Inquiries concerning the Magnetism of the Earth. 15T 
as consisting of an infinite number of rings, possessed of intensi- 
ties augmenting from the centre to the outermost circumference. 
In prismatic magnets, the ratio of the distribution is probably 
more complicated. It appears to me most likely, that this third 
elementary law, as well as the second, may be deduced theoretical- 
ly from the first, which states the mutual action of two particles 
to be always inversely as the square of their distance. On the 
other hand, it appears equally certain, that a complete solution 
of this problem is one of the hardest tasks to which analysis has 
yet been applied, — a task worthy of a La Place.^’ 
It is a fortunate circumstance that both these laws, concern- 
ing which our information is still so defective, are limited in their 
operation to the immediate neighbourhood of the magnet, and 
produce no considerable effect at a distance. From the first law 
alone can it be proved, that the effect of a linear magnet on a 
magnetic particle is inversely as the third power of that par- 
ticle’' s distance from the middle point f the magnet.^ in all cases 
where the distance is very great. It is also shewn, that, in si- 
milar circumstances, the effect of two linear magnets upon each 
other, is inversely as the fourth power of their distance. 
These propositions help us to understand, how, by confounding 
the entire effect of the magnet with the effect of a single particle, 
magnetic attraction has been sometimes reckoned inversely as 
the cube, sometimes as the fourth power of the distance. — What 
follows, bears more directly on the subject of terrestrial magne- 
tism, to which it is now time to direct our attention. It is de- 
monstrated, that the distance from the middle f a magnet being 
the same, the force opposite the poles, or in the direction of the 
axis, is double of the force in the magnetic equator. The two 
following results are strikingly confirmed in the case of the ter- 
restrial magnet : On the supposition of a globe containing at its 
centre a magnet infinitely small, near the magnetic equator, the 
dip must increase twice as rapidly as the magnetic latitude ; 
near the pole haf as rap’idly ; and, the 'increment of the dip 
must he equal to the alteration of the latitude, at that part of the 
globe where the dip z=z 54° 44'. It is also of importance to re- 
mark, that, f the earth had only one magnetic axis, zvhose centre 
coincides xeith that of the earth, the lines of equal dip would 
cmncide w'lth the lines of equal intensity. As this is not by any 
