I had better perhaps at once indicate in a general way the magnitude
of the forces with which we have to deal.

The weight of a single grain is not to our senses appreciable, while
the weight of a ton is sufficient to crush the life out of any one in
a moment. A ton is about 15,000,000 grains. It is quite possible to
measure with unfailing accuracy forces which bear the same relation to
the weight of a grain that a grain bears to a ton.

To show how the torsion of wires or threads is made use of in
measuring forces, I have arranged what I can hardly dignify by the
name of an experiment. It is simply a straw hung horizontally by a
piece of wire. Resting on the straw is a fragment of sheet iron
weighing ten grains. A magnet so weak that it cannot lift the iron yet
is able to pull the straw round through an angle so great that the
existence of the feeble attraction is evident to every one in the
room.

Now it is clear that if, instead of a straw moving over the table
simply, we had here an arm in a glass case and a mirror to read the
motion of the arm, it would be easy to observe a movement a hundred or
a thousand times less than that just produced, and therefore to
measure a force a hundred or a thousand times less than that exerted
by this feeble magnet.

Again, if instead of wire as thick as an ordinary pin I had used the
finest wire that can be obtained, it would have opposed the movement
of the straw with a far less force. It is possible to obtain wire ten
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 x 10 = 100, 100 x 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) i