point p’ as a center we sweep the arc b v n, which defines the curve of the impulse faces of the teeth.  From A as a center through the point p’ we sweep the arc p, and in all instances where we desire to delineate the curved face of a tooth we locate either the position of the point or the heel of such tooth, and setting one leg of our dividers at such point, the other leg resting on the arc p, we establish the center from which to sweep the arc defining the face of said tooth.

ADVANTAGES GAINED IN SHAPING.

The reason for giving a curved form to the impulse face of the teeth of cylinder escape wheels are somewhat intricate, and the problem involves several factors.  That there are advantages in so shaping the incline or impulse face is conceded, we believe, by all recent manufacturers.  The chief benefit derived from such curved impulse faces will be evident after a little thought and study of the situation and relation of parts as shown in Fig. 129.  It will be seen on inspection that the angular motion imparted to the cylinder by the impulse face of the tooth when curved as shown, is greater during the first half of the twelve degrees of escape-wheel action than during the last half, thus giving the escape wheel the advantage at the time the balance spring increases its resistance to the passage of the escape-wheel tooth across the lip of the cylinder.  Or, in other words, as the ratio of resistance of the balance spring increases, in a like ratio the curved form of the impulse face of the tooth gives greater power to the escape-wheel action in proportion to the angular motion of the escape wheel.  Hence, in actual service it is found that cylinder watches with curved impulse planes to the escape-wheel teeth are less liable to set in the pocket than the teeth having straight impulse faces.

THE OUTER DIAMETER OF THE CYLINDER.

[Illustration:  Fig. 129]

To define the remainder of the form of our escape-wheel tooth we will next delineate the heel.  To do this we first define the outer diameter of our cylinder, which is the extent from the point n to c, and after drawing the line n c we halve the space and establish the point x, from which point as a center we sweep the circle w w, which defines the outer circumference of our cylinder.  With our dividers set to embrace the extent from the point n to the point c we set one leg at the point b, and with the other leg establish on the arc k the point h.  We next draw the line b h, and from the point b draw the line b f at right angle to the line b h.  Our object for drawing these lines is to define the heel of our escape-wheel tooth by a right angle line tangent to the circle w, from the point b; which circle w represents the curve of the outer circumference of the cylinder.  We shape the point of the tooth as shown to give it the proper stability, and draw the full line j to a curve from the center A.  We have now defined the form of the upper face of the tooth.  How to delineate the U arms will be taken up later on, as, in the present case, the necessary lines would confuse our drawing.