An event of the first importance was the_Encyclopaedia Britannica, 11th Edition, "McKinley, William" to "Magnetism, Terrestrial" Volume 17, Slice 3

Oersted [100] that a magnet placed near a wire carrying an electric

current tended to set itself at right angles to the wire, a phenomenon

which indicated that the current was surrounded by a magnetic field.

This discovery constituted the foundation of electromagnetism, and its

publication in 1820 was immediately followed by A. M. Ampère's

experimental and theoretical investigation of the mutual action of

electric currents,[101] and of the equivalence of a closed circuit to a

polar magnet, the latter suggesting his celebrated hypothesis that

molecular currents were the cause of magnetism. In the same year D. F.

Arago[102] succeeded in magnetizing a piece of iron by the electric

current, and in 1825 W. Sturgeon[103] publicly exhibited an apparatus

"acting on the principle of powerful magnetism and feeble galvanism"

which is believed to have constituted the first actual electromagnet.

Michael Faraday's researches were begun in 1831 and continued for more

than twenty years. Among the most splendid of his achievements was the

discovery of the phenomena and laws of magneto-electric induction, the

subject of two papers communicated to the Royal Society in 1831 and

1832. Another was the magnetic rotation of the plane of polarization of

light, which was effected in 1845, and for the first time established a

relation between light and magnetism. This was followed at the close of

the same year by the discovery of the magnetic condition of all matter,

a discovery which initiated a prolonged and fruitful study of

paramagnetic and diamagnetic phenomena, including magnecrystallic action

and "magnetic conducting power," now known as permeability. Throughout

his researches Faraday paid special regard to the medium as the true

seat of magnetic action, being to a large extent guided by his pregnant

conception of "lines of force," or of induction, which he considered to

be "closed curves passing in one part of the course through the magnet

to which they belong, and in the other part through space," always

tending to shorten themselves, and repelling one another when they were

side by side (_Exp. Res._ §§ 3266-8, 3271). In 1873 James Clerk Maxwell

published his classical _Treatise on Electricity and Magnetism_, in

which Faraday's ideas were translated into a mathematical form. Maxwell

explained electric and magnetic forces, not by the action at a distance

assumed by the earlier mathematicians, but by stresses in a medium

filling all space, and possessing qualities like those attributed to the

old luminiferous ether. In particular, he found that the calculated

velocity with which it transmitted electromagnetic disturbances was

equal to the observed velocity of light; hence he was led to believe,

not only that his medium and the ether were one and the same, but,

further, that light itself was an electromagnetic phenomenon. Since the

experimental confirmation of Maxwell's views by H. R. Hertz in 1888

(_Weid. Ann._, 1888, 34, 155, 551, 609; and later vols.) they have

commanded universal assent, and his methods are adopted in all modern

work on electricity and magnetism.

The practice of measuring magnetic induction and permeability with

scientific accuracy was introduced in 1873 by H. A. Rowland,[104] whose

careful experiments led to general recognition of the fact previously

ignored by nearly all investigators, that magnetic susceptibility and

permeability are by no means constants (at least in the case of the

ferromagnetic metals) but functions of the magnetizing force. New light

was thrown upon many important details of magnetic science by J. A.

Ewing's _Experimental Researches_ of 1885; throughout the whole of his

work special attention was directed to that curious lagging action to

which the author applied the now familiar term "hysteresis."[105] His

well-known modification[106] of Weber's molecular theory, published in

1890, presented for the first time a simple and sufficient explanation

of hysteresis and many other complexities of magnetic quality. The

amazing discoveries made by J. J. Thomson in 1897 and 1898[107] resulted

in the establishment of the electron theory, which has already effected

developments of an almost revolutionary character in more than one

branch of science. The application of the theory by P. Langevin to the

case of molecular magnetism has been noticed above, and there can be

little doubt that in the near future it will contribute to the solution

of other problems which are still obscure.

See W. Gilbert, _De magnete_ (London, 1600; trans. by P. F. Mottelay,

New York, 1893, and for the Gilbert Club, London, 1900); M. Faraday,

_Experimental Researches in Electricity_, 3 vols. (London, 1839, 1844

and 1855); W. Thomson (Lord Kelvin), _Reprint of Papers on

Electrostatics and Magnetism_ (London, 1884, containing papers on

magnetic theory originally published between 1844 and 1855, with

additions); J. C. Maxwell, _Treatise on Electricity and Magnetism_

(3rd ed., Oxford, 1892); E. Mascart and J. Joubert, _Leçons sur

l'électricité et le magnétisme_ (2nd ed., Paris, 1896-1897; trans.,

not free from errors, by E. Atkinson, London, 1883); J. A. Ewing,

_Magnetic Induction in Iron and other Metals_ (3rd ed., London,

1900); J. J. Thomson, _Recent Researches in Electricity and Magnetism_

(Oxford, 1893); _Elements of Mathematical Theory of Electricity and

Magnetism_ (3rd ed., Cambridge, 1904); H. du Bois, _The Magnetic

Circuit_ (trans. by E. Atkinson, London, 1896); A. Gray, _Treatise on

Magnetism and Electricity_, vol. i. (London, 1898); J. A. Fleming,

_Magnets and Electric Currents_ (London, 1898); C. Maurain, _Le

magnétisme du fer_ (Paris, 1899; a lucid summary of the principal

facts and laws, with special regard to their practical application);

_Rapports présentés au Congrès international de physique_, vol. ii.

(Paris, 1900); G. C. Foster and A. W. Porter, _Treatise on Electricity

and Magnetism_ (London, 1903); A. Winkelmann, _Handbuch der Physik_,

vol. v. part i. (2nd ed., Leipzig, 1905; the most exhaustive

compendium of magnetic science yet published, containing references to

all important works and papers on every branch of the subject).

(S. Bi.)

FOOTNOTES:

[1] In London in 1910 the needle pointed about 16° W. of the

geographical north. (See TERRESTRIAL MAGNETISM.)

[2] For the relations between magnetism and light see MAGNETO-OPTICS.

[3] Clerk Maxwell employed German capitals to denote vector

quantities. J. A. Fleming first recommended the use of blockletters

as being more convenient both to printers and readers.

[4] The C.G.S. unit of current = 10 amperes.

[5] The principal theoretical investigations are summarized in

Mascart and Joubert's _Electricity and Magnetism_, i. 391-398 and ii.

646-657. The case of a long iron bar has been experimentally studied

with great care by C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 509.

[6] _Wied. Ann._, 1884, 22, 411.

[7] See C. G. Lamb, _loc. cit._ p. 518.

[8] Hopkinson specified the retentiveness by the numerical value of

the "residual induction" (= 4[pi]I).

[9] For all except ferromagnetic substances the coefficient is

sensibly equal to [kappa].

[10] See W. Thomson's _Reprint_, §§ 615, 634-651.

[11] Ibid. §§ 646, 684.

[12] Faraday, _Exp. Res._ xxi.

[13] J. J. Thomson, _Electricity and Magnetism_, § 205.

[14] Maxwell, _Electricity and Magnetism_, § 431.

[15] H. du Bois, _Electrician_, 1898, 40, 317.

[16] M. Faraday, _Exp. Res._ xxii., xxiii.; W. Thomson, _Reprint_, §

604; J. C. Maxwell, _Treatise_, § 435; E. Mascart and J. Joubert,

_Electricity and Magnetism_, §§ 384, 396, 1226; A. Winkelmann,

_Physik_, v. 287.

[17] See A. Winkelmann, _Physik_, v. 69-94; Mascart and Joubert.

_Electricity and Magnetism_, ii. 617.

[18] _Sci. Abs._ A, 1906, 9, 225.

[19] See C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 517.

[20] _Soc. Franc. Phys. Séances_, 1904, 1, 27.

[21] E. G. Warburg, _Wied. Ann._ 1881, 13, 141; Ewing, _Phil.

Trans._, 1885, 176, 549; Hopkinson, _Phil. Trans._ 1885, 176, 466.

For a simple proof, see Ewing, _Magnetic Induction_ (1900), p. 99.

Hopkinson pointed out that the greatest dissipation of energy which

can be caused by a to-and-fro reversal is approximately represented

by _Coercive force_ × _maximum induction_ /[pi].

[22] _Magnetic Induction_, 1900, 378.

[23] _Phil. Trans._, 1902, 198, 33.

[24] _Phil. Mag._, 1903, 5, 117.

[25] Some experiments by F. G. Baily showed that hysteresis ceased to

increase when B was carried beyond 23,000. This value of B

corresponds to I = 1640, the saturation point for soft iron.--_Brit.

Assoc. Rep._, 1895, p. 636.

[26] _Tokyo Phys.-Math. Soc._, 1904, 2, No. 14.

[27] _Phil. Mag._, 1873, 46, 140.

[28] S. Bidwell, _Proc. Roy. Soc._, 1886, 40, 495.

[29] Since in most practicable experiments H³ is negligible in

comparison with B², the force may be taken as B²/8[pi] without

sensible error.

[30] The same phenomenon is exhibited in a less marked degree when

soft iron is magnetized in stronger fields (Ewing, _Phil. Trans._,

1885, 176, 569).

[31] Principal publications: J. P. Joule, _Scientific Papers_, pp.

46, 235; A. M. Meyer, _Phil. Mag._, 1873, 46, 177; W. F. Barrett,

_Nature_, 1882, 26, 585; S. Bidwell, _Phil. Trans._, 1888, 179A, 205;

_Proc. Roy. Soc._, 1886, 40, 109 and 257; 1888, 43, 406; 1890, 47,

469; 1892, 51, 495; 1894, 55, 228; 1894, 56, 94; 1904, 74, 60;

_Nature_, 1899, 60, 222; M. Cantone, _Mem. d. Acc d. Lincei_, 1889,

6, 487; _Rend. d. Acc. d. Lincei_, 1890, 6, 252; A. Berget, _C.R._,

1892, 115, 722; S. J. Lochner, _Phil. Mag._, 1893, 36, 498; H.

Nagaoka, _Phil. Mag._, 1894, 37, 131; _Wied. Ann._, 1894, 53, 487; C.

G. Knott, _Proc. Roy. Soc. Ed._, 1891, 18, 315; _Phil. Mag._, 1894,

37, 141; _Trans. Roy. Soc. Ed._, 1896, 38, 527; 1898, 39, 457; C. G.

Knott and A. Shand, _Proc. Roy. Soc. Ed._, 1892, 19, 85 and 249;

1894, 20, 295; L. T. More, _Phil. Mag._, 1895, 40, 345; G.

Klingenberg, _Rostock Univ. Thesis_, Berlin, 1897; E. T. Jones,

_Phil. Trans._, 1897, 189A, 189; B. B. Brackett, _Phys. Rev._, 1897,

5, 257; H. Nagaoka and K. Honda, _Phil. Mag._, 1898, 46, 261; 1900,

49, 329; _Journ. Coll. Sci. Tokyo_, 1900, 13, 57; 1903, 19, art. 11;

J. S. Stevens, _Phys. Rev._, 1898, 7, 19; E. Rhoads, _Phys. Rev._,

1898, 7, 5; _Phil. Mag._, 1901, 2, 463; G. A. Shakespear, _Phil.

Mag._, 1899, 17, 539; K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13,

77; L. W. Austin, _Phys. Rev._, 1900, 10, 180; _Deutsch. Phys.

Gesell. Verh._, 1904, 6, 4, 211; K. Honda and S. Shimizu, _Phil.

Mag._, 1902, 4, 338; 1905, 10, 548.

[32] The loads were successively applied in decreasing order of

magnitude. They are indicated in fig. 25 as kilos per sq. cm.

[33] Joule believed that the volume was unchanged.

[34] For a discussion of theories of magnetic stress, with copious

references, see Nagaoka, _Rap. du Congrès International de Physique_

(Paris, 1900), ii. 545. Also Nagaoka and Jones, _Phil. Mag._, 1896,

41, 454.

[35] S. Bidwell, _Phil. Trans._, 1888, 179a, 321.

[36] _Phil. Mag._, 1895, 40, 345.

[37] J. C. Maxwell, _Treatise_, § 643.

[38] See correspondence in _Nature_, 1896, 53, pp. 269, 316, 365,

462, 533; 1906, 74, pp. 317, 539; B. B. Brackett, _loc. cit._, quotes

the opinion of H. A. Rowland in support of compressive stress.

[39] J. A. Ewing, _Phil. Trans._, 1885, 176, 580; 1888, 179, 333;

_Magnetic Induction_, 1900, ch. ix.; J. A. Ewing and G. C. Cowan,

_Phil. Trans._, 1888, 179a, 325; C. G. Knott, _Trans. Roy. Soc. Ed._,

1882-1883, 32, 193; 1889, 35, 377; 1891, 36, 485; _Proc. Roy. Soc.

Ed._, 1899, 586; H. Nagaoka, _Phil. Mag._, 1889, 27, 117; 1890, 29,

123; H. Nagaoka and K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13,

263; 1902, 16, art. 8; _Phil. Mag._, 1898, 46, 261; 1902, 4, 45; K.

Honda and S. Shimizu, _Ann. d. Phys._, 1904, 14, 791; _Tokyo

Physico-Math. Soc. Rep._, 1904, 2, No. 13; K. Honda and T. Terada,

_Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4.

[40] H. Tomlinson found a critical point in the "temporary

magnetization" of nickel (_Proc. Phys. Soc._, 1890, 10, 367, 445),

but this does not correspond to a Villari reversal. Its nature is

made clear by Ewing and Cowan's curves (_Phil. Trans._, 1888, 179,

plates 15, 16).

[41] _Wied. Ann._, 1894, 52, 462; _Electrician_, 1894, 34, 143.

[42] _Phil. Trans._, 1890, 131, 329.

[43] _Magnetic Induction_, 1900, 222.

[44] _Phys. Rev._, 1904, 18, 432.

[45] _Phil. Mag._, 1886, 22, 50.

[46] _Ibid._ 251.

[47] _Phil. Mag._, 1891, 32, 383.

[48] _C.R._, 1896, 122, 1192; 1898, 126, 463.

[49] _Phil. Mag._, 1889, 27, 117.

[50] _Journ. Coll. Sci. Tokyo_, 1904, 19, art. 9.

[51] _Phil. Mag._, 1905, 10, 548; _Tokyo Phys.-Math. Soc. Rep._,

1904, 2, No. 14; _Journ. Coll. Sci. Tokyo_, 1905, 20, art. 6.

[52] _C.R._, 1888, 106, 129.

[53] _Proc. Phys. Soc._, 1888, 9, 181.

[54] _C.R._, 1892, 115, 805; 1894, 118, 796 and 859.

[55] _Elekt. Zeits._, 1894, 15, 194.

[56] _Phil. Mag._, 1900, 50, 1.

[57] _Phil. Trans._, 1903, 201, 1.

[58] _Phil. Mag._, 1904, 8, 179.

[59] A. M. Thiessen (_Phys._, 1899, 8, 65) and G. Claude (C. R.,

1899, 129, 409) found that for considerable inductions (B = 15,000)

the permeability and hysteresis-loss remained nearly constant down to

-186°; for weak inductions both notably diminished with temperature.

[60] _Proc. Roy. Soc._, 1898, 62, 210.

[61] _C.R._, 1895, 120, 263.

[62] _Amer. Journ. Sci._, 1898, 5, 245.

[63] _Phys. Rev._, 1901, 14, 181.

[64] _C.R._, 1897, 124, 176 and 1515; 1897, 125, 235; 1898, 126, 738.

[65] Ibid., 1898, 126, 741.

[66] Ibid., 1899, 128, 304 and 1395.

[67] See also J. Hopkinson, _Journ. Inst. Elect. Eng._, 1890, 19, 20,

and J. A. Ewing, _Phil. Trans._, 1889, 180, 239.

[68] Many of the figures which, through an error, were inaccurately

stated in the first paper are corrected in the second.

[69] The marked effect of silicon in increasing the permeability of

cast iron has also been noticed by F. C. Caldwell, _Elect. World_,

1898, 32, 619.

[70] _Trans. Roy. Dub. Soc._, 1902-4, 8, 1 and 123.

[71] J. Trowbridge and S. Sheldon, _Phil. Mag._, 1890, 29, 136; W. H.

Preece, _Journ. Inst. Elec. Eng._, 1890, 19, 62; _Electrician_, 1890,

25, 546; I. Klemençiç, _Wien. Ber._, 1896, 105, IIa, 635; B. O.

Peirce, _Am. Journ. Sci._, 1896, 2, 347; A. Abt, _Wied. Ann._, 1898,

66, 116; F. Osmond, _C. R._, 1899, 128, 1513.

[72] _Deutsch. phys. Gesell. Verh._, 1903, 5, 220 and 224.

[73] _Exp. Res._, iii. 440.

[74] No record can be found of experiments with manganese at the

temperature of liquid air or hydrogen; probably, however, negative

results would not be published.

[75] The critical temperature of iron, for instance, is raised more

than 100° by the addition of a little carbon and tungsten.

[76] _Bull. Soc. Int. des Électriciens_, 1906, 6, 301.

[77] _Proc. Roy. Soc._, 1905, 76A, 271.

[78] E. H. Hall, _Phil. Mag._, 1880, 9, 225; 1880, 10, 301; 1881, 12,

157; 1883, 15, 341; 1885, 19, 419.

[79] The large Hall effect in bismuth was discovered by Righi,

_Journ. de Phys._, 1884, 3, 127.

[80] REFERENCES.--(2) A. von Ettinghausen, _Wied. Ann._, 1887, 31,

737.--(4) H. W. Nernst, ibid., 784.--(i.) and (iv.); A. von

Ettinghausen and H. W. Nernst, _Wied. Ann._, 1886, 29, 343.--(ii.)

and (iii.); A. Righi, _Rend. Acc. Linc._, 1887, 3 II, 6 and I, 481;

and A. Leduc, _Journ. de Phys._, 1887, 6, 78. Additional authorities

are quoted by Lloyd, _loc. cit._

[81] P. Drude, _Ann. d. Phys._, 1900, 1, 566; 1900, 3, 369; 1902, 7,

687. See also E. van Everdingen, _Arch. Néerlandaises_, 1901, 4, 371;

G. Barlow, _Ann. d. Phys._, 1903, 12, 897; H. Zahn, ibid. 1904, 14,

886; 1905, 16, 148.

[82] _Phil. Trans._, 1856, p. 722. According to the nomenclature

adopted by the best modern authorities, a metal A is said to be

thermo-electrically positive to another metal B when the

thermo-current passes from A to B through the cold junction, and from

B to A through the hot (see THERMO-ELECTRICITY).

[83] _C.R._, 1893, 116, 997.

[84] _Journ. de Phys._, 1896, 5, 53.

[85] _Phil. Trans._, 1887, 177, 373.

[86] _Proc. Roy. Soc._, 1885, 39, 513.

[87] _Phys. Rev._, 1902, 15, 321. The sign of the thermo-electric

effect for nickel, as given by Rhoads, is incorrect.

[88] _Proc. Roy. Soc._, 1904, 73, 413.

[89] _C.R._, 1903, 136, 1131.

[90] _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4. The paper contains

40 tables and 85 figures.

[91] This deduction from Ewing's theory appears to have been first

suggested by J. Swinburne. See _Industries_, 1890, 289.

[92] R. Beattie (_Phil. Mag._, 1901, 1, 642) has found similar

effects in nickel and cobalt.

[93] The charge associated with a corpuscle is the same as that

carried by a hydrogen atom. G. J. Stoney in 1881 (_Phil. Mag._, 1881,

11, 387) pointed out that this latter constituted the indivisible

"atom of electricity" or natural unit charge. Later he proposed

(_Trans. Roy. Dub. Soc._, 1891, 4, 583) that such unit charge should

be called an "electron." The application of this term to Thomson's

corpuscle implies, rightly or wrongly, that notwithstanding its

apparent mass, the corpuscle is in fact nothing more than an atom of

electricity. The question whether a corpuscle actually has a material

gravitating nucleus is undecided, but there are strong reasons for

believing that its mass is entirely due to the electric charge.

[94] _Jour. de Phys._, 1905, 4, 678; translated in _Electrician_,

1905, 56, 108 and 141.

[95] The quotations are from the translation published by the Gilbert

Club, London, 1900.

[96] C. A. Coulomb, _Mem. Acad. Roy. Paris_, 1785, p. 578.

[97] _Intensitas vis magneticae_, § 21, C. F. Gauss's _Werke_, 5, 79.

See also J. J. Thomson, _Electricity and Magnetism_, § 132.

[98] S. D. Poisson, _Mém. de l'Institut_, 1821 and 1822, 5, 247, 488;

1823, 6, 441; 1838, 16, 479.

[99] For outlines of the mathematical theory of magnetism and

references see H. du Bois, _Magnetic Circuit_, chs. iii. and iv.

[100] Gilbert's _Ann. d. phys._, 1820, 6, 295.

[101] _Ann. de chim. et de phys._, 1820, 15, 59, 170; _Recueil

d'observations électrodynamiques_, 1822; _Théories des phénomènes

électrodynamiques_, 1826.

[102] _Ann. de chim. et de phys._, 1820, 15, 93.

[103] _Trans. Soc. Arts_, 1825, 43, 38.

[104] _Phil. Mag._, 1873, 46, 140; 1874, 48, 321.

[105] _Phil. Trans._, 1885, 176, 523; _Magnetic Induction_, 1900.

[106] _Proc. Roy. Soc._, 1890, 48, 342.

[107] _Phil. Mag._, 1897, 44, 293; 1898, 46, 528.

MAGNETISM, TERRESTRIAL, the science which has for its province the study

of the magnetic phenomena of the earth.

Historical.

§ 1. Terrestrial magnetism has a long history. Its early growth was

slow, and considerable uncertainty prevails as to its earliest

developments. The properties of the magnet (see MAGNETISM) were to some

small extent known to the Greeks and Romans before the Christian era,

and compasses (see COMPASS) of an elementary character seem to have been

employed in Europe at least as early as the 12th century. In China and

Japan compasses of a kind seem to have existed at a much earlier date,

and it is even claimed that the Chinese were aware of the declination of

the compass needle from the true north before the end of the 11th

century. Early scientific knowledge was usually, however, a mixture of

facts, very imperfectly ascertained, with philosophical imaginings. When

an early writer makes a statement which to a modern reader suggests a

knowledge of the declination of the compass, he may have had no such

definite idea in his mind. So far as Western civilization is concerned,

Columbus is usually credited with the discovery--in 1492 during his

first voyage to America--that the pointing of the compass needle to the

true north represents an exceptional state of matters, and that a

_declination_ in general exists, varying from place to place. The credit

of these discoveries is not, however, universally conceded to Columbus.

G. Hellmann[6][A] considers it almost certain that the departure of the

needle from the true north was known in Europe before the time of

Columbus. There is indirect evidence that the declination of the compass

was not known in Europe in the early part of the 15th century, through

the peculiarities shown by early maps believed to have been drawn solely

by regard to the compass. Whether Columbus was the first to observe the

declination or not, his date is at least approximately that of its

discovery.

The next fundamental discovery is usually ascribed to Robert Norman, an

English instrument maker. In _The Newe Attractive_ (1581) Norman

describes his discovery made some years before of the _inclination_ or

_dip_. The discovery was made more or less by accident, through Norman's

noticing that compass needles which were truly balanced so as to be

horizontal when unmagnetized, ceased to be so after being stroked with a

magnet. Norman devised a form of dip-circle, and found a value for the

inclination in London which was at least not very wide of the mark.

Another fundamental discovery, that of the secular change of the

declination, was made in England by Henry Gellibrand, professor of

mathematics at Gresham College, who described it in his _Discourse

Mathematical on the Variation of the Magneticall Needle together with

its Admirable Diminution lately discovered_ (1635). The history of this

discovery affords a curious example of knowledge long delayed. William

Borough, in his _Discourse on the Variation of the Compas or Magneticall

Needle_ (1581), gave for the declination at Limehouse in October 1580

the value 11°¼ E. approximately. Observations were repeated at

Limehouse, Gellibrand tells us, in 1622 by his colleague Edmund Gunter,

professor of astronomy at Gresham College, who found the much smaller

value 6° 13´. The difference seems to have been ascribed at first to

error on Borough's part, and no suspicion of the truth seems to have

been felt until 1633, when some rough observations gave a value still

lower than that found by Gunter. It was not until midsummer 1634 that

Gellibrand felt sure of his facts, and yet the change of declination

since 1580 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 positive assertion made on the point by Gilbert of

Colchester in his _De magnete_ (1600).

A third fundamental discovery, that of the diurnal change in the

declination, is usually credited to George Graham (1675-1751), a London

instrument maker. Previous observers, e.g. Gellibrand, had obtained

slightly different values for the declination at different hours of the

day, but it was natural to assign them to instrumental uncertainties. In

those days the usual declination instrument was the compass with pivoted

needles, and Graham himself at first assigned the differences he

observed to friction. The observations on which he based his conclusions

were made in 1722; an account of them was communicated to the Royal

Society and published in the _Philosophical Transactions_ for 1724.

The movements of the compass needle throughout the average day represent

partly a regular diurnal variation, and partly irregular changes in the

declination. The distinction, however, was not at first very clearly

realized. Between 1756 and 1759 J. Canton observed the declination-changes

on some 600 days, and was thus able to deduce their general character. He

found that the most prominent part of the regular diurnal change in

England consisted of a westerly movement of the north-pointing pole from 8

or 9 a.m. to 1 or 2 p.m., followed by a more leisurely return movement to

the east. He also found that the amplitude of the movement was

considerably larger in summer than in winter. Canton further observed that

in a few days the movements were conspicuously irregular, and that aurora

was then visible. This association of magnetic disturbance and aurora had,

however, been observed somewhat before this time, a description of one

conspicuous instance being contributed to the Royal Society in 1750 by

Pehr Vilhelm Wargentin (1717-1783), a Swede.

Another landmark in the history of terrestrial magnetism was the

discovery towards the end of the 18th century that the intensity of the

resultant magnetic force varies at different parts of the earth. The

first observations clearly showing this seem to be those of a Frenchman,

Paul de Lamanon, who observed in 1785-1787 at Teneriffe and Macao, but

his results were not published at the time. The first published

observations seem to be those made by the great traveller Humboldt in

tropical America between 1798 and 1803. The delay in this discovery may

again be attributed to instrumental imperfections. The method first

devised for comparing the force at different places consisted in taking

the time of oscillation of the dipping needle, and even with modern

circles this is hardly a method of high precision. Another discovery

worth chronicling was made by Arago in 1827. From observations made at

Paris he found that the inclination of the dipping needle and the

intensity of the horizontal component of the magnetic force both

possessed a diurnal variation.

§ 2. Whilst Italy, England and France claim most of the early

observational discoveries, Germany deserves a large share of credit for

the great improvement in instruments and methods during the first half

of the 19th century. Measurements of the intensity of the magnetic force

were somewhat crude until Gauss showed how absolute results could be

obtained, and not merely relative data based on observations with some

particular needle. Gauss also devised the bifilar magnetometer, which is

still largely represented in instruments measuring changes of the

horizontal force; but much of the practical success attending the

application of his ideas to instruments seems due to Johann von Lamont

(1805-1879), a Jesuit of Scottish origin resident in Germany.

The institution of special observatories for magnetic work is largely

due to Humboldt and Gauss. The latter's observatory at Göttingen, where

regular observations began in 1834, was the centre of the Magnetic Union

founded by Gauss and Weber for the carrying out of simultaneous magnetic

observations and it was long customary to employ Göttingen time in

schemes of international co-operation.

In the next decade, mainly through the influence of Sir Edward Sabine

(1788-1883), afterwards president of the Royal Society, several magnetic

observatories were established in the British colonies, at St Helena,

Cape of Good Hope, Hobarton (now Hobart) and Toronto. These, with the

exception of Toronto, continued in full action for only a few years; but

their records--from their widely distributed positions--threw much fresh

light on the differences between magnetic phenomena in different regions

of the globe. The introduction of regular magnetic observatories led ere

long to the discovery that there are notable differences between the

amplitudes of the regular daily changes and the frequency of magnetic

disturbances in different years. The discovery that magnetic phenomena

have a period closely similar to, if not absolutely identical with, the

"eleven year" period in sun-spots, was made independently and nearly

simultaneously about the middle of the 19th century by Lamont, Sabine

and R. Wolf.

The last half of the 19th century showed a large increase in the number

of observatories taking magnetic observations. After 1890 there was an

increased interest in magnetic work. One of the contributory causes was

the magnetic survey of the British Isles made by Sir A. Rücker and Sir

T. E. Thorpe, which served as a stimulus to similar work elsewhere;

another was the institution by L. A. Bauer of a magazine. _Terrestrial

Magnetism_, specially devoted to the subject. This increased activity

added largely to the stock of information, sometimes in forms of marked

practical utility; it was also manifested in the publication of a number

of papers of a speculative character. For historical details the writer

is largely indebted to the works of E. Walker[1] and L. A. Bauer.[3]

Observational Methods and Records.

§ 3. All the more important magnetic observatories are provided with

instruments of two kinds. Those of the first kind give the absolute

value of the magnetic elements at the time of observation. The

unifilar magnetometer (q.v.), for instance, gives the absolute values

of the declination and horizontal force, whilst the inclinometer

(q.v.) or dip circle gives the inclination of the dipping needle.

Instruments of the second kind, termed magnetographs (q.v.), are

differential and self-recording, and show the changes constantly

taking place in the magnetic elements. The ordinary form of

magnetograph records photographically. Light reflected from a fixed

mirror gives a base line answering to a constant value of the element

in question; the light is cut off every hour or second hour so that

the base line also serves to make the time. Light reflected from a

mirror carried by a magnet gives a curved line answering to the

changes in position of the magnet. The length of the ordinate or

perpendicular drawn from any point of the curved line on to the base

line is proportional to the extent of departure of the magnet from a

standard position. If then we know the absolute value of the element

which corresponds to the base line, and the equivalent of 1 cm. of

ordinate, we can deduce the absolute value of the element answering to

any given instant of time. In the case of the declination the value of

1 cm. of ordinate is usually dependent almost entirely on the distance

of the mirror carried by the magnet from the photographic paper, and

so remains invariable or very nearly so. In the case of the horizontal

force and vertical force magnetographs--these being the two force

components usually recorded--the value of 1 cm. of ordinate alters

with the strength of the magnet. It has thus to be determined from

time to time by observing the deflection shown on the photographic

paper when an auxiliary magnet of known moment, at a measured

distance, deflects the magnetograph magnet. Means are provided for

altering the sensitiveness, for instance, by changing the effective

distance in the bifilar suspension of the horizontal force magnet, and

by altering the height of a small weight carried by the vertical force

magnet. It is customary to aim at keeping the sensitiveness as

constant as possible. A very common standard is to have 1 cm. of

ordinate corresponding to 10´ of arc in the declination and to

50[gamma] (1[gamma] = 0.00001 C.G.S.) in the horizontal and vertical

force magnetographs.

As an example of how the curves are standardized, suppose that

absolute observations of declination are taken four times a month, and

that in a given month the mean of the observed values is 16° 34´.6 W.

The curves are measured at the places which correspond to the times of

the four observations, and the mean length of the four ordinates is,

let us say, 2.52 cms. If 1 cm. answers to 10´, then 2.52 cms.

represents 25´.2, and thus the value of the base line--i.e. the value

which the declination would have if the curve came down to the base

line--is for the month in question 16° 34´.6 less 25´.2 or 16° 9´.4.

If now we wish to know the declination at any instant in this

particular month all we have to do is to measure the corresponding

ordinate and add its value, at the rate of 10´ per cm., to the base

value 16° 9´.4 just found. Matters are a little more complicated in

the case of the horizontal and vertical force magnetographs. Both

instruments usually possess a sensible temperature coefficient, i.e.

the position of the magnet is dependent to some extent on the

temperature it happens to possess, and allowance has thus to be made

for the difference from a standard temperature. In the case of the

vertical force an "observed" value is derived by combining the

observed value of the inclination with the simultaneous value of the

horizontal force derived from the horizontal force magnetograph after

the base value of the latter has been determined. In themselves the

results of the absolute observations are of minor interest. Their main

importance is that they provide the means of fixing the value of the

base line in the curves. Unless they are made carefully and

sufficiently often the information derivable from the curves suffers

in accuracy, especially that relating to the secular change. It is

from the curves that information is derived as to the regular diurnal

variation and irregular changes. In some observatories it is customary

to publish a complete record of the values of the magnetic elements at

every hour for each day of the year. 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. Greenwich, to reproduce the more disturbed

curves in the annual volume. In calculating the regular diurnal

variation it is usual to consider each month separately. So far as is

known at present, it is entirely or almost entirely a matter of

accident at what precise hours specially high or low values of an

element may present themselves during an individual highly disturbed

day; whilst the range of the element on such a day may be 5, 10 or

even 20 times as large as on the average undisturbed day of the month.

It is thus customary when calculating diurnal inequalities to omit the

days of largest disturbance, as their inclusion would introduce too

large an element of uncertainty. Highly disturbed days are more than

usually common in some years, and in some months of the year, thus

their omission may produce effects other than that intended. Even on

days of lesser disturbance difficulties present themselves. There may

be to and fro movements of considerable amplitude occupying under an

hour, and the hour may come exactly at the crest or at the very lowest

part of the trough. Thus, if the reading represents in every case the

ordinate at the precise hour a considerable element of chance may be

introduced. If one is dealing with a mean from several hundred days

such "accidents" can be trusted to practically neutralize one another,

but this is much less fully the case when the period is as short as a

month. To meet this difficulty it is customary at some observatories

to derive hourly values from a freehand curve of continuous curvature,

drawn so as to smooth out the apparently irregular movements. Instead

of drawing a freehand curve it has been proposed to use a planimeter,

and to accept as the hourly value of the ordinate the mean derived

from a consideration of the area included between the curve, the base

line and ordinates at the thirty minutes before and after each hour.

§ 4. Partly on account of the uncertainties due to disturbances, and

partly with a view to economy of labour, it has been the practice at

some observatories to derive diurnal inequalities from a comparatively

small number of undisturbed or quiet days. Beginning with 1890, five

days a month were selected at Greenwich by the astronomer royal as

conspicuously quiet. In the selection regard was paid to the

desirability that the arithmetic mean of the five dates should answer

to near the middle of the month. In some of the other English

observatories the routine measurement of the curves was limited to

these selected quiet days. At Greenwich itself diurnal inequalities

were derived regularly from the quiet days alone and also from all the

days of the month, excluding those of large disturbance. If a quiet

day differed from an ordinary day only in that the diurnal variation

in the latter was partly obscured by irregular disturbances, then

supposing enough days taken to smooth out irregularities, one would

get the same diurnal inequality from ordinary and from quiet days. It

was found, however, that this was hardly ever the case (see §§ 29 and

30). The quiet day scheme thus failed to secure exactly what was

originally aimed at; on the other hand, it led to the discovery of a

number of interesting results calculated to throw valuable sidelights

on the phenomena of terrestrial magnetism.

The idea of selecting quiet days seems due originally to H. Wild. His

selected quiet days for St Petersburg and Pavlovsk were very few in

number, in some months not even a single day reaching his standard of

freedom from disturbance. In later years the International Magnetic

Committee requested the authorities of each observatory to arrange the

days of each month in three groups representing the quiet, the

moderately disturbed and the highly disturbed. The statistics are

collected and published on behalf of the committee, the first to

undertake the duty being M. Snellen. The days are in all cases counted

from Greenwich midnight, so that the results are strictly synchronous.

The results promise to be of much interest.

§ 5. The intensity and direction of the resultant magnetic force at a

spot--i.e. the force experienced by a unit magnetic pole--are known if

we know the three components of force parallel to any set of

orthogonal axes. It is usual to take for these axes the vertical at

the spot and two perpendicular axes in the horizontal plane; the

latter are usually taken in and perpendicular to the geographical

meridian. The usual notation in mathematical work is X to the north, Y

to the west or east, and Z vertically downwards. The international

magnetic committee have recommended that Y be taken positive to the

east, but the fact that the declination is westerly over most of

Europe has often led to the opposite procedure, and writers are not

always as careful as they should be in stating their choice. Apart

from mathematical calculations, the more usual course is to define the

force by its horizontal and vertical components--usually termed H and

V--and by the declination or angle which the horizontal component

makes with the astronomical meridian. The declination is sometimes

counted from 0° to 360°, 0° answering to the case when the so-called

north pole (or north seeking pole) is directed towards geographical

north, 90° to the case when it is directed to the east, and so on. It

is more usual, however, to reckon declination only from 0° to 180°,

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 horizon of the dipping

needle. Instead of H and D some writers make use of N the northerly

component, and W the westerly (or E the easterly). The resultant force

itself is denoted sometimes by R, sometimes by T (total force). The

following relationships exist between the symbols

X [equiv] N, Y [equiv] W or E, Z [equiv] V, R [equiv] T,

H [equiv] [root](X² + Y²), R [equiv] [root](X² + Y² + Z²),

tan D = Y/X, tan I = V/H.

The term _magnetic element_ is applied to R or any of the components,

and even to the angles D and I.

Charts.

§ 6. Declination is the element concerning which our knowledge is most

complete and most reliable. With a good unifilar magnetometer, at a

fixed observatory distant from the magnetic poles, having a fixed mark

of known azimuth, the observational uncertainty in a single observation

should not exceed 0´.5 or at most 1´.0. It cannot be taken for granted

that different unifilars, even by the best makers, will give absolutely

identical values for the declination, but as a matter of fact the

differences observed are usually very trifling. The chief source of

uncertainty in the observation lies in the torsion of the suspension

fibre, usually of silk or more rarely of phosphor bronze or other metal.

A very stout suspension must be avoided at all cost, but the fibre must

not be so thin as to have a considerable risk of breaking even in

skilled hands. Near a magnetic pole the directive force on the

declination magnet is reduced, and the effects of torsion are

correspondingly increased. On the other hand, the regular and irregular

changes of declination are much enhanced. If an observation consisting

of four readings of declination occupies twelve minutes, the chances are

that in this time the range at an English station will not exceed 1´,

whereas at an arctic or antarctic station it will frequently exceed 10´.

Much greater uncertainty thus attaches to declination results in the

Arctic and Antarctic than to those in temperate latitudes. In the case

of secular change data one important consideration is that the

observations should be taken at an absolutely fixed spot, free from any

artificial source of disturbance. In the case of many of the older

observations of which records exist, the precise spot cannot be very

exactly fixed, and not infrequently the site has become unsuitable

through the erection of buildings not free from iron. Apart from

buildings, much depends on whether the neighbourhood is free from

basaltic and other magnetic rocks. If there are no local disturbances of

this sort, a few yards difference is usually without appreciable

influence, and even a few miles difference is of minor importance when

one is calculating the mean secular change for a long period of years.

When, however, local disturbances exist, even a few feet difference in

the site may be important, and in the absence of positive knowledge to

the contrary it is only prudent to act as if the site were disturbed.

Near a magnetic pole the declination naturally changes very rapidly when

one travels in the direction perpendicular to the lines of equal

declination, so that the exact position of the site of observation is

there of special importance.

The usual method of conveying information as to the value of the

declination at different parts of the earth's surface is to draw

curves on a map--the so-called _isogonals_--such that at all points on

any one curve the declination at a given specified epoch has the same

value. The information being of special use to sailors, the

preparation of magnetic charts has been largely the work of naval

authorities--more especially of the hydrographic department of the

British admiralty. The object of the admiralty world charts--four of

which are reproduced here, on a reduced scale, by the kind permission

of the Hydrographer--is rather to show the general features boldly

than to indicate minute details. Apart from the immediate necessities

of the case, this is a counsel of prudence. The observations used have

mostly been taken at dates considerably anterior to that to which the

chart is intended to apply. What the sailor wants is the declination

now or for the next few years, not what it was five, ten or twenty

years ago. Reliable secular change data, for reasons already

indicated, are mainly obtainable from fixed observatories, and there

are enormous areas outside of Europe where no such observatories

exist. Again, as we shall see presently, the rate of the secular

change sometimes alters greatly in the course of a comparatively few

years. Thus, even when the observations themselves are thoroughly

reliable, the prognostication made for a future date by even the most

experienced of chart makers may be occasionally somewhat wide of the

mark. Fig. 1 is a reduced copy of the British admiralty declination

chart for the epoch 1907. It shows the isogonals between 70° N. and

65° S. latitude. Beyond the limits of this chart, the number of exact

measurements of declination is somewhat limited, but the general

nature of the phenomena is easily inferred. The geographical and the

magnetic poles--where the dipping needle is vertical--are fundamental

points. The north magnetic pole is situated in North America near the

edge of the chart. We have no reason to suppose that the magnetic pole

is really a fixed point, but for our present purpose we may regard it

as such. Let us draw an imaginary circle round it, and let us travel

round the circle in the direction, west, north, east, south, starting

from a point where the north pole of a magnet (i.e. the pole which in

Europe or the United States points to the north) is directed exactly

towards the astronomical north. The point we start from is to the

geographical south of the magnetic pole. As we go round the circle the

needle keeps directed to the magnetic pole, and so points first

slightly to the east of geographical north, then more and more to the

east, then directly east, then to south of east, then to due south, to

west of south, to west, to north-west, and finally when we get round

to our original position due north once more. 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.

[Illustration: FIG. 1.--Isogonals, or lines of equal magnetic

declination.]

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 close to this pole will occupy a fixed direction relative to the

ground underneath. Let us draw on the ground through the pole a

straight line parallel to the direction taken there by the compass

needle, and let us carry a compass needle round a _small_ circle whose

centre is the pole. At all points on the circle the positions of the

needle will be parallel; but whereas the north pole of the magnet will

point exactly towards the centre of the circle at one of the points

where the straight line drawn on the ground cuts the circumference, it

will at the opposite end of the diameter point exactly away from the

centre. The former part is clearly on the isogonal where the

declination is 0°, the latter on the isogonal where it is 180°.

Isogonals will thus radiate out from the north geographical pole (and

similarly of course from the south geographical pole) in all

directions. If we travel along an isogonal, starting from the north

magnetic pole, our course will generally take us, often very

circuitously, to the north geographical pole. If, for example, we

select the isogonal of 10° E., we at first travel nearly south, but

then more and more westerly, then north-westerly across the north-east

of Asia; the direction then gets less northerly, and makes a dip to

the south before finally making for the north geographical pole. It is

possible, however, according to the chart, to travel direct from the

north magnetic to the south geographical pole, provided we select an

isogonal answering to a small westerly or easterly declination (from

about 19° W. to 7° E.).

Special interest attaches to the isogonals answering to declination

0°. These are termed _agonic lines_, but sailors often call them

_lines of no variation_, the term _variation_ having at one time been

in common use in the sense of declination. If we start from the north

magnetic pole the agonic line takes us across Canada, the United

States and South America in a fairly straight course to the south

geographical pole. A curve continuous with this can be drawn from the

south geographical to the south magnetic pole at every point of which

the needle points in the geographical meridian; but here the north

pole of the needle is pointing south, not north, so that this portion

of curve is really an isogonal of 180°. In continuation of this there

emanates from the south magnetic pole a second isogonal of 0°, or

agonic line, which traverses Australia, Arabia and Russia, and takes

us to the north geographical pole. Finally, we have an isogonal of

180°, continuous with this second isogonal of 0° which takes us to the

north magnetic pole, from which we started. Throughout the whole area

included within these isogonals of 0° and 180°--excluding locally

disturbed areas--the declination is westerly; outside this area the

declination is in general easterly. There is, however, as shown in the

chart, an isogonal of 0° enclosing an area in eastern Asia inside

which the declination is westerly though small.

§ 7. Fig. 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

lie on curves called _isoclinals_. The dip is northerly (north pole

dips) or southerly (south pole dips) according as the place is north

or south of the isoclinal of 0°. At places actually on this isoclinal

the dipping needle is horizontal. The isoclinal of 0° is nowhere very

far from the geographical equator, but lies to the north of it in Asia

and Africa, and to the south of it in South America. As we travel

north from the isoclinal of 0° along the meridian containing the

magnetic pole the dipping needle's north pole dips more and more,

until when we reach the magnetic pole the needle is vertical. Going

still farther north, we have the dip diminishing. The northerly

inclination is considerably less in Europe than in the same latitudes

of North America; and correspondingly the southerly inclination is

less in South America than in the same latitudes of Africa.

[Illustration: FIG. 2.--Isoclinals, or lines of equal magnetic dip.]

Fig. 3 is a reduced copy of the admiralty horizontal force chart for

1907. The curves, called _isomagnetics_, connect the places where the

horizontal force has the same value; the force is expressed in C.G.S.

units. The horizontal force vanishes of course at the magnetic poles.

The chart shows a maximum value of between 0.39 and 0.40 in an oval

including the south of Siam and the China Sea. The horizontal force is

smaller in North America than in corresponding latitudes in Europe.

[Illustration: FIG. 3.--Isomagnetics, lines of equal horizontal

force.]

Charts are sometimes drawn for other magnetic elements, especially

vertical force (fig. 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 horizontal force. The

total force is least in equatorial regions, where values slightly

under 0.4 C.G.S. are encountered. In the northern hemisphere there are

two distinct maxima of total force. One of these so-called _foci_ is

in Canada, the other in the north-east of Siberia, the former 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 Canadian the other the Siberian focus.

Magnetic Elements and their Secular Change.

§ 8. As already explained, magnetic charts for the world or for large

areas give only a general idea of the values of the elements. If the

region is undisturbed, very fairly approximate values are derivable

from the charts, but when the highest accuracy is necessary the only

thing to do is to observe at the precise spot. In disturbed areas

local values often depart somewhat widely from what one would infer

from the chart, and occasionally there are large differences between

places only a few miles apart. Magnetic observatories usually publish

the mean value for the year of their magnetic elements. It has been

customary for many years to collect and publish these results in the

annual report of the Kew Observatory (Observatory Department of the

National Physical Laboratory). The data in Tables I. and II. are

mainly derived from this source. The observatories are arranged in

order of latitude, and their geographical co-ordinates are given in

Table II., longitude being reckoned from Greenwich. Table I. gives the

mean values of the declination, inclination and horizontal force for

January 1, 1901; they are in the main arithmetic means of the mean

annual values for the two years 1900 and 1901. The mean annual secular

changes given in this table are derived from a short period of

years--usually 1898 to 1903--the centre of which fell at the beginning

of 1901. 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

majority of the stations have declination west and inclination north;

it has thus been convenient to attach the + sign to increasing

westerly (or decreasing easterly) declination and to increasing

northerly (or decreasing southerly) inclination. In other words, in

the case of the declination + means that the north end of the needle

is moving to the west, while in the case of the inclination + means

that the north end (whether the dipping end or not) is moving towards

the nadir. In the case, however, of the vertical force + means simply

_numerical_ increase, irrespective of whether the north or the south

pole dips. The unit employed in the horizontal and vertical force

secular changes is 1[gamma], i.e. 0.00001 C.G.S. Even in the

declination, at the very best observatories, it is hardly safe to

assume that the apparent change from one year to the next is

absolutely truthful to nature. This is especially the case if there

has been any change of instrument or observer, or if any alteration

has been made to buildings in the immediate vicinity. A change of

instrument is a much greater source of uncertainty in the case of

horizontal force or dip than in the case of declination, and dip

circles and needles are more liable to deterioration than

magnetometers. Thus, secular change data for inclination and vertical

force are the least reliable. The uncertainties, of course, are much

less, from a purely mathematical standpoint, for secular changes

representing a mean from five or ten years than for those derived from

successive years' values of the elements. The longer, however, the

period of years, the greater is the chance that one of the elements

may in the course of it have passed through a maximum or minimum

value. This possibility should always be borne in mind in cases where

a mean secular change appears exceptionally small.

[Illustration: FIG. 4.--Isomagnetics, lines of equal vertical force.]

As Tables I. and II. show, the declination needle is moving to the

east all over Europe, and the rate at which it is moving seems not to

vary much throughout the continent. The needle is also moving to the

east throughout the western parts of Asia, the north and east of

Africa, and the east of North America. It is moving to the west in the

west of North America, in South America, and in the south and east of

Asia, including Japan, south-east Siberia, eastern China and most of

India.

§ 9. The information in figs. 1, 2, 3 and 4 and in Tables I. and II.

applies only to recent years. Owing to secular change, recent charts

differ widely from the earliest ones constructed. The first charts

believed to have been constructed were those of Edmund Halley the

astronomer. According to L. A. Bauer,[7] who has made a special study

of the subject, Halley issued two declination charts for the epoch

1700; one, published in 1701, was practically confined to the Atlantic

Ocean, whilst the second, published in 1702, contained also data for

the Indian Ocean and part of the Pacific. These charts showed the

isogonic lines, but only over the ocean areas. Though the charts for

1700 were the first published, there are others which apply to earlier

epochs. W. van Bemmelen[8] has published charts for the epochs 1500,

1550, 1600, 1650 and 1700, whilst H. Fritsche[9] has more recently

published charts of declination, inclination and horizontal force for

1600, 1700, 1780, 1842 and 1915. A number of early declination charts

were given in Hansteen's Atlas and in G. Hellmann's reprints. _Die

Altesten Karten der Isogonen, Isoklinen, Isodynamen_ (Berlin, 1895).

The data for the earlier epochs, especially those prior to 1700, are

meagre, and in many cases probably of indifferent accuracy, so that

the reliability of the charts for these epochs is somewhat open to

doubt.

If we take either Hansteen's or Fritsche's declination chart for 1600

we notice a profound difference from fig. 1. In 1600 the agonic line

starting from the north magnetic pole, after finding its way south to

the Gulf of Mexico, doubled back to the north-east, and passed across

or near Iceland. 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 understood 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 Bond and Halley. The observations from 1787

to 1805 were due to George Gilpin, who published particulars of his

own and the earlier observations in the _Phil. Trans._ for 1806. The

data for 1817 and 1820 were obtained by Col. Mark Beaufoy, at Bushey,

Herts. They seem to come precisely at the time when the needle, which

had been continuously moving to the west since the earliest

observations, began to retrace its steps. The data from 1860 onwards

apply to Kew.

TABLE I.--Magnetic Elements and their Rate of Secular Change for

January 1, 1901.

+----------------+------------------------------+----------------------+

| | Absolute values. | Secular change. |

| Place. +----------+----------+--------+-------+------+-------+

| | D. | I. | H. | D. | I. | H. |

+----------------+----------+----------+--------+-------+------+-------+

| | ° ´ | ° ´ | | ´ | ´ |[gamma]|

| Pavlovsk | 0 39.8E | 70 36.8N | .16553 | - 4.1 | -0.8 | + 7 |

| Ekatarinburg | 10 6.3E | 70 40.5N | .17783 | - 4.6 | +0.5 | -13 |

| Copenhagen | 10 10.4W | 68 38.5N | .17525 | | | |

| Stonyhurst | 18 10.3W | 68 48.0N | .17330 | - 4.0 | | +22 |

| Wilhelmshaven | 12 26.0W | 67 39.7N | .18108 | - 4.1 | -2.1 | +20 |

| Potsdam | 9 54.2W | 66 24.5N | .18852 | - 4.2 | -1.6 | +16 |

| Irkutsk | 2 1.0E | 70 15.8N | .20122 | + 0.5 | +1.6 | -14 |

| de Bilt | 13 48.3W | 66 55.5N | .18516 | - 4.4 | -2.2 | +14 |

| Kew | 16 50.8W | 67 10.6N | .18440 | - 4.2 | -2.2 | +25 |

| Greenwich | 16 27.5W | 67 7.3N | .18465 | - 4.0 | -2.2 | +23 |

| Uccle | 14 11.0W | 66 8.8N | .18954 | - 4.2 | -2.1 | +23 |

| Falmouth | 18 27.3W | 66 44.0N | .18705 | - 3.8 | -2.7 | +26 |

| Prague | 9 4.4W | | .19956 | - 4.4 | | +20 |

| St Helier | 16 58.1W | 65 44.1N | | - 3.5 | -2.7 | |

| Parc St Maur | 14 43.4W | 64 52.3N | .19755\| - 4.0 | -2.2 | +23 |

| Val Joyeux | 15 13.7W | 65 0.0N | .19670/| | | |

| Munich | 10 25.8W | 63 18.1N | .20629 | - 4.8 | -2.7 | +21 |

| O'Gyalla | 7 26.1W | | .21164 | - 4.8 | | +13 |

| Pola | 9 22.7W | 60 14.5N | .22216 | - 4.0 | | +23 |

| Toulouse | 14 16.4W | 60 55.9N | .21945 | - 3.9 | -2.5 | +25 |

| Perpignan | 13 34.7W | 59 57.6N | .22453 | | | |

| Capo di Monte | 9 8.0W | 56 22.3N | | - 5.2 | -2.3 | |

| Madrid | 15 39.0W | | | | | |

| Coimbra | 17 18.1W | 59 22.0N | .22786 | - 3.7 | -4.3 | +34 |

| Lisbon | 17 15.7W | 57 53.0N | .23548 | | | |

| Athens | 5 38.2W | 52 7.5N | .26076 | | | |

| San Fernando | 15 57.5W | 55 8.8N | .24648 | | | |

| Tokyo | 4 34.9W | 49 0.3N | .29932 | | | |

| Zi-ka-wei | 2 23.5W | 45 43.5N | .32875 | + 1.5 | -1.5 | +37 |

| Helwan | 3 39.7W | 40 30.8N | .30136 | - 7.0 | -0.4 | - 7 |

| Hong-Kong | 0 17.5E | 31 22.8N | .36753 | + 1.8 | -4.3 | +45 |

| Kolaba | 0 23.2E | 21 26.5N | .37436 | + 2.2 | +7.0 | - 9 |

| Manila | 0 52.2E | 16 13.5N | .38064 | + 0.1 | -5.3 | +47 |

| Batavia | 1 7.3E | 30 35.5S | .36724 | + 3.0 | -7.3 | -11 |

| Mauritius | 9 25.2W | 54 9.4S | .23820 | - 4.7 | +4.6 | -39 |

| Rio de Janeiro | 8 2.9W | 13 20.1S | .2501 | +10.4 | -2.3 | |

| Melbourne | 8 25.6E | 67 24.6S | .23295 | | | |

+----------------+----------+----------+--------+-------+------+-------+

The rate of movement of the needle to the east at London--and

throughout Europe generally--fell off markedly subsequent to 1880. The

change of declination in fact between 1880 and 1895 was only about 75%

of that between 1865 and 1880, and the mean annual change from 1895 to

1900 was less than 75% of the mean annual change of the preceding

fifteen years. Thus in 1902 it was at least open to doubt whether a

change in the sign of the secular change were not in immediate

prospect. Subsequent, however, to that date there was little further

decline in the rate of secular change, and since 1905 there has been

very distinct acceleration. Thus, if we derive a mean value from the

eighteen European stations for which declination secular changes are

given in Tables I. and II. we find

mean value from table I. -4.18

" " " " II. -5.21

The epoch to which the data in Table II. refer is somewhat variable,

but is in all cases more recent than the epoch, January 1, 1901, for

Table I., the mean difference being about 5 years.

§ 10. 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 Rome resembled those at Paris and London, but

the extreme westerly position is believed to have been attained

earlier. The rate of change near the turning point seems to have been

very slow, and as no fixed observatories existed in those days, the

precise time of its occurrence is open to some doubt.

Perhaps the most complete observations extant as to the declination

phenomena near a turning point relate to Kolaba observatory at Bombay;

they were given originally by N. A. F. Moos,[11] the director of the

observatory. Some of the more interesting details are given in Table

IV.; here W denotes movement to be west, and so answers to a numerical

diminution in the declination, which is easterly.

Prior to 1880 the secular change at Kolaba was unmistakably to the

east, and subsequent to 1883 it was clearly to the west; but between

these dates opinions will probably differ as to what actually

happened. The fluctuations then apparent in the sign of the annual

change may be real, but it is at least conceivable that they are of

instrumental origin. From 1870 to 1875 the mean annual change was

-1´.2; from 1885 to 1890 it was +1´.5, from 1890 to 1895 it was +2´.0,

while from 1895 to 1905 it was +2´.35, the + sign denoting movement to

the west. 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.

Beattie's _Magnetic Survey of South Africa_ the movement to the west

ceased shortly after 1870. A persistent movement to the east then set

in, the mean annual change increasing from 1´.8 between 1873 and 1890

to 3´.8 between 1890 and 1900.

§ 11. Secular changes of declination have been particularly

interesting in the United States, an area about which information is

unusually complete, thanks to the labours and publications of the

United States Coast and Geodetic Survey.[13] At present the agonic

line passes in a south-easterly direction from Lake Superior to South

Carolina. To the east of the agonic line the declination is westerly,

and to the west it is easterly. In 1905 the declination varied from

about 21° W. in the extreme north-east to about 24° E. in the extreme

north-west. At present the motion of the agonic line seems to be

towards the west, but it is very slow. To the east of the agonic line

westerly declination is increasing, and to the west of the line, with

the exception of a narrow strip immediately adjacent to it, easterly

declination is increasing. The phenomena in short suggest a motion

southwards in the north magnetic pole. Since 1750 declination has

always been westerly in the extreme east of the States, and always

easterly in the extreme west, but the position of the agonic line has

altered a good deal. It was to the west of Richmond, Virginia, from

1750 to about 1772, then to the east of it until about 1838 when it

once more passed to the west; since that time it has travelled farther

to the west. Table VI. is intended to show the nature of the secular

change throughout the whole country. As before, + denotes that the

north pole of the magnet is moving to the west,--that it is moving to

the east.

The data in Table VI. represent the mean change of declination per

annum, derived from the period (ten years, except for 1900-1905) which

ended in the year put at the top of the column. The stations are

arranged in four groups, the first group representing the extreme

eastern, the last group the extreme western states, the other two

groups being intermediate. In each group the stations are arranged, at

least approximately, in order of latitude. The data are derived from

the values of the declination given in the Geodetic Survey's _Report_

for 1906, appendix 4, and _Magnetic Tables and Magnetic Charts_ by L.

A. 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 1670 in New Jersey and about

1675 in Maryland. They suggest that this maximum was experienced all

along the Atlantic border some time in the 17th century, but earlier

in the extreme north-east than in New York or Maryland.

Examination of Table VI. shows that the needle continued to move to

the east for some time after 1750 even in the Eastern States. But the

rate of movement was clearly diminishing, and about 1765 the extreme

easterly position was reached in Eastport, Maine, the needle then

beginning to retrace its steps to the west. The phenomena visible at

Maine are seen repeating themselves at places more and more to the

west, in Boston about 1785, in Albany about 1800, in Washington, D.C.,

about 1805, in Columbus (Ohio) about 1815, in Montgomery (Alabama)

about 1825, in Bloomington (Ill.) about 1830, in Des Moines (Iowa)

about 1840, in Santa Rosa (New Mexico) about 1860 and in Salt Lake

about 1870. In 1885 the needle was moving to the west over the whole

United States with the exception of a comparatively narrow strip along

the Pacific coast. Even an acute observer would have been tempted to

prophesy in 1885 that at no distant date the secular change would be

pronouncedly westerly right up to the Pacific. 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 lay to the east of a line drawn from the west end of

Lake Superior to the west of Georgia. If we take a station like Little

Rock (Arkansas), we have the secular change to the west lasting for

about sixty years. Further west the period shortens. At Pueblo

(Colorado) it is about forty years, at Salt Lake under thirty years,

at Prescott (Arizona) about twenty years. Considering how fast the

area throughout which the secular change is easterly has extended to

the east since 1885, one would be tempted to infer that at no distant

date it will include the whole of the United States. In the extreme

north-east, however, the movement of the needle to the west, which had

slackened perceptibly after 1860 or 1870, is once more accelerating.

Thus the auspices do not all point one way, and the future is as

uncertain as it is interesting.

TABLE II.--Recent Values of the Magnetic Elements and their Rate of

Secular Change.

+----------------+-----------------------+----------------------------------------------+-----------------------------------

| Place. +-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+

| | 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 |

| (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 |

| (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 |

| (Kansas) | 38 47N | 95 10W | 1906 | 8 30.1E | 68 45.1N | .21807 | .56081 | 4 | -1.7 | +1.8 | -36 | - 8 |

| (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 |

| (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 |

| (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 | | | | | |

| N.Z. | 43 32S | 172 37E | 1903 |16 18.4E | 67 42.3S | .22657 | .55259 | | | | | |

+----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+

TABLE III.--Declination at London.

+-------+--------------+-------+--------------+-------+--------------+

+-------+--------------+-------+--------------+-------+--------------+

| | ° ´ | | ° ´ | | ° ´ |

| 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. |

+--------+-------------+--------+-------------+

+--------+-------------+--------+-------------+

| | ° ´ | | ° ´ |

| 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 | | | | | | | | |

+------+-------+------+---------+------+---------+--------+------+---------+--------+

[Illustration: FIG. 5.]

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).

+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+

+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+

| 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.)

+--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+

+--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+

| 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. |

+--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+

| 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]).

+--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+

+--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+

| 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.

Encyclopaedia Britannica, 11th Edition, "McKinley, William" to "Magnetism, Terrestrial" Volume 17, Slice 3 · 第 43 / 45 章

An event of the first importance was the discovery made in 1819 by H. C.