334 Intelligence and Miscellaneous Articles. 



of the noodle is seen to vary at the same time as the coordinates of 

 its centre of rotation. Among these directions there are some re- 

 markable ones to which we would call attention — namely, those 

 normal to the surface of the magnet. For the sake of brevity, we 

 will give to the points to which they correspond the name of ortho- 

 gonal points. 



To take an example, let us consider a magnetized bar having the 

 form of a rectangular parallelepiped; on each half of the bar we 

 shall find five orthogonal points : — one on the terminal face, at the 

 point where the magnetic axis meets it ; and one on each of the 

 four lateral faces, situated on the right line joining the centres of 

 the short sides of this face, the last four points being symmetrical, 

 two and two. 



Around each of the points we are considering, the directions are 

 such that, reckoning from the surface of the magnet inwards, they 

 are always convergent in any plane drawn through the normal. 



A first property of orthogonal points is the following : — 



If a small magnetic body he placed on an orthogonal point, more me- 

 chanical work will be requisite, in order to remove the small body thence 

 to infinity, than, if it had been placed on any other neighbouring point 

 of the surface of the magnet. In other terms, the orthogonal point 

 presents a maximum of the work above-mentioned. 



The demonstration of this theorem is very simple. 



With respect to terrestrial magnetism, the orthogonal points of the 

 surface of the earth are what are somewhat improperly called the mag- 

 netic poles. Halley and Hansteen believed in the existence of four 

 of these poles ; Gauss and Duperrey admit only two, or, more pre- 

 cisely, two polar regions. Parry, John Boss, James Ross, Duinont 

 d'Urville, and Wilke were able to determine approximately their 

 positions. 



On a given line, also, points possessing the same property of 

 maximum of work of removal to infinity are found ; they are those 

 for which the magnetic action is normal to the curve. 



We will remark that all these maxima presented by orthogonal 

 points might be replaced by minima for surfaces presenting suitable 

 ratios of curvature with the surfaces of equal potential. A simple 

 change of sign of the work of sliding conducts immediately to this 

 result. 



A second curious property is the following : — 



The positions of spontaneous equilibrium of a small magnetic body 

 with respect to a magnet are precisely the orthogonal points. This pro- 

 position flows immediately from the fact that the positions of equi- 

 librium of a point situated on a polished surface are those for which 

 the forces acting on the point produce no tangential component. 



This is confirmed by the following experiment : — A particle of 

 iron is fixed on a flat cork, which is then put to float upon water. 

 If a magnet be brought quite close to the surface of the water, with 

 its lower face horizontal, the cork will be seen to move until the 

 iron particle which it carries is placed precisely under the orthogo- 

 nal point. If the magnet be placed in any manner whatever in 

 space, the final situation of the iron will indicate the point of con- 



