ON THE PHENOMENA OF TERRESTRIAL MAGNETISM. 77 
Proceeding then from these laws, M. Hansteen pursues the 
following investigations, based upon them, viz. 
The line of repose of an infinitely small magnetic needle within 
the sphere of action of a linear magnet. 
The dip of the magnetic line of repose towards the surface of 
a sphere, having in its centre an infinitely small linear 
magnet. 
The same, the magnet being eccentric. 
The situations of dip 0 and dip 90°, with the intermediate 
lines of dip, in the two cases, first, when the magnet is in 
the centre of the sphere; second, when it is eccentric. 
The magnetic intensity, and the isodynamic lines in both the 
preceding suppositions. 
The action of a magnet, being in shape a parallelogram, upon 
a magnetic point in the prolongation of its axis, and in its 
equator. 
The action of a cylindrical magnet upon a magnetic point in 
the prolongation of its axis, and in its equator. 
Upon these investigations are founded problems contained in 
the succeeding or sixth chapter, which is entitled 66 Application 
of the Theory of Magnets to the Theory of the Dip, Variation, 
and Force, at any given place of the earth’s surface of known 
geographical position.” 
Suppose a (3, fig. 1 ., a single magnetic axis in the interior of 
the earth ; its prolongation, till it meets the surface of the earth, 
forms A B, the magnetic chord, of which A and B are the extre¬ 
mities. It is possible that the centre of the chord y, the mathe¬ 
matical centre of the magnet, and its neutral point (or the point 
in which the opposite forces are equal, and where there is con¬ 
sequently neither attraction nor repulsion), might be three dif¬ 
ferent points; but they are at present considered to coincide all 
three in y, the centre of the chord. 
The circle E B F A is a great circle passing through C, the 
centre of the earth, and the magnetic chord. C y is the eccen¬ 
tricity of the chord. The magnetic equator is a great circle 
passing through the centre of the earth, perpendicular to the 
magnetic chord, and passing through its centre y : its poles are 
a and b, the extremities of a diameter of the earth parallel to 
the magnetic chord. If the magnetic axis were not eccentric, 
and the chord passed through the centre of the earth, its ex¬ 
tremities A and B would coincide with a and b , the poles of the 
magnetic equator. The radius of the earth being unity, the ec¬ 
centricity C y is the sine of the arcs A a and B b which measure 
the distance between the ends of the magnetic chord and the 
poles of the magnetic equator. 
