lse when it does occur. The velocity of the ruby pin at P; Fig. 14,
is much greater than at W, consequently it will not be overtaken as soon
by the fork as at W. The velocity of the fork at the latter point is
greater than at P; the intersection of _ii_ and _cc_ is also not as
great; therefore the lower the proportion the finer and more exact must
the workmanship be.

We will notice that the unlocking action has been overruled by the
impulse. The only point so far in which the former has been favored is
in the diminished action before the line of centers, as previously
pointed out at P, Fig. 14.

We will now consider the width of the ruby pin and to get a good insight
into the question, we will study Fig. 17. A is the pallet center, A' the
balance center, the line AA' being the line of centers; the angle WAA
equals half the total motion of the fork, the other half, of course,
taking place on the opposite side of the center line. WA is the _center_
of the fork when it rests against the bank. The angle AA'X represents
half the impulse angle; the other half, the same as with the fork, is
struck on the other side of the center line. At the point of
intersection of these angles we will draw _cc_ from the pallet center A,
which equals the acting length of the fork, and from the balance center
we will draw _ii_, which equals the _theoretical_ impulse radius; some
writers use it as the _real_ radius. The wider the ruby pin the greater
will the latter be, which we will explain presently.

The ruby pin in entering the fork must have a certain amount of freedom
for action, from 1 to 1 1/4deg. Should the watch receive a jar at the
moment the guard point enters the crescent or passing hollow in the
roller, the fork would fly against the ruby pin. It is important that
the angular freedom between the fork and ruby pin at the moment it
enters into the slot be _less_ than the total locking angle on the
pallets. If we employ a locking angle of 1 1/2deg. and 1/2deg. run, we
would have a total lock on the pallets of 2deg. By allowing 1 1/4deg.
of freedom for the ruby pin at the moment the guard point enters the
crescent, in case the fork should strike the face of the ruby pin, the
pallets will still be locked 3/4deg. and the fork drawn back against the
bankings through the draft angle.

We will see what this shake amounts to for a given acting length of
fork, which describes an arc of a circle, therefore the acting length is
only the r