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XLFV^ On the Fariafions of the Terrestrial Magnetism 

 in different Latitudes. By Messrs. Hdmboldt and 

 BiOT. Read by M. Biot in the Mathematical mid 

 Physical Cla^s of the French National Institute 2i5th 

 Frimaire, An 13. {Uth December 1804.) 



[Concluded from p. '237.] 



The calculation is as follows :— T suppose that the point B 

 (fig. 3.) is the north magnetic pole of the earth, and that 

 the point A is the south inagnctic pole : I suppose also that 

 there is in the point M, at the surface of the earth, a mo- 

 lecula of the austral fluid which is attracted by B and re- 

 pelled by A in the inverse ratio of the square ot the di- 

 stance; 'and I require what will be the direction ot the 

 power resultine from these two forces acting on that mole- 

 cula. It is evident that this direction will be that also 

 which would be assumed in the point M by the needle of 

 a -compass freely suspended : for, in consequence of the 

 smallncss of the needle in comparison of the radius of the 

 earth, the lines drawn from its points to one centre, B or A, 

 may be considered as parallel, especially if the points A 

 and B are near the centre of the earth ; which is the case 

 with nature, as mav be seen. 



I shall lirst suppose that the earth has a spherical figure, 

 and that the two poles A and B are equal in force; I shall 

 then examine how far the latter supposition agrees with the 

 results observed. 



Let AM then = D', B M = D, C P = .r ; PM = y, 

 the angle M C P = u, C A = C B == a, and I shall make 

 a = ^r; r being equal to the radius of the earth, and K a 

 constant but indeterminate quantity. 



Let X, Y, also he the forces which attract M m a direc- 

 tion parallel to the axes of the co-ordinates, and 3 the angle 

 which the resulting force makes with the axis A BC. 



We shall first have the following equations, in which 

 F it; the magnetic force, at a distance equal to unity. 



X = -^ cos. MBD - -^ COS. M AD i 



O''^ - y- ^ (x + a)" = r^ -f 2 axis -f- a 

 Y = -^ sin. MBD - -7;-— sill. AI AD: 

 D* t= i/« 4- (r — c)- =-• r^ - -' •■i>^i^ + '^' 



