An introduction to the mathematical theory of attraction ...

Tubes of Induction. 51
must be some lines of force inside the tube Tfor which R does
not change its sign so long as T does not pass through mass.
We can now see that T cannot return to the conductor A;
for if it did, a line of force L inside T, on which R does not
change its sign, would meet the conductor A in points Q and
Q'; and the circuit partly composed of L would be completed
by the line Q'Q on the conductor, in a displacement along
which no work would be done on an element of mass by the
forces of the system. Hence the forces of the system would
do work in the displacement of an element of mass round a
complete circuit which is impossible.
From Art. 25 it appears that a tube of force cannot be
a closed tube returning into itself. On the whole, therefore,
we may conclude that a positive tube of force starts from a
conductor on which the charge on the portion of surface
enclosed by the tube is positive, and either goes on to infinity
or ends on a conductor on which the charge on the corresponding portion of surface is negative, the two charges
being equal in magnitude.
The leading property of tubes of force in reference to
electrical science is the numerical equality of the charges on
the portions of the conductors by which they are terminated.
Tubes or solenoids along which this equality is propagated
through an insulating medium are termed tubes of induction.
It must be remembered that the identification of tubes of
force with tubes of induction in the manner effected above
holds good only under the limitations laid down in the preceding Article.
In reference to electric phenomena it would seem that
the existence of tubes of induction is the primary fact. This
was recognized by Clerk Maxwell who indicated a method of
basing on them the explanation of the observed phenomena
of electricity.
Another mode of doing this has been developed by Professor J. J. Thomson. These investigations do not come
within the scope of the present treatise.
In accordance with the theory adopted in this Article, the
tuit tube qf induction may be defined as that in which f RdZ
taken over the portion of an equipotential surface enclosed by
the tube is unity. The charge E on a conductor may be
E 2