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 tropical stations, an inadequate idea of the importance of the lunar influence. In January Figee finds for the range of the lunar diurnal inequality 0′.62 in D, 3.1 in H and 3.5 in V, whereas the corresponding ranges in June are only 0′.13, 1.1 and 2.2 respectively. The difference between summer and winter is essentially due to solar action, thus the lunar influence on terrestrial magnetism is clearly a somewhat complex phenomenon. From a study of Trivandrum data, Broun concluded that the action of the moon is largely dependent on the solar hour at the time, being on the average about twice as great for a day hour as for a night hour. Figee’s investigations at Batavia point to a similar conclusion. Following a method suggested by Van der Stok, Figee arrives at a numerical estimate of the “lunar activity” for each hour of the solar day, expressed in terms of that at noon taken as 100. In summer, for instance, in the case of D he finds the “activity” varying from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in the case of H are 139 at 10 a.m. and 54 at 6 a.m.

.—Lunar Diurnal Inequality at Batavia in Winter and Summer.

The question whether lunar influence increases with sun-spot frequency is obviously of considerable theoretical interest. Balfour Stewart in the 9th edition of this encyclopaedia gave some data indicating an appreciably enhanced lunar influence at Trivandrum during years of sun-spot maximum, but he hesitated to accept the result as finally proved. Figee recently investigated this point at Batavia, but with inconclusive results. Attempts have also been made to ascertain how lunar influence depends on the moon’s declination and phase, and on her distance from the earth. The difficulty in these investigations is that we are dealing with a small effect, and a very long series of data would be required satisfactorily to eliminate other periodic influences.

§ 41. From an analysis of seventeen years data at St Petersburg and Pavlovsk, Leyst concluded that all the principal planets sensibly influence the earth’s magnetism. According to his figures, all the planets except Mercury—whose influence he found opposite to that of the others—when

nearest the earth tended to deflect the declination magnet at St Petersburg to the west, and also increased the range of the diurnal inequality of declination, the latter effect being the more conspicuous. Schuster, who has considered the evidence advanced by Leyst from the mathematical standpoint, considers it to be inconclusive.

§ 42. The best way of carrying out a magnetic survey depends on where it has to be made and on the object in view. The object that probably still comes first in importance is a knowledge of the declination, of sufficient accuracy for navigation in all navigable waters. One might thus infer that

magnetic surveys consist mainly of observations at sea. This cannot however be said to be true of the past, whatever it may be of the future, and this for several reasons. Observations at sea entail the use of a ship, specially constructed so as to be free from disturbing influence, and so are inherently costly; they are also apt to be of inferior accuracy. It might be possible in quiet weather, in a large vessel free from vibration, to observe with instruments of the highest precision such as a unifilar magnetometer, but in the ordinary surveying ship apparatus of less sensitiveness has to be employed. The declination is usually determined with some form of compass. The other elements most usually found directly at sea are the inclination and the total force, the instrument employed being a special form of inclinometer, such as the Fox circle, which was largely used by Ross in the Antarctic, or in recent years the Lloyd-Creak. This latter instrument differs from the ordinary dip-circle fitted for total force observations after H. Lloyd’s method mainly in that the needles rest in pivots instead of on agate edges. To overcome friction a projecting pin on the framework is scratched with a roughened ivory plate.

The most notable recent example of observations at sea is afforded by the cruises of the surveying ships “Galilee” and “Carnegie” under the auspices of the Carnegie Institution of Washington, which includes in its magnetic programme a general survey. To see where the ordinary land survey assists navigation, let us take the case of a country with a long seaboard. If observations were taken every few miles along the coast results might be obtained adequate for the ordinary wants of coasting steamers, but it would be difficult to infer what the declination would be 50 or even 20 miles off shore at any particular place. If, however, the land area itself is carefully surveyed, one knows the trend of the lines of equal declination, and can usually extend them with considerable accuracy many miles out to sea. One also can tell what places if any on the coast suffer from local disturbances, and thus decide on the necessity of special observations. This is by no means the only immediately useful purpose which is or may be served by magnetic surveys on land. In Scandinavia use has been made of magnetic observations in prospecting for iron ore. There are also various geological and geodetic problems to whose solution magnetic surveys may afford valuable guidance. Among the most important recent surveys may be mentioned those of the British Isles by A. Rücker and T. E. Thorpe, of France and Algeria by Moureaux, of Italy by Chistoni and Palazzo, of the Netherlands by Van Ryckevorsel, of South Sweden by Carlheim Gyllenskiöld, of Austria-Hungary by Liznar, of Japan by Tanakadate, of the East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A survey of the United States has been proceeding for a good many years, and many results have appeared in the publications of the U.S. Coast and Geodetic Survey, especially Bauer’s Magnetic Tables and Magnetic Charts, 1908. Additions to our knowledge may also be expected from surveys of India, Egypt and New Zealand.

For the satisfactory execution of a land survey, the observers must have absolute instruments such as the unifilar magnetometer and dip circle, suitable for the accurate determination of the magnetic elements, and they must be able to fix the exact positions of the spots where observations are taken. If, as usual, the survey occupies several years, what is wanted is the value of the elements not at the actual time of observation, but at some fixed epoch, possibly some years earlier or later. At a magnetic observatory, with standardized records, the difference between the values of a magnetic element at any two specified instants can be derived from the magnetic curves. But at an ordinary survey station, at a distance from an observatory, the information is not immediately available. Ordinarily the reduction to a fixed epoch is done in at least two stages, a correction being applied for secular change, and a second for the departure from the mean value for the day due to the regular diurnal inequality and to disturbance.

The reduction to a fixed epoch is at once more easy and more accurate if the area surveyed contains, or has close to its borders, a well distributed series of magnetic observatories, whose records are comparable and trustworthy. Throughout an area of the size of France or Germany, the secular change between any two specified dates can ordinarily be expressed with sufficient accuracy by a formula of the type

= 0 + a(l − l0) + b( − 0)&emsp;. &emsp; .&emsp; (i),

where denotes secular change, l latitude and  longitude, the letters with suffix 0 relating to some convenient central position. The constants 0, a, b are to be determined from the observed secular changes at the fixed observatories whose geographical co-ordinates are accurately known. Unfortunately, as a rule, fixed observatories are few in number and not well distributed for survey purposes; thus the secular change over part at least of the area has usually to be found by repeating the observations after some years at several of the field stations. The success attending this depends on the