246 Prof. Thomson's Elementary Demonstrations of 



direction SN, and a force perpendicular to it towards the centre 

 of curvature, bearing the same ratio to either ml or ml', or to mJ 

 (which is their mean, and is infinitely nearly equal to each of 

 them), as NS to the radius of curvature, or (by Prop. II.) the 

 ratio of the excess of the intensity at P' above that at P to the 

 intensity at either, that is the ratio of J'— J to J, and therefore 

 itself equal to m(J' — J). The bar therefore experiences a force 

 the same as the resultant of m(I — I') acting along it from S 

 towards N, and m(J' — J) perpendicularly across it towards P', 

 through its middle point. 



Cor. The direction of the resultant force on the bar is that in 

 which the total intensity of the field increases most rapidly ; or, 

 which is the same, it is perpendicular to the surface of no varia- 

 tion of the total intensity. 



Prop. VII. The resultant force on an infinitely small magnet 

 of any kind placed in a magnetic field, with its magnetic axis 

 along the lines of force, is in the line of most rapid variation of 

 the total intensity of the field, and is equal to the magnetic 

 moment of the magnet multiplied by the rate of variation of the 

 total intensity per unit of distance ; being in the direction in 

 which the force increases when the magnetic axis is " direct/'' 

 (that is, in the position it would rest in if the magnet were free 

 to turn about its centre of gravity) . 



Cor. 1. The resultant force experienced by the magnet will be 

 in the contrary direction, that is, the direction in which the total 

 intensity of the field diminishes most rapidly, when it is held 

 with its magnetic axis reverse along the lines of force of the 

 field. 



Cor. 2. A ball of soft iron, or of any non-crystalline paramag- 

 netic substance, held anyhow in a non-uniform magnetic field, 

 or a ball or small fragment of any shape, of any kind of para- 

 magnetic substance whether crystalline or not, left free to turn 

 about its centre of gravity, will experience a resultant force in 

 the direction in which the total intensity of the field increases 

 most rapidly, and in magnitude equal to the magnetic moment 

 of the magnetization induced in the mass multiplied by the rate 

 of variation of the total intensity per unit distance in the line of 

 greatest variation in the field. For such a body in such a posi- 

 tion is known to be a magnet by induction, with its magnetic 

 axis direct along the lines of force. 



Cor. 3. A ball of non-crystalline diamagnetic substance held 

 anyhow in a magnetic field, or a small bar or fragment of any 

 shape of any kind of diamagnetic substance, crystalline or non- 

 crystalline, held by its centre of gravity, but left free to turn 

 about this point, experiences the same resultant force as a small 

 6teel or other permanent magnet substituted for it, and held with 



