Astronomical and Nautical Collections. 331 
DENT OF THE THICKNESS OF THE METAL: it is determined only 
by the radius of the external surface, and by the co-ordinates be- 
longing to the position of the point on which the forces act. When 
the distance of this point from the centre of the sphere is very great 
in comparison with the radius, each of the three forces is very 
nearly as the cube of the radius directly, and as the cube of the 
distance inversely. Wemay reduce them to two, one directed to 
or from the centre of the sphere, the other coinciding with the di- 
rection of the dipping needle. The former vanishes when the point 
of action is situated in the plane passing through the centre of the 
sphere, and perpendicular to the latter: hence it follows that if a 
small magnetic needle be placed in this plane, the direction which» 
it would assume, in virtue of the action of the earth, will not be 
altered by the attraction of the sphere. We must, however, be 
careful to avoid inferring from this circumstance that this attraction 
vanishes in the supposed plane; for the second elementary force 
does not vanish at the same time with the first; it will be sub- 
tracted from the action of the earth, and its effect will be to retard 
more and more the oscillations of the needles, in proportion as the 
needle is brought nearer and nearer to the sphere. At the surface 
itself, and in any plane intersecting it, this foree is equal and 
contrary to the action of the earth; so that in this situation the 
little needle will only be urged in the direction of the radius: and 
in the plane perpendicular to the dipping needle, and very near the 
surface of the sphere, the needle would be exempt from all magnetic 
action, and would have no determinate direction, provided, however, 
that it were so small as to have its influence on the magnetism of 
the sphere inconsiderable. 
_ Mr. Professor Barlow, of Woolwich, has lately made. a great 
number of experiments on the deviations of the compass, and of the 
dipping needle, produced by the influence of a sphere of iron mag- 
netized by the influence of the earth. His observations are recorded 
in his Essay on Magnetic Attractions, 2 ed. Lond. 1823. They 
have enabled him to conclude that the effect on the needle is the 
same whether the sphere that produces them is completely solid or 
hollow: and at the actual distances of the needle from the sphere, 
