The Rev. H. Lloyd on the mutual Action of permanent Magnets. 165 



ridian at the angle = 35° 16'. Mr. Weber has already arrived at this result 

 by other methods. 



With respect to the deviations of the magnet from its mean position, (or the 

 apparent variations of the declination,) it is manifest that they will be increased 

 or diminished in a given ratio, the action of the second magnet on the first 

 being in the same direction as that of the earth, and therefore altering the 

 directive force in a given ratio. The true variations will therefore be obtained 

 from the apparent, simply by multiplying by a constant coefficient. 



The reciprocal action of the first magnet on the second, however, is not 

 directed either in the magnetic meridian, or in the line perpendicular to it, and 

 the second magnet is therefore disturbed by the first. With two magnets, ac- 

 cordingly, it is impossible to neutralize the effects of mutual action. 



Now let a third magnet be introduced ; and let us suppose, in the first 

 instance, that this magnet h fixed, being destined only for the purposes of cor- 

 rection. We have, in this case, only to consider the forces exerted upon the 

 first and second magnets. 



Let A, B, c, (Fig. 4) be the three magnets — of which a is the declination 

 bar, having its axis in the magnetic meridian ; b the horizontal intensity bar, 

 whose axis is perpendicular to the magnetic meridian ; and c the third, or cor- 

 recting bar, the azimuth of whose axis is arbitrary. Lines being supposed 

 drawn joining the centres of these magnets, let the sides of the triangle opposite 

 to the points a, b, c, be denoted by a, b, c, respectively, and the angles which 

 these lines form with the magnetic meridian by a, |3, 7 ; let the angle which 

 the axis of the third magnet c makes with the same meridian be denoted by f ; 

 and finally, let the magnetic moments of the three magnets be A, B, C. 



The forces exerted by the magnet b, upon any element m of the magnet a, 



in the direction ab, and in the direction perpendicular to ab, respectively, 



are (5) 



, 2Bm . Bm 



+ —^ sm 7, - —3- COS7 ; 



the magnetism of m being supposed to be northern, and the positive and ne- 

 gative signs being employed in the usual conventional manner. Let these forces 



