_x_ equal parts. For instance, to
divide the stem of a thermometer from the freezing-point to the
boiling-point into one hundred degrees.

The following outline will explain how a line may be so divided. Suppose
the line _AB_ (Fig. 40) is to be divided into nine equal parts. Adjust a
hinged rule so that the points _A_ and _B_ coincide with the inside
edges of the limbs, one of them, _A_, being at the ninth division
(_e.g._ the ninth inch) of _CE_. Then if lines parallel to _ED_ be drawn
from each division of the scale to meet _AB_, _AB_ will be divided into
nine equal parts.

[Illustration: FIG. 40.]

A very convenient and simple arrangement on this principle for dividing
a line into any number of equal parts with considerable accuracy, is
described by Miss S. Marks in the _Proceedings of the Physical Society_,
July 1885.[20] One limb of a hinged rule _D_ is made to slide upon a
plain rule fixed to it; the plain rule carries needles on its under
surface which hold the paper in position. The position of the divided
rule and line to be divided being adjusted, the hinged rule is gently
pushed forwards, as indicated by the arrow in Fig. 40, till division
eight coincides with the line _AB_. A mark is made at the point of
coincidence, and division seven on the scale is similarly brought to the
line _AB_, and so on. The inner edge of _EC_ should have the divisions
marked upon it, that their coincidence with _AB_ maybe more accurately
noted. The joint _E_ must be a very stiff one.

[20] Since this was printed I have observed that the above method is not
identical with that described by Miss Marks, but for ordinary purposes I
do not think it will be found to be inferior.

A line drawn of given length or a piece of paper may be divided into any
given number of equal parts, and will then serve as the scale _A_ of
Fig. 39, p. 74, the thermometer or other object to be graduated taking
the place of _B_.

Scales carefully divided according to any of the methods described will
be fairly accurate _if trustworthy instruments have been employed as
standards_.

It will be found possible when observing the volume of a gas over
mercury, or the height of a column of mercury in a tube, to measure
differences of one-sixth to one-eighth of a millimetre with a
considerable degree of accuracy. To obtain more delicate measurements a
vernier[21] must be employed.

[21] For the nature and use of the vernier, a treatise on Physics or
Physi