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 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.

§ 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 λ is given by an expression of the type c + a(l − l₀) + b(λ − λ₀), where a, b, c are constants, l₀ and 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. Schmidt^[1] as 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 − l₀ and λ − λ₀ have also been used, e.g., by A. Tanakadate in the Magnetic Survey of Japan.

^[1]