265 



magnet will be undisturbed by the second, so as to give the 

 absolute decimation truly ; and, as to the variations of the 

 declination, it is manifest that they will be thereby increased 

 or diminished in a given ratio ; so that the true variations 

 will be obtained by simply altering the coefficient of the 

 scale. When the above-mentioned condition is introduced 

 into the equation which determines the direction of the re- 

 sultant force exerted by one magnet on another, (the length 

 of the magnets being supposed small in comparison with 

 the distance between them,) we find, for the azimuth of the 

 line connecting the two magnets, referred to the magnetic 

 meridian, 



arc (tan = -^J^ — 35° 16'. 



This result has been already obtained by Gauss and Weber. 



It is manifest that, in this case, the action of the first 

 magnet on the second will not take place, either in the mag- 

 netic meridian, or in the plane perpendicular to it ; so that 

 the second magnet is necessarily disturbed. With two mag- 

 nets, accordingly, it is impossible to avoid the effects of 

 mutual action. The case is different, however, when a 

 third magnet is introduced. It is then possible to annul 

 completely all action, with the exception of that exerted 

 on the third magnet by the first and second ; and this, in 

 the case under consideration, is destroyed by the nature of 

 the suspension. 



The third magnet about to be employed in the Dublin 

 Observatory is intended for the observation of the vertical 

 component of the magnetic force. It is a bar supported on 

 knife-edges, capable of motion in a vertical plane, and 

 brought into the horizontal position by means of a weight. 

 The three instruments being in the same horizontal plane, 

 it is manifest that the action of the first and second on the 

 third must take place in that plane ; and this action can 

 have no effect in disturbing the magnet, its motion being 



