380 MAGNETIC INDUCTION. 



greatest, and diamagnetic along the axis of the feeblest magneti- 

 sation ; it would turn in the direction of increasing forces, when the 

 first of these axes was parallel to the field, and in the opposite 

 direction when it is the second. These actions, however, would be 

 so feeble that it would be difficult to make them evident. 



398. EQUILIBRIUM OF LONG BODIES IN A UNIFORM FIELD. 

 We have seen in electrostatics (185) that an elongated conductor 

 placed in a uniform field is in equilibrium when the axis of the 

 cylinder is perpendicular or parallel to the force of the field, and 

 that the equilibrium is unstable in the first case, and stable in the 

 second. 



This must also be the case with a long iron cylinder placed in a 

 uniform magnetic field, for the magnetisation of a soft iron sphere is 



a fraction very near unity, h = - , of the electrification which this 



sphere would acquire in a uniform electrical field in which the forces 

 had the same absolute values. 



It has been known in fact, since Gilbert's time, that a soft iron 

 needle movable about a vertical axis sets in the magnetic meridian, 

 and that if it were movable about its centre of gravity it would take 

 up the direction of the dipping needle. 



Nevertheless, in order to explain this experiment it is not suffi- 

 cient to say that the magnet is everywhere magnetised parallel to the 

 force of the field, for in that case the needle should be in equilibrium 

 in all positions ; hence the magnetisation of the mass cannot be 

 uniform. 



The couple which acts on the needle when it is oblique to the 

 forces of the field, is due to the fact that the reactions of the various 

 particles have modified the magnetisation ; the direction parallel to 

 the field is that therefore which, in consequence of these reactions, 

 corresponds to the maximum of magnetisation. 



399. Consider, in fact, a series of balls of soft iron B, B', B" 

 fixed on a non-magnetic axis, and placed in a uniform field ; let a be 

 the angle of the axis with the direction of the field. 



If the balls are so far apart as not to act on each other, the 

 magnetisation is parallel to the field, and the resultant is null. But 

 if the distance of the balls is not very great compared with their 

 dimensions, it is clear that the magnetisation of each of them is 

 increased by their mutual action, and that it takes place along 

 directions which make, with the axis, angles o>, c/ . . . smaller than a, 

 and changing from one sphere to another. Each sphere is no longer 

 in equilibrium ; it is under the action of a couple, and the whole of 



