318 Intelligence and Miscellaneous Articles. 



of the bundle broken parallel to the axis the suhpermanent magnetism 

 is contrary in direction to the permanent magnetism. It would be 

 the same in direction in the case of a needle broken in a plane per- 

 pendicular to its axis, and of which the two fragments were sepa- 

 rated or reunited end to end. This result has been verified by ex- 

 periment. — Comptes Bendas de VAcad. des Sciences, Feb. 23, 1874. 



CONTRIBUTION TO THE THEORY OF THE MAGNETIC FORCES. 

 BY M. STEFAN. 



The memoir consists of three parts. In the first, " on the cal- 

 culation of the magnetic forces of electric currents," it is pointed 

 out that the equivalence between the forces emanating from mag- 

 nets and those from electric currents is complete, not only, as is 

 known, in the exterior, but also in the interior space, and that in 

 this the action of a magnet on a point outside of its elements must 

 be different from its action on a point within them. A simple rule 

 is given for the calculation of the electromagnetic forces ; and it is 

 specially noted that the interior of a sphere round which currents 

 run in parallel circles presents a homogeneous magnetic field, that 

 the same property belongs to an ellipsoid, and that such systems of 

 currents furnish galvanometer- and magnetizing spirals of constant 

 force. 



In the second part, " on the action of a magnet on an internal 

 point," this problem, already touched upon in the first part, is 

 treated more in detail. It is shown that the action of a magnet on 

 an internal point is not completely determined by the magnetic 

 potential — that other forces besides those given by that potential 

 are operative, differing in direction and quantity according as the 

 point affected is within or without a molecule of the magnet. These 

 forces are dependent on the form and arrangement of the molecules, 

 and so constituted that the sum of their works on a finite path is =0. 

 Only when the magnetism of the molecules consists of electric cur- 

 rents is the latter generally not the case, and the principle of the 

 conservation of energy requires the entrance of induction currents. 



The third part has for its subject the " theory of magnetic in- 

 duction." The basis of it is formed by the theorem, found in the 

 second part, of the action of a magnet on a point in the interior of 

 its molecules. On the foundation of this theorem the general equa- 

 tions of the theory of magnetic induction and of the theory, iden- 

 tical with it, of dielectric polarization can be immediately written, 

 and, with the aid of some theorems found in the first part, some 

 problems on the magnetizing of a sphere, an ellipsoid, a ring, be 

 solved without further calculation. Several series of experiments 

 are then discussed, from which it results that all sorts of iron and 

 steel admit the same maximum of magnetization, that the resist- 

 ance of iron and nickel to magnetizing is initially very great, then 

 diminishes to a minimum, which is reached when the induced mag- 

 netic moment is one third of its maximum, and that thenceforward 

 the resistance again increases till it reaches an infinite value. From 

 these data and some general considerations is deduced a formula for 



