392 Permanent Magnetism [OH. xi 



The expression in brackets is necessarily a biaxial harmonic of order unity 

 (cf. 276) ; it is easily found to be equal to *3224 cos 7 where 7 is the 

 angular distance of the point (I, X) from the point 



lat. 7820'N, long. 6717'W (389). 



The potential is now 



n = . 3224^, 



r 2 



which is the potential of a uniformly magnetised sphere, having as direction 

 of magnetisation the radius through the point ( 415). Or again, it is the 

 potential of a single magnetic particle at the centre of the earth, pointing 

 in this same direction. It is naturally impossible to distinguish between 

 these two possibilities by a survey of the field outside the earth. Green's 

 theorem has already shewn that we cannot locate the sources of a field 

 inside a closed surface by a study of the field outside the surface. 



REFERENCES. 



On the general theory of permanent magnetism : 



J. J. THOMSON, Elements of Electricity and Magnetism, Chap. vi. 



Encyc. Brit., 9th ed. Art. Magnetism. 



MAXWELL, Elect, and Mag., Vol. n, Part in, Chaps, i in. 



On Terrestrial Magnetism : 



J. J. THOMSON, Elements of Electricity and Magnetism, Chap. vii. 

 WINKELMANN, Handbuch der Physik (2te Auflage), 5, (1), pp. 471515. 



EXAMPLES. 



1. Two small magnets float horizontally on the surface of water, one along the 

 direction of the straight line joining their centres, and the other at right angles to it. 

 Prove that the action of each magnet on the other reduces to a single force at right 

 angles to the straight line joining the centres, and meeting that line at one-third of its 

 length from the longitudinal magnet. 



2. A small magnet ACB, free to turn about its centre C, is acted on by a small fixed 

 magnet PQ. Prove that in equilibrium the axis ACB lies in the plane PQC, and that 

 tan# = -tan#', where 6, 6' are the angles which the two magnets make with the line 

 joining them. 



3. Three small magnets having their centres at the angular points of an equilateral 

 triangle ABC, and being free to move about their centres, can rest in equilibrium with 

 the magnet at A parallel to BC, and those at B and C respectively at right angles to AB 

 and AC. Prove that the magnetic moments are in the ratios 



3 : 4 : 4. 



