258 MAGNETISM 



observations that a paramagnetic body in a more paramagnetic 



medium behaves as if it were diamagnetic is at once explained by 



7TT2 

 the expression for the volume force, -2 -= . For suppose that 



the body is first in air : the force on unit volume in direction x is 

 ^- T> where -= may be determined from the value of the field 



before the introduction of the body, since when K is small the 

 intensity of the field is not sensibly altered by its introduction. 



Now surround the body by a medium with susceptibility K^ 

 and the force changes to 



AT 2 - KI dR* 



2 dx 



and if ^ is greater than K Z the force changes sign. 



Forces on an elongated bar in a uniform field in air 

 when its permeability differs very slightly from 1. If 

 we neglect the outward tension proportional to /c 2 the other term 

 in the surface force is H 2 <r or /cH 2 a cos 2 per unit area of 

 surface in the direction H 2 . This is a force /cH 2 2 per unit area of 

 the tube of induction. Then to the extent to which we can adopt 

 the supposition that the tubes go straight through the body, that 

 is, that their course is unaltered by its presence, these forces will 

 neutralise each other in pairs at the entrance and exit of the tube. 

 The body will to this approximation rest in any position. But 

 Lord Kelvin showed* that when we take into account the altera- 

 tion of field due to the induced magnetism, it follows that both 

 paramagnetic and diamagnetu bar> tend to set with their longer 

 axes along the lines of force. This result is important, for it 

 implies that the equatorial setting of small diamagnetic bars 

 placed midway between the poles of a magnet i> not due to a 

 tendency to set transverse to the lines of force, but to a tendency 

 of the material to get into a weaker field. By setting transversely, 

 the two ends of the bar get into the weakest fields available, 

 for the field diminishes in the equatorial plane as we move out 

 from the centre. 



To understand the longitudinal setting in a uniform field let 

 us imagine a bar of square section to be made of separate cubes 

 placed end to end. First let the body be paramagnetic and let it 

 be held longitudinally in the field. Each cube will tend to increase 

 the magnetisation of its neigh bours, just as each of a series of 

 magnets tends to increase the magnetisation when they are placed 

 end to end. Thus the polarity at the ends is increased. Next let 

 the bar be placed transversely to the field ; then each cube will 

 tend to weaken the magnetisation of its neighbours, just as each of 

 a mumber of magnets set side by side tends to weaken its neighbours. 



* Papers on Electrostatics and Magnetism, Sect. 691. 



