times finer than this stubborn material, but wire ten times finer is
much more than ten times more easily twisted. It is ten thousand times
more easily twisted. This is because the torsion varies as the fourth
power of the diameter. So we say 10 × 10 = 100, 100 × 100 = 10,000.
Therefore, with the finest wire, forces 10,000 times feebler still
could be observed.

It is therefore evident how great is the advantage of reducing the
size of a torsion wire. Even if it is only halved, the torsion is
reduced sixteenfold. To give a better idea of the actual sizes of such
wires and fibers as are in use, I shall show upon the screen a series
of such photographs taken by Mr. Chapman, on each of which a scale of
thousandths of an inch has been printed.

[Illustration: Scale of 1000ths of an inch for Figs. 1 to 7. The scale
of Figs. 8 and 9 is much finer.]

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

[Illustration: FIG. 3.]

The first photograph (Fig. 1) is an ordinary hair--a sufficiently
familiar object, and one that is generally spoken of as if it were
rather fine. Much finer than this is the specimen of copper wire now
on the screen (Fig. 2), which I recently obtained from Messrs. Nalder
Brothers. It is only a little over one-thousandth of an inch in
diameter. Ordinary spun glass, a most beautiful material, is about
one-thousandth of an inch in diameter, and this would appear to be an