t50 Variatidns of the Terrestrial Magnetism 



tudes, and its increase proceeding from the equator t6 the 

 poles. 



The compass, indeed, which at the departure of M. 

 Humboldt gave at Paris 245 oscillaiions in 10 minutes, 

 gave no more in Peru than 211, and it ccjnstantly varied in 

 the same direction ; that is to say, the number of the oscil- 

 lations always decreased, in apjiroachius:^ the equator^ and 

 always increased in advancing towardf^ the north. 



These differences cannot be ascribed to a diminution of 

 force in the magnetism of the cwnpass, nor can wc sup- 

 pose that it is weakened by the effect of time and of heat ; 

 for, after three yciu's* residence in the v.armest countries of 

 the earth, the same compass gave again in Mexico oscilla- 

 tions as rapid as at Paris. 



There is no reason, either, to doubt the justness of M. 

 Humboldt's observations, for he often observed the oscilla- 

 tions in the vertical plane perpendicular to that meridian j 

 but bv decomposing the magnetic force in the latter plane, 

 and comparing it with its total action, which is exercised in 

 the former, we may from these data calculate its direction, 

 and consequently the direction of the needle*. This in-' 

 clinaiion, thus calculated, is found always conformable to 

 that which M. Humboldt observed directly. When he 

 made his experiments, however, he could not foresee that 

 they would be subjected lo this proof by which M. La 

 Place verified them. 



As the justness of these observations cannot be contested, 

 we must allow also the truth of the result which they indi'^ 



* Let HOC (plate V. fig. 1.) be the plane of the mag;netic meridian pass- 

 ins: through the vertical O C; let OL be the direction of the needle situated in 

 that plane, and OH a horizontal. The angle LOH will be the inclination 

 of the needle, which we shall denote by I. If F represent the total mag- 

 netic force which acts in the direction OL, the part of this force, which acts 

 according to OC, will be F sine of I : but the magnetic forces which deter- 

 mine the oscillations of the needle in any plane, are to each other as the 

 squares of the oscillations made in the same tim.e. If we denote then by M, 

 the number of the oscillations made in 1 0' of time in the magnetic meridian, 

 and by P, the number of oscillatiens made also in 10', in the perpendicular 

 plane, we shall have the following proportion. 

 F sin. I P-' 



from which we deduce 



Sin. I 



M'^ 



M- 



The inclination then may be calculated by this formula, when we have 

 oscillations made in the two planes. 



In like manner, by making a needle oscillate successively in several vertical 

 planes,, we might determine the direction of the magnetic meridian. 



cate. 



