POLES OF MAGNETS. 655 



Coulomb found that for similar bars, magnetised to saturation, 

 the magnetic moments are proportional to the cube of homologous 

 dimensions ; the mean is then constant, and the distribution of 

 magnetism should be independent of the dimensions. 



For needles 2 lines in diameter the length of which increases to 

 5 inches, or 30 times the diameter, the magnetic moment is nearly 

 proportional to the square of the length. 



When the ratio of the length to the diameter is greater than 30, 

 the increase of the magnetic moment is nearly proportional to the 

 increase of length, although a little more rapid ; if m and x l are 

 two constants and 2/ is the length, 



(9) M-a (/-*!>. 



In this case, the mean magnetisation, being proportional to the 



*JC 



ratio i - y , will increase with the length. 



If we consider the factor m as representing the mass of each 

 pole, the distance x 1 of the pole from the end will be constant ; but 

 the restriction introduced into the exactitude of this experimental 

 relation by Coulomb himself, shows that the mass of the poles 

 increases with the length ; and this should be the case, for with the 

 same distribution at the ends, the demagnetising force diminishes as 

 the length of the magnet increases. 



The same is the case, according to M. Bouty,* for the temporary 

 magnetisation of steel needles of various lengths in the uniform field 

 of a coil. The distance from the pole to the ends, calculated by 

 equation (9), is seen to be sensibly independent of the length of the 

 needle and of the magnetising force ; this latter result, however, 

 does not agree with an ingenious experiment by which Professor 

 Rowland! has observed that the distribution of the induced mag- 

 netism changes with the magnitude of the magnetising force. 



Green's formula (422) 



gives, for the distance of the pole from the end, a constant quantity 



* BOUTY. Journal de Physique, Vol. iv., p. 367. 1875. 

 t ROWLAND. Phil. Mag. (4) Vol. XLVI, p. 142. 1873. 



