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368
MAGNETISM, TERRESTRIAL


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. 30m. 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. November. December.


(From Phil. Trans.) FIC" 8,

The utilit of a Fourier anal sis de ends lar el n y y p g y 0 whether the

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

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


midsummer, in addition to one near midwinter. On the other hand, the phase angle phenomena vary much for the different elements. The 24-hour term, for instance, has its maximum earlier in winter than in summer in the case of the declination and vertical force, but the exact reverse holds for the inclination and the horizontal force.

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

MOHth. 61. CQ. 63. 64. 0.1. 0.2. 0.3. 0.4.

1 1) 1 O 0 0 0

January 1-79 0-86 0-41 0-27 251-2 29-8 254 64 February 2-41 1-11 0-57 0-30 242-0 27-7 235 39 March . 3-05 ~1-98 1 II 0-45 233-2 36-1 223 49 April 3-35 2-48 1 17 0-39 224-8 39-2 228 61 May 3-57 2-38 0-87 0-17 221-3 50-8 245 89

June 3-83 2-39 0-74 0-05 212-6 46-7 239 72

July . 3-72 2-30 0-77 0-11 214-6 48-1 233 8

August . 3-64 2-43 1 05 0-18 228-2 57-2 244 SI September 3-35 2-02 1 O4 0-35 236-9 55-3 245 70 October 2-69 1-69 0-92 O-48 240-1 35-6 235 65 November 1-94 I'O6 0-51 0-32 248-3 28-3 247 61 December 1-61 O°8I 0-35 0-20 255-1 22-0 243 56 § 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 A I whole year, by the formula E, .=E+(2n~13)s/24, I nnuam where S is the secular change per annum. For the pre- "aqua 'V sent purpose, difference in the lengths of the months may be neglected. If one applies to En-E the correction - (211 - 13)s/24 one eliminates a regularly progressive secular change; what remains is known as the annual inequality. If only a short period of years is dealt with, irregularities in the secular change from year to year, or errors of observation, may obviously simulate the effect of a real annual inequality. Even when a long series of years is included, there is always a possibility of a spurious inequality arising from annual variation in the instruments, or from annual change in D 1 the conditions of observation. J. Liznar, 11 from a study CC 111211011 of data from a number of stations, arrived at certain mean " results for the annual inequalities in declination and incli-121aC@- EPOC11- 51- 02- CS- 54- 21- °-2- “lr “1~ nation in the northern and southern hemispheres, and Q 0 ' -, , 'TQ' ]. Hann 21 hasTmto1re£§§ ently dealt withfléiznafs and newer resu ts. a e . ivesa variet 0 ata, includ-F011 Rae (3112 - - 1382-1883 18'49 8'22 1'99 2'°7 156'5 41'9 308 104 ing the mean results givenziioy Liznar an1d Hann. In the ”. 111111211 H 9'°9 4'-51 1'32 O73 1685 37'-5 225 35° case of declination + denotes westerly position; in the Ekatarinburg . 1841-1862 2-57 1 81 0-73 0-22 223-3 7'4 204 351 case of inclination it denotes a larger dip (whether the Potsdam . ' ' ° 18921899 2 81 1'90 °'83 0'31 239'9 32'6 237 49 inclination be north or south). According to Liznar Kew (O1(111121y) ' 189°“19°° 2'91 1°79 079 O'27, 234'° 397 239 57 declination in summer is to the west of the normal posi-Kew (Q111211 . ' ' H 2'-37 1 82 °'9° 0 30 ' 227'3 42'1 2110 52 tion in both hemispheres. The phenomena, however, at Falmouth (quiet) . 1891-1902 2 18 I°82 0-91 0 29 226-2 40'5 208 5 Parc St Maur are, it will be seen, the exact opposite of Parc St M2111 - ~ 18834899 2'70 1°87 085 0 30 238'6 32'5 235 95 what Liznar regards as normal; and whilst the Potsdam 1119101110 - ~ ~ 18421848 2 65 2134 1'00 0'33 2137 34'9 238 35° results resemble his mean in type, the range of the in-W2S11111g1°11 - ~ 1840-1842 2 38 1 86 °'65 O 53 223° 226 223 53 equality there, as at Parc St Maur, is relatively small. Mff11111a ~ - - 1890-1900 0'53 0'58 0'43 0 17 2683 50'7 226 89 Of the three sets of data given for Kew the first two are Tflvaedfum ' ' 1853'1864 °'54 0 46 0'29 0 10 28911 49'6 114 derived in a similar way to those for other stations; the B312-V12 - - 1883 1899 0'80 0'88 0'43 0 13 3320 163'2 5 236 first set are based on quiet days only, the second 'on all St' 11212112 ' ' ' 18424847 068 °'61 O'63 0 34 275'8 171'4 27 244 but highly disturbed days. Both these sets of results M51U1'1UUS - - - 18764890 0'86 1 11 0'76 0 22 21'6 172'7 350 161 are fairly similar in type to the Parc St Maur results, C. of G. Hope . . 1841-1846 I 15 1 13 0-80 O 35 287°7 156'° 351 195 but give larger ranges; they are thus even more opposed 1V1@1b0'-11112 - - - 18584863 2 52 2'4-5 1'23 0 35 27'4 176'7 9 193 to Liznar's normal type. The last set of data for Kew 11011211; - - 1841 1848 2 29 2 15 0'87 0 32 336 17°'8 349 185 is of a special kind. During the II years 1890 to 1900 S'.GeQ1g1a - - 1882-1883 2 13 1 28 076 0 31 3033 185'3 7 180 the Kew declination magneto graph showed to within 1 VW10112 1-211f1 (211)- 19024903 20'51 4'81 1'21 1 32 158'7 3059 292 303 the exact secular change as derived from the absolute — (q111e1@1')~, 15'34,4-'05,1'24 1 13 1638 312'9 261 observations; also, if any annual variation existed § 21. Fourier coedicients 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 oi 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 eriod 1890-1900. Fourier analysis has been applied to the diurnal inequalities of the other magnetic elements, but more sparingly. Such results are illustrated by Table XIX., which contains data derived from quiet days at Kew from 1890 to 1900. Winter includes November to February. Summer May to August, and Equinox the remaining four months. In this case the data are derived from mean diurnal inequalities for the season specified. In the case of the c or amplitude coefficients the unit is 1' for l (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 in the position of the base lines of the curves it was exceedingly small. Thus the accumulation of the daily non-cyclic changes shown by the curves should closely represent the combined TABLE XIX.-Kew Diurnal Inequality: Amplitudes and Phase Angles (local mean time).

61. C2. C3. 64. 0.1. 412. 0.3. 0.4.

Winter 0-240 0-222 0-104 0-076 250-0 91-8 344 194 I Equinox 0-601 0-290 0-213 0-127 290-3 135-5 4 207 Summer 0-801 0-322 0 172 0-070 312-5 155-5 39 238 Winter. 3-62 3'86 181 1-13 82-9 277-3 154 6

H Equinox 10-97 5-87 332 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 I-67 0 86 0-42 153-9 300-8 IOS 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