An introduction to the mathematical theory of attraction ...

2 lIntroductory.
As regards their mutual action, charges of electricity
behave therefore to a certain extent like masses of gravitating
matter, but there is an important difference which is immediately manifested. In the case of gravitating matter, the
mutual force between two particles is always attractive; but
charges of electricity, on the other hand, sometimes attract
and sometimes repel one another.
The observed phenomena can be explained by supposing
that an electric charge, or in common language electricity,
is one or other of two different kinds; that two charges or
quantities of electricity of the same kind repel one another;
and that two charges of opposite kinds attract one another,
the force in each case being proportional to the product of
the charges or quantities of electricity.
To express mathematically what has been said above, we
must regard one kind of electricity as positive and the other
kind as negative. A quantity of electricity which occupies a
space so small that it may be regarded as a point may be
called an electric particle; and if a force which is repulsive be
considered as positive, we may enunciate the fundamental
law of electric forces by saying, that two particles of electricity
act on each other with a force directly proportional to the proclct
of their masses, and inversely proportional t the square of the
distance between them. The word ' mass ' is here used only in
reference to the amount of bfrce which the corresponding
quantity of electricity is capable of producing, and is not
meant to imply inertia or exclusive occupation of space.
Looked at from a mathematical point of view, electric
forces are of a more general character than those resulting
from gravitation, and the study of the former includes that
of the latter.
3. Distribution of Electricity.-As the electric forces
due to the elements of an electrified body have each a definite
magnitude, and pass through the elements to which they
correspond, it may be said that there is a certain quantity of
electricity accumulated in each space-element of the body,
and we may consider the distribution of electricity in an electrified conductor.
4. Magnetic Forces.-The elementary forces due to
the presence of a magnetized body are in some respects