Geometric Properties of the Magnetic Curve. 317 



position of the tangent to the curve at its origin from the 

 pole S. 



When the two poles which give rise to the magnetic curves 

 are of the same, instead of being of different, denominations, a 

 different system of curves is produced, which have been termed 

 the divergent, in contradistinction to the former, which are 

 convergent to the poles. The divergent curves preserve, with 

 slight modifications, the same geometrical relations to the axis 

 as the convergent curves, and admit of a similar mode of 

 mechanical description. Instead of the south pole S, in the 

 preceding figures, let another north pole N' be substituted; 

 thai is, let the north poles N, N', Fig. 7, of two different mag- 



Fig. 7, 



nets, be placed so as to front each other ; and let the actions 

 of their remote south poles be neglected. In the former case, 

 where the actions of the two poles of the magnet were of an 

 opposite kind, the resultant of their joint action, or the line 

 CT, Figs. 1 and 3, passed in a direction intermediate between 

 N C prolonged, and S C (the former line being the direction of 

 the repulsion, and the latter that of the attraction) : it there- 

 fore cut the axis N X at some point in the prolongation of 

 N S. But in the present case, the two magnetic poles being 

 of the same kind, their action is similar, and their resultant is 

 a force, of which the direction is intermediate to the lines 

 C N and C N', Fig. 7. ; and this line produced, must cut the 

 axis somewhere between N and N'. The angle C N' T being 

 reversed from the situation with respect to C N', which it had 

 in the former case, the sign of its cosine must be changed, 

 and the equation becomes 



c + x = C. 

 VOL. I. FEU. 1831. Y 



