into use in exceptional cases, and if the watch was lying still
would theoretically never be required. Where fork and pallets are poised
on their arbor, pocket motion (except torsional) should but very little
affect the fork and pallet action of a watch, and torsional motion is
something seldom brought to act on a watch to an extent to make it
worthy of much consideration. In the double-roller action which we shall
consider, we shall adopt three-fifths of the pitch diameter of the
jewel-pin action as the proper size. Not but what the proportions given
by Grossmann will do good service; but we adopt the proportions named
because it enables us to use a light fork, and still the friction of the
guard point on the roller is but little more than where a guard roller
of half the diameter of the acting roller is employed.

The fork action we shall consider at present is ten degrees, but
subsequently we shall consider a double-roller action in which the fork
and pallet action is reduced to eight degrees. We shall conceive the
play between the guard point and the safety roller as one degree, which
will leave half a degree of lock remaining in action on the engaged
pallet.

THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.

In the drawing at Fig. 81 we show a diagram of the action of the
double-roller escapement. The small circle at _A_ represents the center
of the pallet staff, and the one at _B_ the center of the balance staff.
The radial lines _A d_ and _A d'_ represent the arc of angular motion of
fork action. The circle _b b_ represents the pitch circle of the jewel
pin, and the circle at _c c_ the periphery of the guard or safety
roller. The points established on the circle _c c_ by intersection of
the radial lines _A d_ and _A d'_ we will denominate the points _h_ and
_h'_. It is at these points the end of the guard point of the fork will
terminate. In construction, or in delineating for construction, we show
the guard enough short of the points _h h'_ to allow the fork an angular
motion of one degree, from _A_ as a center, before said point would come
in contact with the safety roller.

[Illustration: Fig. 81]

We draw through the points _h h'_, from _B_ as a center, the radial
lines _B g_ and _B g'_. We measure this angle by sweeping the short arc
_i_ with any of the radii we have used for arc measurement in former
delineations, and find it to be a trifle over sixty degrees. To give
ourselves a practical object less