296 PRELIMINARY. 



force at any point in the interior, and which we have called layers 

 of gliding (157), will produce on the exterior the same effects as 

 two infinitely near masses. The values of the densities of these 

 layers at the poles will be 



and, at a point of the magnetic latitude A, 



o- = cr sinA. 



From this point of view, the earth must be considered as covered 

 with two magnetic layers, the one negative in the northern hemi- 

 sphere and the other positive in the southern one, the density at 

 each point being proportional to the sine of the magnetic latitude. 



The total mass of each of the layers is expressed by 



it may therefore be easily calculated if we know the absolute value 

 of the force at the equator. 



We shall see, in the sequel, that there are other modes of repre- 

 senting terrestrial magnetism; the infinitely small central magnet, 

 which of itself is inadmissible, is really the very simple mathematical 

 expression of several equivalent states, which are quite compatible 

 with the known properties of magnetic substances. 



309. VARIATIONS OF TERRESTRIAL MAGNETISM. The elements 

 of the earth's magnetism also undergo changes with the time ; one 

 kind are purely accidental, while others have a well-marked periodical 

 character. The variations of long periods, which are called secular 

 variations, may be represented, as a first approximation, by a rotation 

 of the magnetic axis about the earth's axis, a rotation in virtue of 

 which the magnetic axis should describe from east to west a cir- 

 cular cone of about 30. 



As the earth's magnetic pole, which at present is in New South 

 Wales in 100 W. longitude, was in 1660 near the North Cape in 20 

 E. longitude, we see that the period of complete revolution is about 

 800 years. The declination at Paris, which at first was east, was 

 null in 1666; since this time it has been west, and went on in- 

 creasing until 1824; it is now decreasing and will be null in 2050, 



