Mr. H. A. Kowland on Magnetic Distribution. 265 



tiou of the magnetization : this source of error is greatest when 

 the contact-piece is long and thin, and is a minimum when it is 

 short and thick and not in contact with the magnet. Hence 

 this method will give the best results when the contact-piece is 

 small and in the shape of a sphere and not in contact with the 

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

 after taking all these precautious, 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 attrac- 

 tive 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 TyndalFs expe- 

 riments (Phil. Mag. April 1851). It is not necessary at pre- 

 sent to consider the cause of this apparent discrepancy between 

 theory and experiment ; suffice it to say that the explanation of 

 the phenomenon is without doubt to be sought for in the vari- 

 able 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 un- 

 suitable 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 coeffi- 

 cients. Calculate the magnetic force due to this distribution 

 for any points along the axis, or else on a line perpendicular to 

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

 points extending through as great a range and as near the mag- 

 net 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 deter- 

 mining 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 labo- 

 rious, 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 dis- 



