660 CONSTANTS OF MAGNETISATION. 



When the magnetic field produced by electromagnets is used, 

 a fresh difficulty is met with. The action is no longer in a simple 

 ratio to the intensity of the exciting current, and the very form of 

 the field may also be considerably modified ; hence in this case 

 the current must be kept unchanged. 



1221. When the field has two symmetrical planes, the oscil- 

 lations of a small needle (404) enable us to determine the co- 

 efficient k. We have then 



B/ 2 ' 



p denoting the density of the substance, A and B constants defined 

 by the shape of the field. In this case, the duration / of oscil- 

 lations is independent of the length of the needles, so that for 

 comparative experiments it is unnecessary to use needles of the 

 same length, or to know the form of the field. 



If the needle is so long that variations of < 2 in the space 

 occupied by the needle cannot be expressed by the two first terms 

 of the expansion of a series (184), we may still put 



t* 



but the coefficient A' is a function of the shape of the field and 

 of the length of the needle. In this case we should restrict our- 

 selves, for comparison, to needles of the same dimensions. 



1222. The torsion balance gives a method frequently employed, 

 which does not require the field to be symmetrical. At one end of 

 the needle is placed a small specimen of the body to be examined 

 a sphere, for instance. When the magnetic field is caused to act, 

 the sphere tends towards points where the force is maximum or 

 minimum, according to the sign of >, and it is restored to its original 

 position by the torsion A of the wire. If / is the length of the arm 

 of the lever, ds the element of the circle described by the sphere, 

 and dO the corresponding angle, the couple produced on the 

 sphere by the action of the field is 



