first produce the arcs _a b c_, Fig. 133, as directed,
and then proceed to delineate a tooth as in previous instances. To
delineate our cylinder in the position we have assumed above, we take
the space between the points _e d_ in our dividers and setting one leg
at _d_ establish the point _g_, to represent the center of our cylinder.
If we then sweep the circle _h_ from the center of _g_ we define the
inner surface of the shell of our cylinder.

Strictly speaking, we have not assumed the position we stated, that is,
the impulse face of the tooth as passing half way into the cylinder. To
comply strictly with our statement, we divide the chord of the impulse
face of the tooth _A_ into eight equal spaces, as shown. Now as each of
these spaces represent the thickness of the cylinder, if we take in our
dividers four of these spaces and half of another, we have the radius of
a circle passing the center of the cylinder shell. Consequently, if with
this space in our dividers we set the leg at _d_, we establish on the
arc _b_ the point _i_. We locate the center of our cylinder when
one-half of an entering tooth has passed into the cylinder. If now from
the new center with our dividers set at four of the spaces into which we
have divided the line _e f_ we can sweep a circle representing the inner
surface of the cylinder shell, and by setting our dividers to five of
these spaces we can, from _i_ as a center, sweep an arc representing the
outside of the cylinder shell. For all purposes of practical study the
delineation we show at Fig. 133 is to be preferred, because, if we carry
out all the details we have described, the lines would become confused.
We set our dividers at five of the spaces on the line _e f_ and from _g_
as a center sweep the circle _j_, which delineates the outer surface of
our cylinder shell.

Let us now, as we directed in our former instructions, draw a flattened
curve to represent the acting surface of the entrance lip of our
cylinder as if it were in direct contact with the impulse face of the
tooth. To delineate the exit lip we draw from the center _g_, Fig. 134,
to the radial line _g k_, said line passing through the point of contact
between the tooth and entrance lip of the cylinder. Let us next continue
this line on the opposite side of the point _g_, as shown at _g k'_, and
we thus bisect the cylinder shell into two equal parts of 180 degrees
each. As we previously explained, the entire extent of the cyl