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



are not of equal practical value ; and I was thus led to consider some less 

 complete solutions of the problem, in which three, or even two only, of these 

 conditions are satisfied. 



But all these solutions are exposed to the objection, that the positions 

 of the magnets which fulfil the conditions are dependent upon their relative 

 forces, and are, therefore, subject to vary along with them : — in other 

 words, that upon any change of these forces, the equilibrium already effected 

 will be destroyed, and a new arrangement of the magnets be required to 

 restore it. 



To obviate the inconvenience arising from such a displacement of the 

 magnets employed in the observations, it has been suggested to fulfil the con- 

 ditions of equilibrium by means of additional magnets, whose positions could be 

 readily altered as the forces varied. To this, however, there are serious objec- 

 tions. In the first place, by thus increasing the number of balancing actions, 

 the chances of error in the positions of the centres of force, as well as the 

 liability to alteration in their intensities, are multiplied ; and, secondly, on 

 account of this liability to change, no absolute measurement could be safely 

 made, without a re-examination of the relative forces of the magnets, and a 

 readjustment of their positions ; so that nothing appears to be gained. 



Under all these circumstances, the best course appears to be, to satisfy so 

 many of the conditions of equilibrium, as are capable of being fulfilled independ- 

 ently of the relative forces of the magnets, and to apply corrections for the 

 actions which remain unbalanced. In this manner, the changes which the forces 

 of the magnets may undergo, in process of time, will not disturb the equilibrium 

 which has been effected ; and the unbalanced actions, being in definite directions, 

 will admit of being determined by an easy experiment, and allowed for by a 

 simple correction. 



In order that any one of the equations of equilibrium* may subsist inde- 

 pendently of the ratios of the forces of the magnets, the part which contains one 

 of these ratios, and that which is independent of it, must separately vanish, and 

 the five equations are resolved into the following : 



* Equations (10, 11, 12, 13, 15), pp. 167, 170. 



