In describing the method for drawing the cylinder escapement we shall make a radical departure from the systems usually laid down in text-books, and seek to simplify the formulas which have heretofore been given for such delineations.  In considering the cylinder escapement we shall pursue an analytical course and strive to build up from the underlying principles.  In the drawings for this purpose we shall commence with one having an escape wheel of 10” radius, and our first effort will be the primary drawing shown at Fig. 129.  Here we establish the point A for the center of our escape wheel, and from this center sweep the short arc a a with a 10” radius, to represent the circumference of our escape wheel.  From A we draw the vertical line A B, and from the intersection of said line with the arc a a we lay off twelve degree spaces on each side of the line A B on said arc a and establish the points b c.  From A as a center we draw through the points b c the radial lines b’ c’.

To define the face of the incline to the teeth we set our dividers to the radius of any of the convenient arcs of sixty degrees which we have provided, and sweep the arc t t.  From the intersection of said arc with the line A b’ we lay off on said arc sixty-four degrees and establish the point g and draw the line b g.  Why we take sixty-four degrees for the angle A b g will be explained later on, when we are discussing the angular motion of the cylinder.  By dividing the eleventh degree from the point b on the arc a a into thirds and taking two of them, we establish the point y and draw the radial line A y’.  Where this line A y’ intersects the line b g we name the point n, and in it is located the point of the escape-wheel tooth.  That portion of the line b g which lies between the points b and n represents the measure of the inner diameter of the cylinder, and also the length of the chord of the arc which rounds the impulse face of the tooth.  We divide the space b n into two equal portions and establish the point e, which locates the position of the center of the cylinder.  From A as a center and through the point e we sweep the arc e’ e’, and it is on this line that the points establishing the center of the cylinder will in every instance be located.  From A as a center, through the point n we sweep the arc k, and on this line we locate the points of the escape-wheel teeth.  For delineating the curved impulse faces of the escape-wheel teeth we draw from the point e and at right angles to the line b g the line e o.  We next take in our dividers the radius of the arc k, and setting one leg at either of the points b or n, establish with the other leg the point p’ on the line e o, and from the