF

§ 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 See also:

• DOUBLE
• DOUBLE (from the Mid. Eng. duble, the form which gives the present pronunciation, through the Old Er. duble, from Lat. duplus, twice as much)

§ 17. Variations of inclination are connected with those of horizontal and vertical force by the relation SI=a sin 2IIV-i SV-H-i all. 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 See also:

• LATE

The type of diurnal inequality seen JUNE DECEMBER 0 Place. Period. an. Feb. See also:

• MARCH
• MARCH (1) (from Fr. marcher, to walk; the earliest sense in French appears to be " to trample," and the origin has usually been found in the Lat. marcus, hammer; Low Lat. marcare, to hammer; hence to beat the road with the regular tread of a soldier: cf.
• MARCH, AUZIAS (c. "1395-1458)
• MARCH, EARLS OF
• MARCH, FRANCIS ANDREW (1825– )

Dec. Pavlovsk 1890-1900 a 4.93 6.15 8.58 10.93 12.18 12.27 II.82 11.38 8.70 6.87 5.54 4.63 q 2.96 4.20 8.73 1I.28 12.89 13.28 12.31 11.70 9.37 6.91 3.95 2.66 Ekatarinburg 1890 o-1900 a 3.33 4.32 7.63 I I.19 I I'82 11.58 I I.09 10.45 8.13 5.6o 3.73 3.14 Greenwich 1865-1896 a 5.87 7.07 9.40 1 1.42 10.55 10'90 Io'82 10.93 9'66 8.15 6.41 5.15 Kew 1890-1900a 4.92 6•o6 9.08 19.95 Io•66 10'92 10.59 I1.01 9'49 7.73 5.37 4'46 q 4.07 4.76 8.82 10.57 10.92 Io•62 ,o•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 _ x890-1900 a 1.79 I.09 2.13 3.02 3.84 3'94 4'21 4.89 4'53 I.83 0.85 I.33 Trivandrum 1853-1864 a 2.06 1.48 0.79 I.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 . 1841-1846a 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 11.8o 9.50 7'26 4.56 3.70 4.61 5'89 8.24 II.0I 12.05 II•8I at the Cape of Good Hope does not differ much from that seen at N =H See also:

• COS
• COS, or STANKO (Ital. Stanchio, Turk. Islan-keui, by corruption from Etc rav KW)

But, corresponding to the evening maximum seen at the Cape, there is now only a secondary maximum, the principal maximum occurring about I p.m. At midsummer the principal maximum is found—as at Kew or Greenwich—about to 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 See also:

• AUGUST (originally Sextilis)

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 See also:

• FEBRUARY

Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. Dec. H (unit 17) 12 20 32 46 47 49 49 44 39 32 17 II Pavlovsk .

. . 1890-1900 a q 12 17 31 42 45 45 42 40 37 31 17 to Ekatarinburg . . „ a iI 15 29 37 40 40 39 36 33 27 13 9 Kew „ q 15 17 26 36 38 39 38 38 35 27 20 II Toronto . 1843-1848 a 23 21 24 28 29 29 26 28 41 25 21 20 Batavia . . 1883-1898 a 49 47 54 6o 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 to 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 Iy) 15 27 29 24 26 20 23 19 23 20 18 14 Pavlovsk . . . 189o-1900 a , q 4 5 9 13 13 12 13 10 9 7 5 4 Ekatarinburg . .. a 10 15 17 21 22 19 20 i6 14 13 II 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 II 17 II 17 II 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 2.88 215 2.64 2.52 2.18 1'20 0'89 Ekatarinburg . . „ a 0.79 0'94 I'70 2'08 2'25 2'19 2'18 2'08 2'00 I.70 o'88 o'69 Kew .

. . q 0.98 1'ot r38 1'86 2.05 2'02 2'05 2'15 F98 1.57 1'27 9'63 Toronto . 1843-1848 a I'15 0'94 1'19 1.43 1'31 1'37 1'13 1'26 r87 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 1'6o 1'41 r54 1'70 1'86 2.03 1'55 2'04 Hobart . 1842-1848 a 1'95 2'16. 1'72 I'62 1'23 1'16 r28 1'42 1'39 1.75 2'04 2 10 variations SN= cosDSH—H sinDSD, SW sinDSH+H cosDSD. If SH and SD denote the departures of H and D at any hour of the day from their mean values, then ON and SW 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 SD 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 HSD=•0000538(number of minutes in SD). In other words, employing IT as unit of force, one replaces HSD by 5'38SD, where SD 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 IT. 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 See also:

• CROSS

Any diurnal inequality can be analysed into a series of See also:

• FOURIER, F
• FOURIER, FRANCOIS CHARLES MARIE (1772-1837)
• FOURIER, JEAN BAPTISTE JOSEPH (1768-1830)

The former method inevitably supplies a larger value for c than the latter, supposing a 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 it-year period. There are, however, few stations which can See also:

• SUPPLY (through Fr. from Lat. supplere, to fill up)

The mean results for Engelenburg's zones must naturally have some of the See also:

• SOURCES

— 2 — 2 — 3 — 4 -6 -9 -13 -17 -19 -13 -3 +II (p.m. +20 +22 +17 +II + 6 + 4 + 2 + I 0 — I — 2 — 2 Table XVI.—Ranges in Diurnal Inequalities at Falmouth (unit 1y). Jan. Feb. See also:

• MAR, EARLDOM OF
• MAR, JOHN ERSKINE, 1ST OR 6TH EARL OF (d. 1572)
• MAR, JOHN ERSKINE, 2ND OR 7TH EARL
• MAR, JOHN ERSKINE, 6TH OR 11TH EARL OF (1675-1732)

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 I5 figures from the terms possessing the periods 24, I2, 8 and 6 hours the physical significance and general utility of the See also:

• ANALYSIS (Gr. avci and Meta, to break up into parts)

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 1+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 150 Thus the times of the maxima are: 24-hour term, 2 h. 24 M. p.m.; 12-hour term, I h. 41 M. a.m. and p.m. 8-hour term, 4 h. 41 M. a.m., o h. 41 M. p.m., and 8 h. 41 M. Q.M. 6-hour term, o h. 33 M. a.m. and p.m., and 6 h. 33 M. a.m. and p.m.

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. (local mean time). Month. c1. C2. C3. C4• al. as. as. a4. o o 0 0 January . . 1.79 0.86 0.41 0.27 251.2 29'8 254 64 February . 2.41 1.11 0.59 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 . . . 3.59 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 O.20 255.1 22'0 243 56 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 oh. Som. and 2h. 3om. p.m. They thus reinforce one another strongly from I to 2 p.m., accounting for the prominence of the maximum in the early afternoon. § 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 See also:

• EQUINOX (from the Lat. aequus, equal, and nox, night)

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 I-y 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 § 22. If secular change proceeded uniformly throughout the year, the value E„ of any element at the middle of the nth month of the year would be connected with E, the mean value for the Annual whole year, by the formula E, =E+(2n-13)s/24, /:equality. where s is the secular change per annum. For the pre-sent purpose, difference in the lengths of the months may be neglected. If one applies toE„-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 in-equality. Even when a long series of years is included, there is always a possibility of a See also:

• SPURIOUS

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 Pare 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 in-equality 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 II 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 See also:

• ACCUMULATION (from Lat. accumulare, to heap up)

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 See also:

• DISTRIBUTION (Lat. distribuere, to deal out)

1890-1900 2.91 1.79 0.79 0.27 234.0 39'7 239 57 Kew (quiet) . . 00 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 0.8o 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 I.32 158.7 306.9 292 303 „ (quieter). 00 15'34 4.05 1.24 1.18 163-8 312.9 261 CI. C2. C3. C4. a1. a2. a3. a4. 0 0 0 0 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- 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 in-equality 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 See also:

• RESEARCH (O. Fr. recerche, from recercher, re- and cercer, mod. chercher, to search; Late Lat. circare, to go round in a circle, to explore)

Allusion has already been made in § 14 to one point which requires See also:

• FULLER, ANDREW (1954-1815)
• FULLER, GEORGE (1822—1884)
• FULLER, M
• FULLER, MARGARET, MARCHIONESS
• FULLER, MELVILLE WESTON (1833-1910)
• FULLER, THOMAS (16o8-1661)
• FULLER, WILLIAM (1670--c. 1717)

Kew. sphere. 1891 1906 1888-1897. q. o. S. mean. I January -0.25 +0.04 +0.01 +0.08 +0.03 +0.32 +0'23 +0.06 +0'49 +0.32 +0'44 -0.03 February -0.54 -0•1I 0.00 +0.48 +0.25 -0.20 +0.19 +0.29 +0.39 +0.56 +0.29 -0.07 March -0.27 +0.04 +0.17 +0.03 +0.05 - 1.02 -0.12 +0.27 +0.20 +0.38 +0.13 +0'53 April -0.03 +0.10 +0.12 -0.31 -0.14 -0.90 -0.11 +0.30 -0.08 -0.02 -0.13 +0.18 May +0.19 +0.07 -0.11 -0.39 -0.28 +0.29 -0.30 +0.08 -0'43 -0.29 -0.37 -0.15 June +0.46 +0.13 -0.14 -0.47 -0.39 +0.78 -0.13 -0.19 -0.70 -0.77 -0.59 -0.35 July +0.48 +0.14 -0.17 -0.30 -0.13 +0.44 -0.08 -0.44 -0.72 -0.67 -0.27 -0.13 August +0.47 +0.11 +0.01 +0.08 +0.05 +0.52 -0.18 -0.38 -0.47 -0.23 -0.05 -0.19 September +0.31 +0.01 0.00 +0.29 +0.24 -0.02 +0.06 -0.06 -0.06 +0.16 +0.01 +0.20 October -0.07 -0.11 +0.09 +0.06 +o•oI -0.26 +0.03 -0°04 +0.31 +0.27 +0.19 0.00 November -0.30 -0.28 -0.05 +0.17 +0•1I -0.02 +0.08 -0.01 +0.51 +o•30 +0.43 +0.18 December -0.36 -0.14 +0.05 +0.26 +0.23 +0.05 +0'35 +0.06 +0'55 +0.19 +0.24 '-0.29 Range 1.02 0.42 0.34 0.95 0.64 I.8o 0.65 0.74 1.27 1'33 1.03 o•88' 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 183o Arago deduced a range of 2' 9". Quiet days at Kew from 1890 to 1894 gave a range of 1'•2, while at Potsdam Ludeling 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. § 23. The inequalities in Table XX. may be analysed-as has in fact been done by Hann-in a series of Fourier terms, whose periods are the year and its submultiples.

Fourier series can Annual also be formed representing the annual variation in the variation amplitudes of the regular diurnal inequality, and its Fourier C0-component 24-hour, 12-hour, &c. waves, or of the etficients. amplitude of the'absolute daily range (§ 24). To secure the highest theoretical accuracy, it would be necessary in calculating the Fourier coefficients to allow for the fact that the " months from which the observational data are derived are not of uniform length. The mid-times, however, of most months of the year are but slightly displaced from the position they would occupy if the 12 months were exactly equal, and these displacements are usually neglected. The loss of accuracy cannot be but trifling, and the simplification is considerable. The Fourier series may be represented by P1 sin (t+B1)+P2 sin (2t+02)+ ... , where t is time counted from the beginning of the year, one month being taken as the equivalent of 30°, PI, P2 represent the amplitudes, and B1, 02 the phase angles of the first two terms, whose periods are respectively 12 and 6 months. Table XXI. gives the values of these coefficients in the case of the range of the regular diurnal inequality for certain specified elements and periods at Kew 23 and Falmouth." In the case of P1 and P2 the 'unit is 1' for D and I, and ly for H and V. M denotes the mean value of the range for the 12 months. The letters q and o represent quiet and ordinary day results. S max. means the years 1892-1895, with a mean sun spot frequency of 75.0. S See also:

• MIN

P1'M and P2/M both increase decidedly as we pass from years of many to years of few sun spots; i.e. relatively considered the range of the regular diurnal inequality is more variable throughout the year when sun spots are few than when they are many. The tendency to an earlier occurrence of the maximum as we pass from quiet days to ordinary days, or from years of sun spot minimum to years of sun spot maximum, which appears in the table, appearssaltum. Suppose further that having formed twelve diurnal inequalities from the days of the individual months of the year, we deduce a mean diurnal inequality for the whole year by combining these twelve inequalities and taking the mean. The hours of maximum and minimum being different for the twelve constituents, it is obvious that the resulting maximum will normally be less than the arithmetic mean of the twelve maxima, and the resulting minimum (arithmetically) less than the arithmetic mean of the twelve minima. The range-or algebraic excess of the maximum over the minimum-in the mean diurnal inequality for the year is thus normally less than the arithmetic mean of the twelve ranges from diurnal inequalities for the individual months. Further, as we shall see later, there are differences in type not merely between the different months of the year, but even between the same months in different years. Thus the range of the mean diurnal inequality for, say, January based on the combined observations of, say, eleven Januarys may be and generally will be slightly less than the arithmetic mean of the ranges obtained from the Januarys separately. At Kew, for instance, taking the ordinary days of the 11 years 189o-I900, the arithmetic mean of the diurnal inequality ranges of declination from the 132 months treated independently was 8'.52, the mean range from the 12 months of the year (the eleven Januarys being combined into one, P1. P2. 01. 02. P1/M P2/M.

Kew D° 3.36 0.94 279° 280° 0.40 0.11 1890-19o0 D2 3.81 1.22 275° 273° 0.47 0.15 o•67 0.16 264° 269° 0.42 0.10 H2 13.6 3.0 269° 261° 0.48 0.11 V2 11.7 2.2 282° 242° 0.63 0.12 S max. Kew 4.50 1.26 277° 282° 0.47 0.13 DQ Falmouth 4.10 1.40 277° 286° 0.43 0.15 S min. Kew 3.35 1•IO 274° 269° 0.49 0.16 D2 Falmouth 3.19 1.14 275° 277° 0.49 0.17 and so on) was 8'•44, but the mean range from the whole 4,000 See also:

• ODD (in middle English odde, from old Norwegian oddi, an angle of a triangle; the old Norwegian oddamann is used of the third man who gives a casting vote in a dispute)

The two remaining columns give the arithmetic means of the five largest and the five least absolute ranges encountered each month. The mean of the twelve monthly diurnal inequality ranges from ordinary days was only 8'.44, but the absolute range during the 11 years exceeded 20' on 492 days, 15' on 1196 days, and lo' on 2784 days, i.e. on 69 days out of every loo. Jan. Feb. Mar. April. May. June. July. Aug. Sept. Oct.

Nov. Dec. Year. Declination. _ Pavlovsk 13.42 17.20 18.22 17.25 17'76 15.91 16.89 16.57 16.75 15.70 13 87 12'37 15.99 Ekatarinburg 7.33 9.54 11.90 12.89 13.63 13.03 12.78 12.21 11.23 9.44 7.86 6.85 10.72 Kew. All days 11.16 13.69 15.93 15.00 14.90 13.65 14.13 14.22 14.57 14'07 11.71 9.80 13.57 Ordinary days 10.14 II.87 14.19 14.24 13.85 13.26 13.47 13.67 13.71 13.10 10.40 9.00 12.58 Quiet „ 6.12 7.57 10.59 11.84 12.09 II•95 II.6o II.93 Io•86 9.16 6.54 5.08 9.61 Zi-ka-wei 3.88 3'25 6.22 7.04 7.15 7.40 7'77 8•o6 6.73 4.68 2.91 2.52 5.63 Mauritius 6.93 7.79 7.11 5.75 4.87 4.03 4'36 6•oo 6.28 6.71 6.99 6.78 6.13 Horizontal force. 52.4 74.5 79.1 80.1 86.2 79.0 86.7 77.6 76.7 67.3 55.7 45.9 7P8 Pavlovsk Ekatarinburg 33.2 43.I 48.4 51.7 56.2 54.1 56.7 51.7 49.3 44.I 34.1 29.3 46.0 Mauritius 37.9 35.0 36.2 37.6 35.0 34.1 33.8 34.5 36.6 37.4 37.8 35.3 35.9 Vertical force. 27.0 50.4 54.7 43.2 45.3 34.8 42.1 35.5 42.5 37.5 33.5 25.5 39.3 Pavlovsk Ekatarinburg 17.4 26.6 29.2 30.1 29.6 27.6 29.6 26•I 25.2 22•I 19.6 16.4 24'9 Mauritius 17.1 19.5 20'1 17.3 16.5 15.5 17.1 22•o 22.7 19.4 16.7 15.2 18.2 means of the 12 monthly values. The Mauritius data are for different periods, viz. declination 1875, 1880 and 1883 to 189o, horizontal force 1883 to 1890, vertical force 1884 to 189o. The other data are all for the, period 1890 to 1900. A comparison of the absolute ranges in Table XXII. with the inequality ranges for the same stations derivable from Tables VIII. to X. is most instructive. At Mauritius the ratio of the absolute to the inequality range is for D 1.38, for H 1.76, and for V 1.19.

At Pavlovsk the corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and 2.05 for V. The declination data for Kew in Table XXII. illustrate other points. The first set of data are derived from all days of the year. The second omit the highly disturbed days. The third answer to the 5 days a month selected as typically quiet. The yearly mean absolute range from ordinary days at Kew in Table XXI I. is 1.49 times the mean inequality range in Table VIII. ; comparing individual months the ratio of the absolute to the in-equality range varies from 2•o6 in January to I.21 in June. Even confining ourselves to the quiet days at Kew, which are free from any but the most trifling disturbances, we find that the mean absolute range for the year is 1.20 times the arithmetic mean of the inequality ranges for the individual months of the year, and P22 times the range from the mean diurnal inequality for the year. In this case the ratio of the absolute to the inequality range varies from 1.55 in December to only 1.09 in May. § 26. Magnetic phenomena, both regular and irregular, at any station vary from year to year.

The extent of this variation is illustrated in Tables See also:

• XXIV

15' to 20'. 20' to 25'. 25' to 30'. 30' to 35'. 35' to 40'. over 40'. 5 largest. 5 least. January 51 145 69 37 24 7 4 3 I 22 90 5 07 February 26 99 84 51 26 Io 4 2 8 27.21 6.55 March I 72 1-38 61 32 21 8 1 7 29.87 8.93 April 0 43 167 73 27 10 6 3 I 23.69 10.31 May o - 57 157 85 20 12 3 0 7 25.36 9.50 June 0 56 185 67 15 I 3 I 2 19.92 9.89 July 0 59 185 70 14 5 2 2 4 22.49 9.96 August 0 37 202 75 22 I 2 0 2 21.27 10.05 September I 68 153 71 19 5 4 5 4 24.55 9.52 October 3 103 III 67 34 10 It 2 0 23.92 8•oi November . 42 140 81 28 14 9 8 5 3 23.58 5.64 December . . 64 166 56 29 14 7 I I 3 20.43 4.36 I Totals . . . r i 88 1045 1588 714 261 98 56 25 42 ranges at Ekaterinburg are larger in 1892 than in 1893, the excess is trifling. The phenomena apparent in Table XXIV. are fairly representative ; other stations and other periods See also:

• ASSOCIATE (Lat. associates, from ad, to, and sociare to join)

The diurnal inequality range it should be noticed is comparatively little influenced by irregular disturbances. Coming to Table XXV., we have ranges of a different character. The absolute range at Kew on quiet days is almost as little influenced by irregularities as is the range of the diurnal inequality, and in its case the phenomena are very similar to those observed in Table XXIV. As we pass from See also:

• LEFT

I. H. V. D4. IQ. HQ. D0. y y y y- I890„ 6.32 I.33 22 5.83 1.05 18 9 6.90 20 7.32 18916 7.31 1'79 30 6.85 1.38 25 14 8.04 1.52 28 8.48 18923 8.75 2'21 37 7.74 1.72 32 19 9.50 P66 31 9.85 1893, 9.64 2.24 38 8.83 1.8o 31 17 to•o6 I.96 35 10.74 18942 8.58 2.17 38 7.80 1.73 30 17 9.32 P94 34 9.80 18954 8.22 2.08 33 7.29 1.64 28 15 8.59 1'66 30 9.54 18965 7.39 1.77 29 6.50 1.38 25 15 7.77 1.31 25 8.50 18976 6.79 I•59 26 6•oi 1.16 21 12 6.71 '•14 22 7.76 1898, 6.25 1.56 26 5.76 1.19 21 II 6.85 P07 21 7.59 1899, 6.02 1.44 24 5.33 I •I2 20 II 6.69 t•01 21 7.30 1900.0 6.20 I.28 22 5.88 0.93 17 8 6.52 I.06 2I 6.83 prominent compared to those for 1893. The yearly range may depend on but a single magnetic See also:

• STORM (in O. Eng..storm, and so in Du. and Low Ger.; in O. H. Ger. and mod. Ger. Sturm; the root is probably that seen in " stir," to rouse, move, disturb, cf. Ger. storen)
• STORM, THEODOR WOLDSEN (1817-1888)

It is visible, for instance, in the amplitudes of the Batavia disturbance results. Thus though the variation from year to year in the amplitude of the absolute ranges is relatively not less but greater than that of the inequality ranges, and though the general tendency is for all ranges to be larger in years of many than in years of few sun-spots, still the parallelism between the changes in sun-spot frequency and in magnetic range is not so close for the absolute ranges and for disturbances as for the inequality ranges. § 27. The relationship between magnetic ranges and sun-spot frequency has been investigated in several ways. W. See also:

• ELLIS (originally SHARPE), ALEXANDER JOHN (1814-189o)
• ELLIS, GEORGE (1753-1815)
• ELLIS, ROBINSON (1834- )
• ELLIS, SIR HENRY (1777-1869)
• ELLIS, WILLIAM (1794 – 1872)

A decline in the number of the larger magnetic storms near sun-spot minimum is recognizable, but the application of the method is less successful than in the case of the inequality range. Another method, initiated by Professor Wolf of See also:

• ZURICH
• ZURICH (Fr. Zurich; Ital. Zurigo)

A change, however, of I' in declination has a significance which alters with the intensity of the horizontal force. During the period 1850-1900 horizontal force in England increased about 5 %, so that the force requisite to produce a declination change of 19' in 1900 would in 1850 have produced a deflection of 20'. It must also be re-membered that secular changes of declination must alter the angle between the needle and any disturbing force acting in a fixed direction. Thus secular alteration in a and b is rather to be anticipated, especially in the case of the declination. Wolf's formula has been applied by Rajna'x to the yearly mean diurnal declination ranges at See also:

• MILAN
• MILAN (Ital. Milano, Ger. Mailand, anc. Mediolanum, q.v.)

There are two sets of data, the first set relating to the range from the mean diurnal inequality for the year, the second to the arithmetic mean of the ranges in the mean diurnal inequalities for the twelve months. It is specified whether the results were derived from all or from quiet days. Milan. Greenwich. Epoch. Declination Epoch. Declination Horizontal Force (unit 1'). (unit 1'). (unit PO. a. b. a. b. a. b. 1836-94 5.31 '047 1841-96 7'29 •0377 26.4 .190 1871-94 5.39 •047 1865-96 7.07 .0396 23.6 •215 1837-50 6'43 •041 1889-96(a) 6.71 .0418 23.7 •218 1854-67 4.62 •047 1889-96(q) 6.36 .0415 25.0 .213 As explained above, a would represent the range in a year of no sun-spots, while too b would represent the excess over this shown by the range in a year when Wolfer's sun-spot frequency is too.

Thus Kew Declina- Pavlovsk. tion. Daily. Daily. Monthly. Yearly. q. o. a. D. H. V. D. H.

V. D. H. V. Y 7. y y / 'Y y 1890„ 8.3 I0•5 10.7 12.1 49 21 28.2 118 8o 42.1 169 179 118916 10.0 12-8 13.7 16.0 70 39 46.3 218 233 92.3 550 614 1892, 12.3 15.4 17.7 21.0 111 73 93'6 698 575 194.0 2416 1385 1893, II.8 15.2 15.6 17.8 79 41 48.3 241 210 87.1 514 457 18942 11'3 14.7 16'5 20.4 97 62 84.1 493 493 145'6 1227 878 18954 ,o•6 '4.8 15.6 18.1 8o 46 47'4 220 223 73'9 395 534 1896, 9'5 12.9 14'5 17.5 74 43 52.4 232 236 88.7 574 6o8 18978 8.2 II.5 12.1 14.6 61 30 43.8 201 170 IOI•I 449 480 1898; 8.2 11.2 12'3 14.7 67 35 46.6 276 242 I18.9 I136 888 18999 7'9 10'5 11.3 13.1 58 27 38.3 178 150 63.8 382 527 190010 7.4 8'9 9'2 10.5 44 r6 32.8 134 89 94.2 457 365 `Means 9.6 12.6 13.6 '6.0 72 39 51.1 274 246 100.2 752 629 Declination Inclination Horizontal Force Vertical Force (unit I'). (unit 1'). (unit Iy). (unit I7). Diurnal Inequality for the Year. a. b. too b/a. a. b. loo b/a. a. b. loo b/a. a. b. loo b/a. Pavlovsk, 189o-1900 all 5'74 •0400 .70 1.24 •0126 I•0I 20.7 •211 I.02 8.1 •265 3.26 Pavlovsk, 189o-1900 quiet 6.17 '0424 .69 .. ..

.. 20.6 •195 . 0.95 5'9 •027 0.46 Ekatarinburg,1890-1900 all 5.29 '0342 •65 0'93 '0105 1.13 16.8 •182 1.09 8.6 •117 1.37 Irkutsk „ „ all 4.82 •0358 .74 0.97 •0087 0.90 18.2 .190 I.04 6.5 .071 I.09 Kew „ quiet 6•1 o •0433 .71 0'87 •0125 1.45 18'1 '194 I.07 14.3 •081 o•56 Falmouth, 1891-1902 quiet 5.90 •0451 .76 .. .. .. 20'I 233 I.16 Kolaba, 1894-1901 quiet 2.37 •0066 •28 .. 3P6 •281 0.89 19.4 •072 0'37 Batavia, 1887-1898 all 2.47 •0179 •72 3.6o •0218 o•61 38.7 •274 0.71 30.1 •156 0.52 1875-1880 Mauritius 1883-1890 . all 4.06 •0164 .40 .. .. .. 15.0 •096 0.64 I1.9 •069 0'58 Mean from individual months :- Pavlovsk , 1890-1900 all 6.81 •0446 .66 1.44 .0151 1.05 22.8 •243 I.07 9.7 '287 2'97 . quiet 6.52 •0442 •68 .. .. ..

22.2 •208 0.94 7.0 .044 0.63 Ekatarinburg,189o-1900 all 6.18 •0355 .58 P12 '0120 1.06 19.2 .195 I.OI 9.2 •156 P70 Greenwich, 1865-1896 . all 7.07 .0396 .56 . . .. .. 23.6 •210.91 Kew, 189o-1900 all 6.65 •0428 '64 .. .. .. .. .. .. .. . . „ quiet 6.49 •0410 •63 1.17 •0130 1.1I 21.5 •191 0.89 16•o '072 0.45 Falmouth, 1891-1902 quiet 6.16 .0450 .73 • 20.9 236 1.13 - J _ Wclinationesterly Inclination.

b/a seems the most natural measure of sun-spot influence. Accepting it, we see that sun-spot influence appears larger at most places for inclination and horizontal force than for declination. In the case of vertical force there is at Pavlovsk, and probably in a less measure at other northern stations, a large difference between all and quiet days, which is not shown in the other elements. The difference between the values of b/a at different stations is also exceptionally large for vertical force. Whether this last result is wholly free from observational uncertainties is, however, open to some doubt, as the agreement between Wolf's formula and observation is in general somewhat inferior for vertical force. In the case of the declination, the mean numerical difference between the observed values and those derived from Wolf's formula, employing the values of a and b given in Table XXVI I., represented on the aver-See also:

• AGE (Fr. age, through late Lat. aetaticum, from aetas)

In these cases the values found for b/a are usually larger than those found for diurnal inequality ranges, but the accordance between observed values and those calculated from Wolf's formula is less good. If instead of the range of the diurnal inequality we take the sum of the 24-hourly differences from the mean for the day-or, what comes to the same thing, the average departure throughout the 24 hours from the mean value for the day-we find that the resulting Wolf's formula gives at least as good an agreement with observation as in the case of the inequality range itself. The formulae obtained in the case of the 24 differences, at places as wide apart as Kew and Batavia, agreed in giving a decidedly larger value for b/a than that obtained from the ranges. This indicates that the inequality curve is relatively less peaked in years of many than in years of few sun-spots. § 28. The applications of Ellis's and Wolf's methods relate directly only to the amplitude of the diurnal changes. There is, however, a change not merely in amplitude but in type. This is clearly seen when we compare the values found in years of many and of few sun-spots for the Fourier coefficients in the diurnal inequality. Such a comparison is carried out in Table See also:

• XXVIII

(sun-spot minimum) applies similarly to the years 1890, 1899 and 1900, having a mean sun-spot frequency of only 9.6. The data relate to the mean diurnal inequality for the whole year or for the season stated. It will be seen that the difference between the c, or amplitude, coefficients in the S max. and S min. years is greater for the 24-hour term than for the 12-hour term, greater for the 12-hour than for the 8-hour term, and hardly apparent in the 6-hour term. Also, relatively considered, the difference between the amplitudes in S max. and S min. years is greatest in winter and least in summer. Except in the case of the 6-hour term, where the differences are uncertain, the phase angle is larger, i.e. maxima and minima occur earlier in the day, in years of S min. than in years of S max. Taking the results for the whole year in Table XXVIII., this advance of phase in the S min. years represents in time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour term, and I4.7 minutes for the 8-hour term. The difference in the phase angles, as in the amplitudes, is greatest in winter. Similar phenomena are shown by the horizontal force, and at Falmouth 24 as well as Kew. Sun-spots. Year. Winter. Equinox.

Summer. S max. S min. S max. S min. S max. S min. S max. S min. I , ci 3.47 2.21 2.41 1.43 3.76 2.41 4.38 2.98 C2 2.04 I.51 I.15 0'78 2.33 1.71 2.73 2.06 c2 0.89 0.72 0.55 0.42 1.16 0.97 0.97 0.77 C4 o•28 0.27 0.30 0.27 0.42 0.42 0•II 0•II 0 0 0 o o 0 0 0 al 228.5 232.4 243.0 256.0 23P3 233.7 218.2 220.3 a2 41'7 46'6 23.5 36.9 40.6 43.9 5o.6 52'5 as 232.6 243.6 234.0 257.6 228.4 236.2 236.8 245'4 a4 58.0 57'3 52.3 6o•8 62•o 58.2 57'4 45'2 § 29. There have already been references to quiet days, for instance in the tables of diurnal inequalities. It seems to have been originally supposed that quiet days differed from other days only Qutet Day in the absence of irregular disturbances, and that mean Phenomena annual values, or secular change data, or diurnal inequal- ities, derived from them might be regarded as truly normal or representative of the station.

It was found, however, by P. A. See also:

• MULLER, FERDINAND VON, BARON (1825–1896)
• MULLER, FRIEDRICH (1749-1825)
• MULLER, GEORGE (1805-1898)
• MULLER, JOHANNES PETER (18o1-1858)
• MULLER, JOHANNES VON (1752-1809)
• MULLER, JULIUS (18oi-1878)
• MULLER, KARL OTFRIED (1797-1840)
• MULLER, LUCIAN (1836-1898)
• MULLER, WILHELM (1794-1827)
• MULLER, WILLIAM JAMES (1812-1845)

Ludeling found this See also:

• PECULIAR

, Mean annual change -5.79 -2.38 +25.97 -22.67 Mean daily change, all days —o•oi6 -0.007 +0.077 -0.067 Meandailychange,quietdays +0.044 -0.245 +3.347 —o.847 Thus the changes during the representative quiet day differed from those of the average day. Before accepting such a phenomenon as natural, instrumental peculiarities must be carefully considered. The secular change is really based on the absolute instruments, the diurnal changes on the magnetographs, and the first idea likely to occur to a See also:

• CRITICAL (in alphabetical order of authors)

M. See also:

• CHRISTIE, RICHARD COPLEY (183o–Igor)

, D + 0.03 + 0.05 + 0.07 H + 4'37 + 3.07 + 3.97 The results are in the same direction as at Kew, + meaning in the case of D movement to the west. At Falmouth32, as at Kew, the non-cyclic change showed a tendency to be small in years of few sun-spots. § 30. In calculating diurnal inequalities from quiet days the non-cyclic effect must be eliminated, otherwise the result would depend on the hour at which the " day " is supposed to commence. If the value recorded at the second midnight of the average day exceeds that at the first midnight by N, the elimination is effected by applying to each hourly value the correction N(12-n)/24, where n is the hour counted from the first midnight (o hours). This assumes the change to progress uniformly throughout the 24 hours. Unless this is practically the case—a matter difficult either to prove or disprove—the correction may not secure exactly what is aimed at. This method has been employed in the previous tables. The fact that differences do exist between diurnal inequalities derived from quiet days and all ordinary days was stated explicitly in § 4, and is obvious in Tables VIII. to XI. An extreme case is represented bybetween all and quiet days at all the north polar stations occupied in 1882—1883 except Kingua See also:

• FJORD, or FIORD

The data for Greenwich are due to W. Ellis30, those for Parc St Maur to T. Moureaux 33. The quantity tabulated is the algebraic excess of the all or ordinary day mean hourly value over the corresponding quiet day value in the mean diurnal inequality for the year. At Greenwich and Kew days of extreme disturbance have been excluded from the ordinary days, but apparently not at Parc St Maur. The number of highly disturbed days at the three stations is, however, small, and their influence is not great. The differences disclosed by Table XXIX. are obviously of a systematic character, which would not tend to disappear however long a period was utilized. In short, while the diurnal inequality from quiet days may be that most truly representative of undisturbed conditions, it does not represent the average state of conditions at the station. To go into full details respecting the differences between all and quiet days would occupy undue space, so the following brief See also:

• SUMMARY

The tendency to a secondary minimum in the range at midsummer is considerably more decided on ordinary than on quiet days. When the variation throughout the year in the diurnal inequality range is expressed in Fourier series, whose periods are the year and its submultiples, the 6-month term is notably larger for ordinary than for quiet days. Also the date of the maximum in the 12-month term is about three days earlier for ordinary than for quiet days. The exact size of the differences between ordinary and quiet day phenomena must depend to some extent on the criteria employed in selecting quiet days and in excluding disturbed days. This raises difficulties when it comes to comparing results at different stations. For stations near together the difficulty is trifling. The astronomer royal's quiet days have been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew, as well as at Greenwich. But when stations are wide apart there are two obvious difficulties: first, the difference of local time; secondly, the fact that a day may be typically quiet at one station but appreciably disturbed at the other. If the typical quiet day were simply the See also:

• ANTITHESIS (the Greek for " setting opposite ")

There are, however, difficulties in accepting this view. Thus, whilst the non-cyclic effect in horizontal force and inclination at Kew and Falmouth appeared on the whole enhanced in years of sun-spot maximum, the difference between years such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other, was by no means proportional to the excess of disturbance in the former years. Again, when the average non-cyclic change of declination was calculated at Kew for 207 days, selected as those of most marked irregular disturbance between 1890 and 1900, the sign actually proved to be the same as fot the average quiet day of the period. Non-cyclic Change. § 31. A satisfactory See also:

• DEFINITION (Lat. definitio, from de-finire, to set limits to, describe)

The first serious See also:

• ATTEMPT (Lat. adtemptare, attentare, to try)

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 See also:

• PROCESS

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, 207 in H, and 12y in V ; the corresponding limits for Batavia were I'.3, 117 and uy. 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 XXXII. shows in some cases a most conspicuous diurnal variation in Sabine's disturbances. The data are percentages of 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 6o 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 I o6 129 67 73 1 10 102 May . Ioi 118 to' 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 ,$0 49 August . 88 113 137 133 154 131 69 69 '86 78 September 134 137 163 139 III 108 135 144 135 114 October . 119 115 101 III 140 128 95 88 124 123 November 99 94 73 85 43 43 106 91 79 III December 75 58 51 72 72 55 124 137 123 130 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 See also:

• LAWS

The last line gives the average size of a disturbance of each type, the unit being 1' in D and tyin H and V. 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 See also:

• FALKLAND
• FALKLAND, LUCIUS CARY

V. H. V. H. V. H. V. January 8, 51 58 56 96 151 89 154 February 96 133 94 74 I05 123 I I0 12$ March . 126 118 94 Io8 116 105 117 103 April . . . 94 111 150 149 104 76 105 73 May. . .

Io8 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 Io8 91 91 98 91 September 119 122 171 16o 113 III 114 115 October . . See also:

• LOT
• LOT (Lat. Oltis)

1890-1894. 1883-1897. 189o- 1900. 1890-1894. 1893-1897. , , I -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•6o +0.51 +0'55 5 -0.28 -0.10 -0.01 +0.46 +0.34 +0.38 6 -0.08 +0.12 +o•18 +0.2I +0.04 +0.07 7 +0.13 +0.30 +0.34 -0.06 -0.24 -0.25 8 +o'29 +0.48 +0.47 -0.27 -0.50 -0.54 9 +0.40 +0.56 +0.53 -0'47 -o.68 -0.74 10 +0.44 +0.58 +0.51 -o•61 -0.78 -0.79 II °+0.48 +0.50 +0'44 -0.62 -0.77 -0'79 12 +0.45 +0.44 +0.38 -0.54 -o•61 ~ -0'67 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 See also:

• COMPARATIVE

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 See also:

• XXXV