OSCILLATIONS OF A MAGNETIC NEEDLE. 569 



the magnetising force (398). As long as the oscillations are very 

 small, it may be assumed that the induced magnetism consists of 

 two terms ; one parallel to the field, which is displaced in reference 

 to the needle during the oscillations and does not produce a couple ; 

 the other, parallel to the greatest length of the needle, which in- 

 creases its magnetic moment by an almost constant quantity, and 

 which is proportional to the intensity of the field. In order to cal- 

 culate the oscillations, we should add to the magnetic moment M , 

 corresponding to the rigid magnetism, a term of the form /H, and 

 equation (i) then becomes 



7r 2 KN2=(Mo+m)H=MoH 



The coefficient </> depends on the shape of the needle and on 

 its initial magnetisation. It is very small for highly magnetised 

 steel bars, such as are used in observations on terrestrial magnetism. 

 The equation 



N^H 

 N' 2 H' 



may then be written 



This simplification is no longer possible in the case of very 

 strong fields, in which temporary magnetisation may acquire a 

 predominant influence. If the needle is of soft iron, or, better, 

 of a substance which is but little magnetic, there remains in each 

 case only the magnetisation proportional to the field. Equation (2) 

 gives then sensibly 



1141. In order to compare any two fields F and F' which may 

 be displaced at will, like those of a current or a magnet, each 

 experiment is arranged so that the field observed is parallel to 

 the terrestrial field in the same or in the opposite direction that 

 is to say, does not deflect the needle, and the action of the earth 



