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 face of our escape-wheel tooth, Fig. 129.

There is no reason why we should take twenty-degrees for the angle k e l except that the practical construction of the larger sizes of cylinder watches has established the fact that this is about the right angle to employ, while in smaller watches it frequently runs up as high as twenty-five.  Although the cylinder is seemingly a very simple escapement, it is really a very abstruce one to follow out so as to become familiar with all of its actions.

THE CYLINDER PROPER CONSIDERED.

[Illustration:  Fig. 131]

We will now proceed and consider the cylinder proper, and to aid us in understanding the position and relation of the parts we refer to Fig. 131, where we repeat the circles d and h, shown in Fig. 130, which represents the inside and outside of the cylinder.  We have here also repeated the line f of Fig. 130 as it cuts the cylinder in half, that is, divides it into two segments of 180 degrees each.  If we conceive of a cylinder in which just one-half is cut away, that is, the lips are bounded by straight radial lines, we can also conceive of the relation and position