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-calledisogonals—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.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 asmallcircle 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 termedagonic lines, but sailors often call themlines of no variation, the termvariationhaving 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 calledisoclinals. 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 correspondinglythe southerly inclination is less in South America than in the same latitudes of Africa.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, calledisomagnetics, 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.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-calledfociis 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 thesefocithroughout a considerable area to the south of Australia. In the northern hemisphere the lines of equal total force—calledisodynamiclines—form two sets more or less distinct, consisting of closed ovals, one set surrounding the Canadian the other the Siberian focus.§ 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 necessaryMagnetic Elements and their Secular Change.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 differencesbetween 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 simplynumericalincrease, irrespective of whether the north or the south pole dips. The unit employed in the horizontal and vertical force secular changes is 1γ,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.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,7who 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 Bemmelen8has published charts for the epochs 1500, 1550, 1600, 1650 and 1700, whilst H. Fritsche9has 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,10may 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 thePhil. 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.Place.Absolute values.Secular change.D.I.H.D.I.H.° ′° ′′′γPavlovsk0 39.8E70 36.8N.16553− 4.1−0.8+ 7Ekatarinburg10 6.3E70 40.5N.17783− 4.6+0.5−13Copenhagen10 10.4W68 38.5N.17525Stonyhurst18 10.3W68 48.0N.17330− 4.0+22Wilhelmshaven12 26.0W67 39.7N.18108− 4.1−2.1+20Potsdam9 54.2W66 24.5N.18852− 4.2−1.6+16Irkutsk2 1.0E70 15.8N.20122+ 0.5+1.6−14de Bilt13 48.3W66 55.5N.18516− 4.4−2.2+14Kew16 50.8W67 10.6N.18440− 4.2−2.2+25Greenwich16 27.5W67 7.3N.18465− 4.0−2.2+23Uccle14 11.0W66 8.8N.18954− 4.2−2.1+23Falmouth18 27.3W66 44.0N.18705− 3.8−2.7+26Prague9 4.4W.19956− 4.4+20+20St Helier16 58.1W65 44.1N− 3.5−2.7Parc St Maur14 43.4W64 52.3N.19755− 4.0−2.2+23Val Joyeux15 13.7W65 0.0N.19670Munich10 25.8W63 18.1N.20629− 4.8−2.7+21O’Gyalla7 26.1W.21164− 4.8+13Pola9 22.7W60 14.5N.22216− 4.0+23Toulouse14 16.4W60 55.9N.21945− 3.9−2.5+25Perpignan13 34.7W59 57.6N.22453Capo di Monte9 8.0W56 22.3N− 5.2−2.3Madrid15 39.0WCoimbra17 18.1W59 22.0N.22786− 3.7−4.3+34Lisbon17 15.7W57 53.0N.23548Athens5 38.2W52 7.5N.26076San Fernando15 57.5W55 8.8N.24648Tokyo4 34.9W49 0.3N.29932Zi−ka−wei2 23.5W45 43.5N.32875+ 1.5−1.5+37Helwan3 39.7W40 30.8N.30136− 7.0−0.4− 7Hong−Kong0 17.5E31 22.8N.36753+ 1.8−4.3+45Kolaba0 23.2E21 26.5N.37436+ 2.2+7.0− 9Manila0 52.2E16 13.5N.38064+ 0.1−5.3+47Batavia1 7.3E30 35.5S.36724+ 3.0−7.3−11Mauritius9 25.2W54 9.4S.23820− 4.7+4.6−39Rio de Janeiro8 2.9W13 20.1S.2501+10.4−2.3Melbourne8 25.6E67 24.6S.23295The 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 findmean value from tableI.−4.18” ” ” ”II.−5.21The 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,11the 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,12both 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’sMagnetic Survey of South Africathe 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.13At 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’sReportfor 1906, appendix 4, andMagnetic Tables and Magnetic Chartsby 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 theReport of the Coast and Geodetic Surveyfor 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.Geographical position.Absolute Values of Elements.Secular change (mean per annum).Latitude.Longitude.Year.D.I.H.V.Intervalin years.D.I.H.V.° ′° ′° ′° ′′′Pavlovsk59 41N30 29E19061 4.2E70 36.6N.16528.469635−4.5+0.1− 6−14Sitka (Alaska)57 3N135 20W190630 3.3E74 41.7N.15502.566464−3.0−1.6+18−38Ekatarinburg56 49N60 38E190610 31.0E70 49.5N.17664.507965−4.5+1.7−23+18Rude Skov (Copenhagen)55 51N12 27E19089 43.3W68 45N.17406.44759Stonyhurst53 51N2 28W190917 28.6W68 42.8N.17424.447225−5.9−1.1+ 6−25Hamburg53 33N9 59E190311 10.2W67 23.5N.18126.43527Wilhelmshaven53 32N8 9E190911 46.8W.181295−5.2− 7Potsdam52 23N13 4E19099 10.6W66 20.0N.18834.429715−5.8+0.1− 9−19Irkutsk52 16N104 16E19051 58.1E70 25.0N.20011.562505+0.6+2.0−24+39de Bilt52 5N5 11E190713 19.0W66 49.9N.18559.433685−4.7−0.6+ 2−16Valencia51 56N10 15W190920 50.3W68 15.1N.17877.448125−5.0−1.2+ 7−25Kew51 28N0 19W190916 10.8W66 59.7N.18506.435885−5.4−1.1+ 2−35Greenwich51 28N0 0190915 47.6W66 53.9N.18526.434325−5.5−0.7+ 1−20Uccle50 48N4 21E190813 36.7W66 1.6N.19061.428674−5.3−0.8− 3−35Falmouth50 9N5 5W190917 48.4W66 30.6N.18802.432665−4.7−1.4+ 9−30Prague50 5N14 25E19088 20.9W5−6.5Cracow50 4N19 58E19095 35.1W64 18N3−7.3St Helier49 12N2 5W190716 27.4W65 34.5N5−5.3−1.2Val Joyeux48 49N2 1E190914 32.9W64 43.9N.19727.417925−5.4−1.7+ 1−51Vienna48 15N16 21E18988 24.1WMunich48 9N11 37E19069 59.5W63 10.0N.20657.408355−4.8−1.3+ 4−31O’Gyalla47 53N18 12E19096 43.9W.210945−5.0−10Odessa46 26N30 46E18994 36.7W62 18.2N.21869.41660Pola44 52N15 51E19088 43.2W60 6.8N.22207.386405−5.5−0.6− 4−23Agincourt (Toronto)43 47N79 16W19065 45.3W74 35.6N.16397.595024+3.4+0.9−23−24Nice43 43N7 16E189912 4.0W60 11.7N.22390.39087Toulouse43 37N1 28E190513 56.3W60 49.1N.22025.394395−4.5−1.5+ 2− 2Perpignan42 42N2 53E190713 4.4W7−4.7Tiflis41 43N44 48E19052 41.6E56 2.8N.25451.377997−5.2+1.7−26+ 2Capo di Monte40 52N14 15E19068 40.3W56 13.5N5−5.1−1.5Madrid40 25N3 40W190115 35.6WCoimbra40 12N8 25W190816 46.2W58 57.3N.22946.381205−4.6−2.9+17−45Baldwin (Kansas)38 47N95 10W19068 30.1E68 45.1N.21807.560814−1.7+1.8−36− 8Cheltenham(Maryland)38 44N76 50W19065 22.0W70 27.3N.20035.564364+3.8+1.2−38−45Lisbon38 43N9 9W190017 18.0W57 54.8N.23516.37484Athens37 58N21 23E19084 52.9W52 11.7N.26197.336135−5.5San Fernando36 28N6 12W190815 25.6W54 48.4N.24829.352065−4.6−2.8+26−24Tokyo35 41N139 45E19014 36.1W49 0.0N.29954.34459Zi-ka-wei31 12N121 26E19062 32.0W45 35.3N.33040.337265+1.5−1.3+30+ 6Dehra Dun30 19N78 3E19072 38.3E43 36.1N.33324.317364+0.8+5.5−26+77Helwan29 52N31 21E19092 49.2W40 40.4N.30031.258045−5.7+1.2− 6+13Havana23 8N82 25W19052 25.0E52 57.4N.30531.40452Barrackpore22 46N88 22E19071 9.9E30 30.2N.37288.219673+4.2+3.4+21+62Hong-Kong22 18N114 10E19080 3.9E31 2.5N.37047.222925+1.9−1.8+43− 1Honolulu21 19N158 4W19069 21.7E40 1.8N.29220.245454−0.9−3.2−19−62Kolaba18 54N72 49E19050 14.0E21 58.5N.37382.150845+2.1+7.2−11+86Alibagh18 39N72 52E19091 0.3E23 29.0N.36845.160083+1.7+6.8−10+82Vieques (Porto Rico)18 9N65 26W19061 33.2W49 47.7N.28927.342242+7.2+6.8−49+66Manila14 35N120 59E19040 51.4E16 0.2N.38215.109605+0.1−3.9+47−34Kodaikanal10 14N77 28E19070 40.7W3 27.2N.37431.022594+4.3+5.5+16+61Batavia6 11S106 49E19060 54.1E30 48.5S.36708.218894+2.1−7.7− 2+110Dar es Salaam6 49S39 18E19037 35.2WMauritius20 6S57 33E19089 14.3W53 44.9S.23415.319325−0.3+2.9−53−131Rio de Janeiro22 55S43 11W19068 55.5W13 57.1S.24772.061645+9.1−6.8−42+44Santiago (Chile)33 27S70 42W190614 18.7E30 11.8S3+6.1+9.9Melbourne37 50S144 58E19018 26.7E67 25.0S.23305.56024Christchurch, N.Z.43 32S172 37E190316 18.4E67 42.3S.22657.55259Table III.—Declination at London.Date.Declination.Date.Declination.Date.Declination.° ′° ′° ′158011 15E177321 9W186021 38.9W16226 0178723 19186520 58.716344 6179523 57187020 18.316570 0180224 6187519 35.616651 22W180524 8188018 52.116722 30181724 36188518 19.216926 0181824 38189017 50.6172314 17181924 36189517 16.8174817 40182024 34190016 52.7190516 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 data14are 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. Theearlier 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 22γ 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:—IHFrom Table I.−2′.35+21.0γFrom Table II.−1.12+1.6γThe 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.DeclinationEast.Change sinceprevious year.Year.DeclinationEast.Change sinceprevious year.° ′ ″′ ″° ′ ″′ ″18760 55 580 37 E18810 57 120 3 E187756 390 41 E18820 56 500 22 W187857 60 27 E188357 20 12 E187957 300 24 E188455 391 23 W188057 90 21 W188555 30 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 island longitude λ is given by an expression of the type c + a(l − l0) + b(λ − λ0), where a, b, c are constants, l0and λ0, 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. Schmidt15as applicable to Northern Europe for the period 1890 to 1900. ΔD, ΔI and ΔH represent the mean annual changes during this period in westerly declination, in inclination and in horizontal force:—′′′ΔD =−5.24− 0.071 (l − 50)+ 0.033 (λ − 10),ΔI =−1.58+ 0.010 (l − 50)+ 0.036 (λ − 10),ΔH =+23.5− 0.59 (l − 50)− 0.35 (λ − 10).Longitude λ 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 1γ. 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 − l0and λ − λ0have also been used,e.g., by A. Tanakadate in the Magnetic Survey of Japan.Table V.—Declination at St Helena and Cape of Good Hope.St Helena.Cape of Good Hope.Date.Declination.Date.Declination.° ′° ′16107 13 E16050 30 E16770 4016090 12 W16911 0 W16758 1417247 30169111 0177512 18177521 14178915 30179224 31179615 48181826 31180617 18183929 9183922 17184229 6184022 53184629 9184623 11185029 19189023 57185729 34187430 4189029 32190328 44Table VI.—Secular Change of Declination in the United States (+ to the West).Place.Epoch17607080901800102030405060708090190050′′′′′′′′′′′′′′′′Eastport, Maine−1.20.0+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+2.4Boston, Mass.−2.7−1.9−1.00.0+1.1+1.9+2.7+3.5+4.2+4.4+4.0+3.3+3.1+3.0+3.2+3.4Albany, 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+3.6Philadelphia, 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+3.4Baltimore, Maryland−3.9−3.4−2.7−2.0−0.90.0+0.9+2.0+2.7+3.4+3.9+4.0+3.9+3.6+3.5+3.2Richmond, Virginia−3.6−3.2−2.5−1.8−0.90.0+0.9+1.8+2.5+3.1+3.6+3.9+3.8+3.7+3.4+3.2Columbia, 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+1.8Macon, Georgia−3.7−3.6−3.2−2.5−1.8−0.90.0+0.9+1.8+2.5+3.2+3.6+3.9+3.5+3.1+1.2Tampa, 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+1.6Marquette, Michigan0.0+1.4+2.6+3.7+4.7+5.1+4.9+3.8+2.4Columbus, Ohio−0.90.0+0.9+2.0+2.9+3.4+3.6+3.7+3.9+4.0+2.4Bloomington, Illinois−2.4−1.5−0.4+0.4+1.5+2.4+2.8+4.2+3.9+2.9+1.0Lexington, Kentucky−0.90.0+0.9+1.8+2.5+3.2+3.6+3.8+3.8+3.4+1.8Chattanooga, Tennessee−0.90.0+0.9+1.8+2.5+3.2+3.6+4.0+3.5+3.1+1.6Little Rock, Arkansas−2.3−1.5−0.9+0.1+0.8+1.7+2.0+3.6+3.7+2.3−1.2Montgomery, 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+0.2Alexandria, Louisiana−2.1−1.6−0.8+0.1+0.8+1.6+2.2+3.6+3.3+2.0−1.4Northome, Minnesota−1.7−0.6+0.6+1.7+2.8+4.2+4.4+3.50.0Jamestown, N. Dakota+1.0+1.9+3.1+4.8+1.9−2.2Des Moines, Iowa−1.5−0.6+0.6+1.5+2.5+3.8+4.5+2.7−0.6Douglas, Wyoming−0.80.0+1.2+2.3+0.5−1.6Emporia, Kansas+0.6+1.6+2.7+3.8+1.7−1.8Pueblo, Colorado−0.3+0.4+1.5+3.1+0.7−2.2Okmulgee, Oklahoma+0.9+1.5+2.7+3.9+1.4−2.4Santa Rosa, New Mexico−0.4+0.4+1.4+2.6+0.4−2.4San Antonio, Texas−1.1−0.5−0.5+1.1+1.8+2.7+0.9−2.4Seattle, Washington−3.3−3.5−3.7−3.7−3.5−3.3−3.0−2.6−2.1−1.3−1.9−2.0−3.2Wilson Creek, Washington−2.1−1.5−0.4−1.0−1.6−3.2Detroit, Oregon−3.8−3.9−3.9−3.7−3.4−2.9−2.5−1.8−0.8−1.8−3.8Salt Lake, Utah−1.1−0.4+1.0+1.0−0.8−2.8Prescott, Arizona−1.4−0.7+0.4+0.4−1.2−3.2San José, California−2.6−2.9−2.9−2.9−2.7−2.5−2.3−2.0−1.5−0.8−0.4−1.9−3.8Los 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
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-calledisogonals—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.
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 asmallcircle 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 termedagonic lines, but sailors often call themlines of no variation, the termvariationhaving 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 calledisoclinals. 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 correspondinglythe southerly inclination is less in South America than in the same latitudes of Africa.
Fig. 3 is a reduced copy of the admiralty horizontal force chart for 1907. The curves, calledisomagnetics, 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.
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-calledfociis 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 thesefocithroughout a considerable area to the south of Australia. In the northern hemisphere the lines of equal total force—calledisodynamiclines—form two sets more or less distinct, consisting of closed ovals, one set surrounding the Canadian the other the Siberian focus.
§ 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 necessaryMagnetic Elements and their Secular Change.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 differencesbetween 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 simplynumericalincrease, irrespective of whether the north or the south pole dips. The unit employed in the horizontal and vertical force secular changes is 1γ,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.
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,7who 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 Bemmelen8has published charts for the epochs 1500, 1550, 1600, 1650 and 1700, whilst H. Fritsche9has 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,10may 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 thePhil. 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.
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
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,11the 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,12both 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’sMagnetic Survey of South Africathe 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.13At 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’sReportfor 1906, appendix 4, andMagnetic Tables and Magnetic Chartsby 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 theReport of the Coast and Geodetic Surveyfor 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.
Table III.—Declination at London.
§ 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 data14are 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. Theearlier 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 22γ 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:—
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).
§ 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 island longitude λ is given by an expression of the type c + a(l − l0) + b(λ − λ0), where a, b, c are constants, l0and λ0, 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. Schmidt15as applicable to Northern Europe for the period 1890 to 1900. ΔD, ΔI and ΔH represent the mean annual changes during this period in westerly declination, in inclination and in horizontal force:—
Longitude λ 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 1γ. 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 − l0and λ − λ0have 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.
Table VI.—Secular Change of Declination in the United States (+ to the West).