old-style workman would take a round broach and calculate the size
of the cylinder by finding a place where the broach would just go
between the teeth, and the size of the broach at this point was supposed
to be the outer diameter of the cylinder. By our method we measure the
diameter of the escape wheel in thousandths of an inch, and from this
size calculate exactly what the diameter of the new cylinder should be
in thousandths of an inch. Suppose, to further carry out our comparison,
the escape wheel which is in the watch has teeth which have been stoned
off to permit the use of a cylinder which was too small inside, or, in
fact, of a cylinder too small for the watch: in this case the broach
system would only add to the trouble and give us a cylinder which would
permit too much inside drop.

DRAWING A CYLINDER.

We have already instructed the pupil how to delineate a cylinder escape
wheel tooth and we will next describe how to draw a cylinder. As already
stated, the center of the cylinder is placed to coincide with the center
of the chord of the arc which defines the impulse face of the tooth.
Consequently, if we design a cylinder escape wheel tooth as previously
described, and setting one leg of our compasses at the point _e_ which
is situated at the center of the chord of the arc which defines the
impulse face of the tooth and through the points _d_ and _b_ we define
the inside of our cylinder. We next divide the chord _d b_ into eight
parts and set our dividers to five of these parts, and from _e_ as a
center sweep the circle _h_ and define the outside of our cylinder. From
_A_ as a center we draw the radial line _A e'_. At right angles to the
line _A e'_ and through the point _e_ we draw the line from _e_ as a
center, and with our dividers set to the radius of any of the convenient
arcs which we have divided into sixty degrees, we sweep the arc _i_.
Where this arc intersects the line _f_ we term the point _k_, and from
this point we lay off on the arc _i_ 220 degrees, and draw the line
_l e l'_, which we see coincides with the chord of the impulse face of the
tooth. We set our dividers to the same radius by which we sweep the arc
_i_ and set one leg at the point _b_ for a center and sweep the arc
_j'_. If we measure this arc from the point _j'_ to intersection of said
arc _j'_ with the line _l_ we will find it to be sixty-four degrees,
which accounts for our taking this number of degrees when we defined the
fac