266 



confined to the vertical plane. It is only necessary to con- 

 sider, therefore, the action on the first and second magnets. 



The author then proceeded to the conditions of equili- 

 brium of these actions, which were expressed by four 

 equations, containing four arbitrary angles; so that this 

 equilibrium is, in general, attainable, by suitably deter- 

 mining the position of the three magnets, whatever be their 

 relative intensities. 



In practice, however, it will seldom happen, that we can 

 regard as arbitrary all the four angles which enter these 

 equations, one or more of them being, in general, determined 

 by some circumstance connected with the locality. In such 

 case the complete destruction of all action is no longer pos- 

 sible ; and we must look for some other solution of the pro- 

 blem of mutual interference. 



Next to the complete destruction of all action, the most 

 desirable course js to give to the resultant action such 

 a direction, that its effect may be readily computed and 

 allowed for. In the case of the declination bar, it is easily 

 seen that this direction is the magnetic meridian itself; 

 the mean position of the bar being thereby unaltered, and 

 the variations of its position only increased or diminished in 

 a given ratio. By means of a simple investigation it is 

 shown, that the same thing is true of the horizontal inten- 

 sity bar ; and that, in order that the variations of declination 

 may not be mixed up with those of force, the resultant force 

 exerted upon this magnet by the other two must lie in the 

 magnetic meridian. The problem, therefore, is reduced to 

 this : — to determine the position of the three magnets 

 A, b, and c, in such a manner, that the resultant actions ex- 

 erted upon a and b, respectively, by the other two, shall 

 lie in the magnetic meridian. 



The solution of this problem was shown by the author 

 to be contained in the two following equations : 



