TRANSACTIONS OP THE SECTIONS. 13 



for observations of horizontal intensity) is in the perpendicular plane, 

 there is nothing to compensate the action of each magnet on the other. 

 The best thing that can be done, then, is to determine the position 

 of the second magnet in such a manner, that the direction of its action 

 on the first shall coincide with the magnetic meridian. In such case, 

 the mean direction of the first magnet will be undisturbed by the second ; 

 and, as to the variations of the direction, it is manifest that they will 

 be thereby increased or diminished in a given ratio ; so that the true 

 variations will be obtained simply by multiplying by a constant coeffi- 

 cient. The reciprocal action of the first magnet on the second, however, 

 will not take place, either in the magnetic meridian, or in the plane 

 perpendicular to it ; so that the second magnet is necessarily disturbed. 

 The case is different when a third magnet is introduced. When this 

 magnet \s, fixed, we have only to consider the disturbing forces exerted 

 upon the other two magnets, and the conditions of equilibrium of these 

 forces are easily shown to be expressed by four equations, containing 

 four arbitrary angles ; and the equilibrium is accordingly attainable by 

 suitably determining the position of the three magnets, whatever be 

 their relative intensities. The third magnet may, however, be a 

 moveable one, and its movements serve to exhibit the changes of one 

 of the magnetic elements. In the Dublin Magnetical Observatory this 

 magnet is employed in the determination of the vertical cowpotient 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 magnets 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 if this force be resolved into two, 

 one in the direction of the axis of the magnet, and the other perpendi- 

 cular to it, the latter component can have no effect on the position of 

 the magnet, being at right angles to the plane in which it is constrained 

 to move ; and, as to the former, it manifestly cannot affect the mean 

 position of the magnet, but merely augments or diminishes the devia- 

 tions from that position in a given ratio. The destruction of this force, 

 in the direction of the axis of the third magnet, introduces d, fifth con- 

 dition of equilibrium ; and, as there are but four arbitrary angles, it 

 follows that complete equilibrium is not attainable, except for deter- 

 minate values of the relative forces of the magnets. We may, however, 

 without inconvenience, dispense with one of the conditions of equili- 

 brium ; and, the other form being fulfilled, the disturbing action upon 

 two of the magnets will be completely balanced, while the effect of that 

 exerted upon the third may be at once eliminated from the results, by 

 altering in a suitable manner the constant in the formula of reduction. 

 The author then proceeded to consider the cases in which the four 

 angles were not all arbitrary, some circumstance connected with the 

 locality determining one or more of these quantities, or establishing 

 one or more relations among them. He pointed out, in such cases, the 

 conditions most important to be fulfilled ; and gave examples of the 

 solution in some particular instances, such as where the three magnets 

 are in the same right line, &c. 



