STUDIES ON MAGNETIC DISTRIBUTION 97 



the magnet, and when the method is applied to steel magnets. But 

 after taking all these precautions, the question next arises as to how 

 to obtain the magnetic surface-density from the experiments. Theory 

 indicates, and M. Jamin has assumed, that the attractive force is nearly 

 proportional to the square of the surface-density. But experiment 

 does not seem to confirm this, except where there is some distance 

 between the two bodies, at least in the case of a sphere and a plane 

 surface, as in Tyndall's experiments (Phil. Mag., April, 1851). It is 

 not necessary at present to consider the cause of this apparent dis- 

 crepancy between theory ar>d experiment; suffice it to say that the 

 explanation of the phenomenon is without doubt to be sought for in 

 the variable character of the magnetizing-function of iron. All I wish 

 to show is that the attraction of iron to a magnet, especially when the 

 two are in contact, is a very complicated phenomenon, whose laws in 

 general are unknown, and hence is entirely unsuitable for experiments 

 on magnetic distribution. 



A third method is that used in determining the correction for the 

 distribution on the magnets in finding the intensity of the earth's 

 magnetism. Usually the distribution is not explicitly found in this 

 case; but it is easy to see how it might be. Thus, one way would be as 

 follows: Take the origin of coordinates at the centre of the magnet. 

 Develop the distribution in an ascending series of powers of x with 

 unknown constant coefficients. Calculate the magnetic force due to 

 this distribution for any points along the axis, or else on a line perpen- 

 dicular to the magnet at its centre. Determine the force at a series of 

 points extending through as great a range and as near the magnet as 

 possible. These experiments give a series of equations from which the 

 coefficients in the expansion can be determined. Other and better 

 methods of expansion might be found, except for short magnets, where 

 the method suggested is very good. 



The similarity of this method to that used by Gauss in determining 

 the distribution on the earth is apparent. 



A fourth method is similar to the above, except that the lines of 

 force around the magnet are measured and calculated instead of the 

 force. 



The last two methods are very exact, but are also very laborious, and 

 therefore only adapted to special investigations. Thus, by the change 

 in direction of the lines of force around the magnet, we have a delicate 

 means of showing the change in distribution, as, for instance, when the 

 current around an electro-magnet varies. 



