OSCILLATIONS OF AN INFINITELY SMALL NEEDLE. 383 



opposite poles of two magnets. If the needles are at considerable 

 distances each of them will tend to put itself parallel to the lines of 

 force, and the entire system will be in equilibrium when perpen- 

 dicular to the line of the poles. If, on the contrary, the needles are 

 gradually shortened, or if they are multiplied so that they are almost 

 in contact, a moment will arrive in which the tendency of each to 

 move towards points of maximum force will predominate, and the 

 whole system will now set parallel to the lines of force that is, to 

 the line of the poles. 



It will be seen that all intermediate cases may present themselves, 

 and even that for a given magnetic system the direction of parallel 

 or transverse equilibrium depends on the law of variation of the 

 field in which it is placed. 



404, OSCILLATIONS OF AN INFINITELY SMALL ISOTROPIC NEEDLE. 

 The problem is identical with that which has already been treated 

 for dielectrics (183, 184). 



As a particular case, if the field is symmetrical in reference to the 

 centre of the needle, the time of the oscillations is given by the 

 formula 



KA + B' 



it is independent of the length of the needle. This latter fact had 

 been found experimentally by Matteucci for non-crystalline bismuth 

 needles ; the explanation was given by Sir W. Thomson. 

 In the present case, the coefficient 



K*-i- 



reduces sensibly to a constant for great 'values of k, and becomes 

 equal to k for small ones. The method of oscillations could not 

 then be employed to determine the coefficient of magnetisation of 

 highly magnetic bodies such as iron ; it serves very well on the 

 contrary for feebly magnetic or for diamagnetic bodies. 



If the field varies in any way, the method of oscillations would 

 with difficulty give good determinations of the value of k even for 

 bodies with a very feeble coefficient. The position of equilibrium 

 of the needle depends then, as we have seen, on the law of the 

 variation of the field, and on the length of the needle ; this is also 

 the case with the duration of the oscillations. 



