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 is 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 wnaltered, 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: 
