l 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 o