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 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 cylinder half shell is 196 degrees.  We now set our dividers to the radius of any convenient arc which we have divided into degrees, and from g