it. When they are satisfactory,
they may be etched by one of the following processes:--

(1.) By moistening some cotton wool, tied to a stick, with solution of
hydrofluoric acid, and gently rubbing this over the scratched surface
for a minute or so; then washing away the acid with water, and cleaning
off the wax. This is the simplest method, but the marks made are
generally transparent, and therefore not very easy to read. The
simplicity of this method is a great recommendation, however.

(2.) Expose the tube to the fumes of hydrofluoric acid generated from a
mixture of powdered fluor-spar and strong sulphuric acid, in a leaden
trough. The marks produced in this way are usually opaque, and are
therefore very visible, and easily read.

After the above detailed account it will only be necessary to give an
outline of the other process of graduating tubes.

[Illustration: FIG. 39.]

The standard scale to be copied, _A_, which may in this case be another
graduated tube, or even a paper scale, and the object to be ruled, _B_,
are securely fixed, end to end, a little distance apart, in a groove
made in a board or in the top of a table. A stiff bar of wood, _C_, has
a point fixed at _D_, and a knife edge at _E_, _D_ is placed in any
division of _A_, _C_ is held firmly at _E_ and _D_, and a cut is made by
the knife through the wax on _B_, the point _D_ is then moved into the
next division, and the operation is repeated. To regulate the length and
position of the cuts, _B_ is usually held in position by two sheets of
brass projecting over the edges of the groove in which it lies; the
metal sheets have notches cut into them at the intervals at which longer
marks are to be made.

When the scale is completed, the equality of the divisions in various
parts of it may be, to some extent, verified as follows:--Adjust a
compass so that its points fall into two divisions 5, 10, or 20 mm.
apart. Then apply the points of the compass to various parts of the
scale. In every part the length of a given number of divisions should be
exactly the same. The individual divisions should also be carefully
inspected by the eye; they should be sensibly equal. If badly ruled,
long and short divisions will be found on the scale. Very often a long
and a short division will be adjacent, and will be the more easily
observed in consequence.

=To Divide a Given Line into Equal Parts.=--Occasionally it is necessary
to divide a line of given length into