encil line, represented by the dotted line _t_ in our drawing; and
where this circle intersects the arc _a_ we name it the point _s_; and
it is at this point the heel of our escape-wheel tooth must part with
the exit lip of the cylinder. From _e_ as a center and through the point
_s_ we draw the line _e l''_. With our dividers set to the radius of any
convenient arc which we have divided into degrees, we sweep the short
arc _d'_. The intersection of this arc with the line _e l''_ we name the
point _u_; and from _e_ as a center we draw the radial line _e u f'_. We
place the letter _f''_ in connection with this line because it (the
line) bears the same relations to the half shell of the cylinder shown
in Fig. 133 that the line _f_ does to the half shell (_D_) shown in Fig.
132. We draw the line _f'' f'''_, Fig. 133, which divides the cylinder
into two segments of 180 degrees each. We take the same space in our
dividers with which we swept the interior of the cylinder in Fig. 132
and sweep the circle _v_, Fig. 133. From _e_ as a center we sweep the
short arc _d''_, Fig. 133, and from its intersection of the line _f''_
we lay off six degrees on said arc _d''_ and draw the line _e' k''_,
which defines the angular extent of our entrance lip to the half shell
of the cylinder in Fig. 133. We draw the full lines of the cylinder as
shown.

We next delineate the heel of the tooth which has just passed out of the
cylinder, as shown at _D'_, Fig. 133. We now have a drawing showing the
position of the half shell of the cylinder just as the tooth has passed
the exit lip. This drawing also represents the position of the half
shell of the cylinder when the tooth rests against it on the outside. If
we should make a drawing of an escape-wheel tooth shaped exactly as the
one shown at Fig. 132 and the point of the tooth resting at _x_, we
would show the position of a tooth encountering the cylinder after a
tooth which has been engaged in the inside of the shell has passed out.
By following the instructions now given, we can delineate a tooth in any
of its relations with the cylinder shell.

DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.

We will now go through the operation of delineating an escape-wheel
tooth while in action. The position we shall assume is the one in which
the cylinder and escape-wheel tooth are in the relation of the passage
of half the impulse face of the tooth into the cylinder. To do this is
simple enough: We