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 to altitude. He considered the agreement not satisfactory. It must be remembered that the Gaussian analysis, especially when only lower order terms are retained, applies only to the earth’s field freed from local disturbances. Now observations at individual high level stations may be seriously influenced not merely by regional disturbances common to low level stations, but by magnetic material in the mountain itself. A method of arriving at the vertical change in the elements, which theoretically seems less open to criticism, has been employed by A. Tanakadate. If we assume that a potential exists, or if admitting the possibility of earth-air currents we assume their effort negligible, we have dX/dz = dZ/dx, dY/dz = dZ/dy. Thus from the observed rates of change of the vertical component of force along the parallels of latitude and longitude, we can deduce the rate of change in the vertical direction of the two rectangular components of horizontal force, and thence the rates of change of the horizontal force and the declination. Also we have dZ/dz = 4 − (dX/dx + dY/dy), where represents the density of free magnetism at the spot. The spot being above ground we may neglect, and thus deduce the variation in the vertical direction of the vertical component from the observed variations of the two horizontal components in their own directions. Tanakadate makes a comparison of the vertical variations of the magnetic elements calculated in the two ways, not merely for Japan, but also for Austria-Hungary and Great Britain. In each country he took five representative points, those for Great Britain being the central stations of five of Rücker and Thorpe’s districts. Table XLVII. gives the mean of the five values obtained. By method (i.) is meant the formula involving 3h/R, by method (ii.) Tanakadate’s method as explained above. H, V, D, and I are used as defined in § 5. In the case of H and V unity represents 1.

—Change per Kilometre of Height.

The − sign in Table XLVII. denotes a decrease in the numerical values of H, V and I, and a diminution in westerly declination. If we except the case of the westerly component of force—not shown in the table—the accordance between the results from the two methods in the case of Japan is extraordinarily close, and there is no very marked tendency for the one method to give larger values than the other. In the case of Great Britain and Austria the differences between the two sets of calculated values though not large are systematic, the 3h/R formula invariably showing the larger reduction with altitude in both H and V. Tanakadate was so satisfied with the accordance of the two methods in Japan, that he employed his method to reduce all observed Japanese values to sea-level. At a few of the highest Japanese stations the correction thus introduced into the value of H was of some importance, but at the great majority of the stations the corrections were all insignificant.

§ 53. Schuster has calculated a potential analogous to the Gaussian potential, from which the regular diurnal changes of the magnetic elements all over the earth may be derived. From the mean summer and winter diurnal variations of the northerly and easterly components of force during

1870 at St Petersburg, Greenwich, Lisbon and Bombay, he found the values of 8 constants analogous to Gaussian constants; and from considerations as to the hours of occurrence of the maxima and minima of vertical force, he concluded that the potential, unlike the Gaussian, must proceed in positive powers of r, and so answer to forces external to the earth. Schuster found, however, that the calculated amplitudes of the diurnal vertical force inequality did not accord well with observation; and his conclusion was that while the original cause of the diurnal variation is external, and consists probably of electric currents in the atmosphere, there are induced currents inside the earth, which increase the horizontal components of the diurnal inequality while diminishing the vertical. The problem has also been dealt with by H. Fritsche, who concludes, in opposition to Schuster, that the forces are partly internal and partly external, the two sets being of fairly similar magnitude. Fritsche repeats the criticism (already made in the last edition of this encyclopaedia) that Schuster’s four stations were too few, and contrasts their number with the 27 from which his own data were derived. On the other hand, Schuster’s data referred to one and the same year, whereas Fritsche’s are from epochs varying from 1841 to 1896, and represent in some cases a single year’s observations, in other cases means from several years. It is clearly desirable that a fresh calculation should be made, using synchronous data from a considerable number of well distributed stations; and it should be done for at least two epochs, one representing large, the other small sun-spot frequency. The year 1870 selected by Schuster had, as it happened, a sun-spot frequency which has been exceeded only once since 1750; so that the magnetic data which he employed were far from representative of average conditions.

§ 54. It was discovered by Folgheraiter that old vases from Etruscan and other sources are magnetic, and from combined observation and experiment he concluded that they acquired their magnetization when cooling after being baked, and retained it unaltered. From experiments, he derived

formulae connecting the magnetization shown by new clay vases with their orientation when cooling in a magnetic field, and applying these formulae to the phenomena observed in the old vases he calculated the magnetic dip at the time and place of manufacture. His observations led him to infer that in Central Italy inclination was actually southerly for some centuries prior to 600, when it changed sign. In 400 it was about 20°N.; since 100  the change has been relatively small. L. Mercanton similarly investigated the magnetization of baked clay vases from the lake dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800 The results he obtained were, however, closely similar to those observed in recent vases made where the inclination was about 63°N., and he concluded in direct opposition to Folgheraiter that inclination in southern Europe has not undergone any very large change during the last 2500 years. Folgheraiter’s methods have been extended to natural rocks. Thus B. Brunhes found several cases of clay metamorphosed by adjacent lava flows and transformed into a species of natural brick. In these cases the clay has a determinate direction of magnetization agreeing with that of the volcanic rock, so it is natural to assume that this direction coincided with that of the dip when the lava flow occurred. In drawing inferences, allowance must of course be made for any tilting of the strata since the volcanic outburst. From one case in France in the district of St Flour, where the volcanic action is assigned to the Miocene Age, Brunhes inferred a southerly dip of some 75°. Until a variety of cases have been critically dealt with, a suspension of judgment is advisable, but if the method should establish its claims to reliability it obviously may prove of importance to geology as well as to terrestrial magnetism.

§ 55. Magnetic phenomena in the polar regions have received considerable attention of late years, and the observed results are of so exceptional a character as to merit separate consideration. One feature, the large amplitude of the regular diurnal inequality, is already illustrated by the data for Jan

Mayen and South Victoria Land in Tables VIII. to XI. In the case, however, of declination allowance must be made for the small size of H. If a force F perpendicular to the magnetic meridian causes a change D in D then D = F/H. Thus at the “Discovery’s” winter quarters in South Victoria Land, where the value of H is only about 0.36 of that at Kew, a change of 45′ in D would be produced by a force which at Kew would produce a change of only 16′. Another feature, which, however, may not be equally general, is illustrated by the data for Fort Rae and South Victoria Land in Table XVII. It will be noticed that it is the 24-hour term in the Fourier analysis of the regular diurnal inequality which is specially enhanced. The station in South Victoria Land—the winter quarters of the “Discovery” in 1902–1904—was at 77° 51′ S. lat.; thus the sun did not set from November to February (midsummer), nor rise from May to July (midwinter). It might not thus have been surprising if there had been an outstandingly large seasonal variation in the type of the diurnal inequality. As a matter of fact, however, the type of the inequality showed exceptionally small variation with the season, and the amplitude remained large throughout the whole year. Thus, forming diurnal inequalities for the three midsummer months and for the three midwinter months, we obtain the following amplitudes for the range of the several elements :—

The most outstanding phenomenon in high latitudes is the frequency and large size of the disturbances. At Kew, as we saw in § 25, the absolute range in D exceeds 20′ on only 12% of the total number of days. But at the “Discovery’s” winter quarters, about sun-spot minimum, the range exceeded 1° on 70%, 2° on 37%, and 3° on fully 15% of the total number of days. One day in 25 had a range exceeding 4°. During the three midsummer months, only one day out of 111 had a range under 1°, and even at midwinter only one day in eight had a range as small as 30′. The H range at the “Discovery’s” station exceeded 100 on 40% of the days, and the V range exceeded 100 on 32% of the days.

The special tendency to disturbance seen in equinoctial months in temperate latitudes did not appear in the “Discovery’s” records in the Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days, but on 40% of midsummer days. The preponderance of large movements at midsummer was equally apparent in the other elements. Thus the percentage of days having a V range over 200 was 21 at midsummer, as against 3 in the four equinoctial months.

At the “Discovery’s” station small oscillations of a few minutes’ duration were hardly ever absent, but the character of the larger disturbances showed a marked variation throughout the 24 hours.