370 



4°, that the continuous branches have the poles as points of in- 

 flexion, and that these are the only points of inflexion within finite 

 limits : 5°, that a tangent at any point of the curve, or, which is 

 the same thing, the direction taken by a small needle placed there, 

 admits of easy construction: 6°, that when the parameter (/3) is 

 such as to cause the convergent and divergent branches to intersect, 

 they do so in a perpendicular to the magnetic axis drawn from the 

 poles : 7°, that the convergent branches are always concave, and 

 the divergent always convex, to a line at right angles to the magnet, 

 drawn from its middle, — besides other properties not less interesting, 

 though less capable of succinct enunciation. 



Having separated the branches belonging to the case of like poles 

 from those belonging to the unlike ones in the magnetic curve, the 

 author proceeds toasimilar separation of the corresponding branches 

 in the curve of verticity. In the former case the curve is composed 

 of four branches infinite in length, having the magnetic axis for as- 

 symptotes, lying above that axis, and emanating from the poles to 

 the right and left ; and of two finite branches, continuous with those 

 just described, and lying below the magnetic axis ; one of which 

 passes through the centre of the earth, and meets the other in the 

 perpendicular from the middle of the axis; so that the whole system 

 is constituted by one continuous curve, extending from negative 

 infinite to positive infinite, and having the lines drawn from the centre 

 of the earth to the magnetic poles as tangents at the poles ; and no 

 part of the curve lies between these tangents. It bears in form 

 some general resemblance to a distorted conchoid • this curve not 

 having either cusp or loop. In the second case, the curve is also 

 composed of four branches, two finite and two infinite ones; the 

 latter having the line drawn from the centre of the earth through 

 the middle of the magnet as assymptotes, and both lying on the 

 same side of it as the more distant pole; and the finite branches 

 joining these continuously at the poles, and each other in the mid- 

 dle of the magnetic axis; the one from the nearer pole lying above 

 the axis, and the one from the remoter pole lying below it. The 

 branches, where they unite at the poles, have the lines drawn from 

 the centre of the earth to the poles as tangents, and the lower in- 

 finite branch passes through the centre. The whole system of 

 branches is comprised between the polar tangents; and the two 

 systems are mutually tangential at the poles, and intersect each 

 other at the centre; but they have no other point in common. 



Lastly, the author proceeds to demonstrate that a circle (namely, 

 the magnetic meridian) described from the centre of the curve of 

 verticity, will always cut the convergent system in two points, but 

 can never cut it in more than two. He remarks, however, that if 

 we could conceive two poles of like kinds to exist without any other 

 whatsoever, we might have either four points of verticity, or only 

 two, according to circumstances ; but he waves the discussion of this 

 particular case, as being irrelevant to the purpose of his present 

 inquiry. 



Mr. Davies announces his intention of shortly laying before the 



