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362
MAGNETISM, TERRESTRIAL


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+ct', 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-l-n), where a, b, m and n are constants, have been used by Schott 1° 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 {o~61(t-1850)+77°-8} Inclination (South) =49°~11-|- 8°-75 sin lo-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 extra-polation is pushed. described in the clockwise direction. This, according to Bauer's 1° 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 1° 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. § 14. All the magnetic elements at any ordinary station show a regular variation in the solar day. To separate this from the irregular chanfges, means of the hourl readings must be formed making use 0 a number of days. 'lyhe amplitude of Di I the diurnal change usually varies considerably with the vain; season of the year. Thus a diurnal inequality derived ara 'ms from all the days of the year combined, or from a smaller Bauer has em lo ed a convenient ra hical method of illustr tin number of days sele

Table V II.-Inclination (northerly) and Horizontal Force at London. cted equally from all the months of the

year, can give only the average effect throughout the year. Also unless the h0urs of

4 maxima an minima at a given station

Date' I' Date' I' Date' I' H' Date I' H' are but slightly variable with the season, 1 Q 1 o 1 6 Q 1 tthe refulti] obtain led tbyh combining Sara 1576 7I 50 1801 70 36~o 1857 68 24~9 -17474 1891 67 33-2 -18193 "°m.a1 he mont S 0 the yea' may e a 6666 66 6 66 6-6 66 66-6 66666 '°95~ 67 66-6 -66666 's1§ “§ .:§ ;§§ .§ °;;S.i.2t.:;f§ ..i'°aY.;§§ 5;;°';Li 1676 73 30 1830 69 38~o 1865 68 8-7 -17662 IQOO6 67 11-8 -18428 fb Th. k J 1. Y. 'rf la 1723 74 42 '838 69 17.3 1870 67 58.6 17791 1905 i 67 3,8 .ISSIO iroofhe iieclinagoliierziltarlaispvligiiilrilthieatrbclicsr Ugg 72 19 '°54 68 31.1 1874 67 50.0 °179O3 X908 i 67 0.9 48515 One consequence ispobviously to makepthe I7 72 9 - range of a diurnal inequality which answers P y g D 26 g

secular change. Radu are drawn from the centre of a sphere go 1

e°°

a.Oq

El|!!|E

6 gg 8 4 0 4

n

41.

Ge

V lllllll °°

a 17

— " i To

s ' .

7:

b- . V 4

74

|llln|ll

Flo. 5.

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.

to the year as a whole less than the arithmetic mean of the twelve 1 ranges obtained for the constituent months. At stations in temperate latitudes, whilst minor differences of type do exist between 1 the diurnal inequalities for different months of the year, the difference 1 is mainly one of amplitude, and the mean diurnal inequality from all the months of the(yea(1i gi;/es a vlery fair idea of the nature of the p enomenain an in 1V1 ua mont .

Tables VIII. tg 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 t e 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 The curve is being lfrom a limited number of days selected as being specially quiet, Table VIII.-Diurnal Inequality of Declination, mean from whole year (-|- to West). Station. ' Ian Mayen. 3:1 dpgfxfgyglg Greenwich. Kew. StP§ , f;ur Tiliis. Kolaba. Batavia. Mauritius. § g:§ ;hL;fd Latitude 1° o' N 59° 41' N 51° 28' N. 51° 23' N- 48° 49' N 41° 43' N i8° 54' 6° II'S 20° 6' S 1 77° 51' S. Longitnde. 8° 28' W. 30° 29' E. 0° 0'. 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. 1390-1900- 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 I I 1 I / -1 1 1 1 I 1

1 -6-6 -4'2 *I'3 -0'7 -1-4 -I'5 -0'9 -1-4 -o-7 -0'2 +0-1 +2'0 +0-9 2 -10-5 -6-4 -I'2 ~0-8 -1-3 -I'4 -0'9 -1-2 -o~6 ~0'I -0-1 -2'I -1-8 3 15.2 -112 -I-0 I.3 -1.5 ].0 !.2 0.6 O.I 0.I -5-2 4 ~16~9 -8-4 -1-4 -1-3 -I'4 -1-7 -1-3 -1-2 -o~5 -o-1 o-o -9-4 -6-8 5 -17-0 -8~1 -1-7 -I~8 -1-7 -2-I -I-8 ~1~6 -o-7 -0-1 oo -I2'2 -9-0 6 -I3°7 ”7'0 -I'9 2'3 -2'I -2°4 ~2'3 -I'9 -I~2 -0-6 +0 I -I5'3 '-II°7 7 -9°3 ”5'I -2'2 '2'3 -2'4 '2'7 *2'8 ~2'4 .*I'9 ~fI~0 -l-0'5 -I7'2 -I5'0 8 -6-8 -3~2 -2-5 -3-2 -2-5 -2-8 -3-1 -2~7 -2~4 -1-2 +1-3 ~2I°5 — I7'3 9 . 0.6 -2.3 -3-0 I.9 2.I .2.5 2.3 . 2.3 O.7 7 IO 2~4 +2-1 -1-0 -1-7 ~O'2 -0-3 -o-7 -0-5 -0-9 0-0 +1 5 -2I'2 -15-8 II -0-5 +4-6 +I'0 +0'4 +2'I +2~2 +I-7 +2-0 +1-0 +0-9 -|-o-9 *I5'3 -9-2 Noon +2-5 +6-5 +3'I +2°7 +4-2 +4~3 +369 +4-2 +2-6 +1-4 +o 1 -9'8 -4'9 1 -l-3~7 -I-763 +4-6 -l-4'3 +5-1 -|~5°3 +4-8 +5-3 +3-3 +1-2 ~o 6 -3-2 -0-1 2 -l-6'4 -l-7°I -l-4'9 +4'5 -l-4-7 +4~9- +4'4 +4'9 -I-3-1 +0-6 -1 1 +3'8 -I-5-9 3 +7-4 +5-9 +4-1 +3-6 +3-6 +3-7 +3-I +3-7 +2-3 +o-1 -13 +11-I +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 -l-16-6 +12~9 5 +10-6 +3-0 +1-5 +1-3 +I'I -H~2 +0-7 +1-1 +0-6 -O°I ~o~9 +I9'9 +14»6 6 +14-2 -|-2~3 +0-6 -l-0°7 -l-0-3 +0°4 -l-0~2 +062 +o~2 o-o -0 6 -l-22-0 -I-1565 7 +15-2 +2'2 o-o +0-4 ~0-3 -0~2 -0-1 -O'4 +0-1 +o~1 -0 4 -l-22-0 +15-9 8 +15-8 +2-6 -0-4 +0'2 -0-9 -0-6 -0-3 -o~9 -O'I +0-2 -0 2 -l-19~9 +14-6 9 +13-2 +2-6 -1-0 0-0 -I'2' -1-0 -0~5 -1-3 -0-4 -l-O'I o-o -l-I6'0 -i-IO-6 IO +7-4 +2-o ~I'4 -0-2 -1-5 -1-3 -0-7 -1-5 -0-6 o-o +0 1 +11-6 +7-2 II +I~I +o~5 -1-6 -0-4 -1~6 -I°4 -0-8 -1-6 -0-7 o-o +0 1 +7-6 +4-2 I2 -3-6 -1-8 -1-5 -0-6 -1~6 ' -1-5 -0-9 -1-6 -0-8 -0-1 -I-0-1 +3-3 +1-9 1 l 1 l

Range 32.8   7.4   W  7.6   7.9 Y 8.0 5.7 2.6 3.0 4.2   34.0%