INDUCED MAGNETISATION. 359 



has a very small value. This is the case with most magnetic sub- 

 stances, with the exception of iron, nickel, and cobalt. In the case 

 of iron or nickel, for which the coefficient k reaches very high 

 values, such as 30 or 40, proportionality exists as long as the force F 

 does not exceed a certain limit ; when the bodies are magnetised by 

 the earth, for example. This is also the case with ordinary iron, 

 twisted iron, cast iron, and steel more or less tempered, the co- 

 efficient of magnetisation of which is considerably weaker. The 

 coefficient k is always very small for diamagnetic bodies j it scarcely 



amounts to for bismuth, which is the most active body 



400,000 



of this second class. 



If the proportionality between the magnetisation and the mag- 

 netic force does not exist, we may consider the coefficient k as being 

 itself a function of magnetisation. We shall first investigate the case 

 in which this coefficient is constant and the same in all directions 

 that is to say, in which the body is isotropic and the induced mag- 

 netisation somewhat feeble. 



375. INDUCED MAGNETISATION is PROPORTIONAL TO THE 

 MAGNETISING FORCE. Consider any given body in the magnetic 

 field. Let V be the potential of the field and 12 that which is pro- 

 duced by induced masses, the value of the actual potential U will be 



u=v+a 



At any given point the components of the magnetising force 

 parallel to the axis are 



X- V- W 7- W 



~' "" L ~~- 



The expression for the force itself is 



dn> 



its direction is that of the perpendicular , to the equipotential 

 surface which passes through the point in question. 



