y a good deal more about pallets and pallet action,
still we think it advisable to drop for the present this particular part
of the lever escapement and take up fork and roller action, because, as
we have stated, frequently the fork and roller are principally at fault.
In considering the action and relation of the parts of the fork and
roller, we will first define what is considered necessary to constitute
a good, sound construction where the fork vibrates through ten degrees
of angular motion and is supposed to be engaged with the roller by means
of the jewel pin for thirty degrees of angular motion of the balance.

There is no special reason why thirty degrees of roller action should be
employed, except that experience in practical construction has come to
admit this as about the right arc for watches of ordinary good, sound
construction. Manufacturers have made departures from this standard, but
in almost every instance have finally come back to pretty near these
proportions. In deciding on the length of fork and size of roller, we
first decide on the distance apart at which to place the center of the
balance and the center of the pallet staff. These two points
established, we have the length of the fork and diameter of the roller
defined at once.

HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.

To illustrate, let us imagine the small circles _A B_, Fig. 54, to
represent the center of a pallet staff and balance staff in the order
named. We divide this space into four equal parts, as shown, and the
third space will represent the point at which the pitch circles of the
fork and roller will intersect, as shown by the arc _a_ and circle _b_.
Now if the length of the radii of these circles stand to each other as
three to one, and the fork vibrates through an arc of ten degrees, the
jewel pin engaging such fork must remain in contact with said fork for
thirty degrees of angular motion of the balance.

[Illustration: Fig. 54]

Or, in other words, the ratio of angular motion of two _mobiles_ acting
on each must be in the same ratio as the length of their radii at the
point of contact. If we desire to give the jewel pin, or, in ordinary
horological phraseology, have a greater arc of roller action, we would
extend the length of fork (say) to the point _c_, which would be
one-fifth of the space between _A_ and _B_, and the ratio of fork to
roller action would be four to one, and ten degrees of fork action wo