An introduction to the mathematical theory of attraction ...

14 Resultant Force.
infinitely near O are continuously zero, but the normal component changes from - 27rc to + 27r, that is, its value in the
direction in which P is moving is increased by 47ra as P passes
through the surface S.
The force components due to mass at a distance from P
greater than a are obviously continuous. Hence on the whole,
when the acting mass is repulsive, the force component along
the normal in the direction in which P is moving increases by
47re as P passes through a surface on which mass of density
o is distributed, but the other force components are not
altered by any finite amount. It is plain that in all cases,
whether P be on the surface or not, all the force components
remain finite.
The algebraical expressions for X, Y, Z as integrals
derived from equations (1), Art. 7, are not in general valid,
in the case of a surface distribution, for a point on the
surface on which the mass is distributed, as the quantities
under the integral sign may in this case become infinite
within the limits of the integration.
17. Magnets.-The leading characteristic of magnetic
forces is the presence in each element of the magnetized body
of two centres of force of equal and opposite intensities, these
centres of force being situated at the extremities of an infinitely short line whose direction is that of the magnetization
of the element. The two centres of force are called poles,
one being a north pole, the other a south pole. Each repels
a pole of like kind to itself and attracts one of the opposite
kind. The direction of magnetization is reckoned from the
south pole to the north. The terms south and north are
used in reference to the Earth's action on the magnet, the
pole which is attracted towards the north being called the
north pole.
When a line of any form is uniformly magnetized in the
direction of its length, the effect in external space of the
north pole at the end of one element is neutralized by that
of the south pole at the beginning of the consecutive element.
Thus the effect of such a magnet on a north pole of unit intensity in external space is entirely due to the south pole at
one of its extremities and the north pole at the other. These
centres of force are called the potes of the magnet. A magnet