159 



VII. On the mutual Action of Permanent Magnets, considered chiefly in 

 reference to their best relative Position in an Observatory. By the Rev. 

 Humphrey Lloyd, A.M., Fellow of Trinity College, and Professor of 

 Natural Philosophy in the University of Dublin, F.R. S., V.P.R.I. A., 

 Honorary Member of the American Philosophical Society. 



Read February 11, 1839. 



It is a problem of much Importance, in connexion with the arrangement of a 

 Magnetical Observatory, to determine the relative position of the magnets in 

 such a manner, that their mutual action may be either absolutely null, or, at 

 the least, readily calculable. 



As a preliminary step to the solution of this problem, it is necessary that we 

 should know the direction and intensity of the resultant force exerted by a 

 magnet upon an element of free magnetism placed in any manner with respect 

 to it. This question has been already solved by Biot, on the supposition 

 that the action of a magnet is equivalent to that oi two forces of equal intensity, 

 one attractive, and the other repulsive, emanating from two definite points or 

 poles. There is no difficulty in generalizing the problem, and in obtaining a 

 solution independent of this particular hypothesis. 



The middle point o, of the magnet ns, (Fig. 1) being taken as the origin 

 of coordinates, and the line connecting it with the magnetic element m as the 

 axis of abscissae, the distance, mq, of that element from any point (x, y) of the 

 axis of the magnet-bar is 



V{a-xf-^y\ 



the distance om being denoted by a. Hence, if m denote the quantity of free 

 magnetism in the magnetic element M, q the corresponding quantity in a given 

 elementary portion of the magnet at q, the force exerted by the latter on the 

 former is 



