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
East.		Change since
previous year.		Year.Declination
East.		Change since
previous year.
°   ′  ″′   ″   °   ′   ″′  ″  
18760 55 580 37 E18810 57 120  3 E
187756 390 41 E18820 56 500 22 W
187857  60 27 E188357  20 12 E
187957 300 24 E188455 391 23 W
188057  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 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[15] 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:—

 ′ ′ ′
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 − l0 and λ − λ0 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.
Date. Declination. Date. Declination.
°  ′ °  ′
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.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+2.4
Boston, 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+3.4
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 −3.9−3.4−2.7−2.0−0.90.0+0.9+2.0+2.7+3.4+3.9+4.0+3.9+3.6+3.5+3.2
Richmond, Virginia −3.6−3.2−2.5−1.8−0.90.0+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 −3.7−3.6−3.2−2.5−1.8−0.90.0+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 −0.90.0+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 −0.90.0+0.9+1.8+2.5+3.2+3.6+3.8+3.8+3.4+1.8
Chattanooga, Tennessee −0.90.0+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+3.50.0
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 −0.80.0+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