an ordinary lathe. The cog-wheels must, however, be specially shaped to
fit them. They consist of a number of round pins arranged in a circle
round the axis of the wheel and parallel to it. The ends are secured in
flanges like the wires of a squirrel cage. The teeth of cog-wheels
engage them and thus drive the wheel round. They were much used at one
time but are now falling out of favour again.

Involute teeth.

It is possible to make toothed wheels that drive with perfect uniformity
by using for the curve of the teeth involutes of circles. These
involutes are traced out by a point on a string that is gradually
unwound from a circle. They are in fact epicycloids traced by a rolling
circle of infinite radius, i.e. a straight line. Involute teeth have the
advantage that they roll on one another instead of sliding. When badly
made they put considerable strain on the axes or shafts that carry them.
Hence they have not been regarded with great favour by clockmakers.

Pitch.

By the pitch of a wheel is meant the number of teeth to the inch of
circumference or diameter of the wheel; the former is called the
circumferential pitch, the latter the diametral pitch. Thus if we say
that a wheel has 40 diametral pitch we mean that it has 40 teeth to each
inch of diameter. The circumferential pitch is of course got by dividing
the diametral pitch by [pi]. Wheel-cutters are made for all sizes of
pitches. If it were needed to make a pair of wheels the ratio of whose
motion was say 6:1 and we determined to use a diametral pitch of 30 to
the inch, that is teeth about 1/10 in. wide at the base, and if the
smaller circle were to have 20 teeth, we should need a blank of a
diameter of 20/30 + 2/30 = 22/30 in. for the smaller wheel, and one of
120/30 + 2/30 = 122/30 in. for the larger wheel which would have 120
teeth to the inch and be 4.06 in diameter to the tips of the teeth. The
smaller toothed wheel would be .73 of an inch in diameter over all. The
pitch circles of the wheels would be 2/3 and 4 in. respectively. For
fine wheel work, where the driver is always much larger than the driven
wheel, the epicycloidal tooth appears preferable, as it is generally
considered to put less side strain on the pinion wheel. But the relative
merits of the two systems have never been properly tested for clock
work.

_Going Barrels._--A clock which is capable of going accurately must have
some contrivance to keep it going while it is being woun