s before stated, the
longer the radius the smaller the angle. The action at P is also closer
to the line of centers than it is at W, which is another advantage.

[Illustration: Fig. 14.]

We will notice that by employing a large impulse angle, and consequently
a short radius, the intersection _m_ of the two circles _ii_ and _cc_ is
very _safe_, whereas, with the conditions reversed in favor of the
impulse action, the intersection at _k_ is more delicate. We have now
seen enough to appreciate the fact that we favor one action at the
expense of another.

By having a lifting angle on pallet and tooth of 8 1/2deg., a locking
angle of 1 1/2deg., and a run of 1/2deg., we will have an angular
movement of the fork of 8 1/2 + 1 1/2 + 1/2 = 10 1/2deg.

[Illustration: Fig. 15.]

Writers generally only consider the movement of the fork from drop to
drop on the pallets, but we will be thoroughly practical in the matter.
With a total motion of the fork of 10 1/2deg. (JAW, Fig. 15), one-half,
or 5 1/4deg. will be performed on each side of the line of centers. We
are at liberty to choose any impulse angle which we may prefer; 3 to 1
is a good proportion for an ordinary well-made watch. By employing it,
the angle XA'Y would be equal to 31 1/2deg. The radius A'X Fig. 16, is
also of the same proportion, but the angle AA'X is greater because the
fork angle WAA' is greater than the same angle in Fig. 15. We will
notice that the intersection _k_ is much smaller in Fig. 15 than in
Fig. 16. The action in the latter begins much further from the line of
centers than in the former and outlines an action which should not be
made.

[Illustration: Fig. 16.]

To come back to the impulse angle, some might use a proportion of 3.5, 4
or even 5 to 1, while others for the finest of watches would only use
2.75 to 1. By having a total vibration of the balance of 1 1/2 turns, which
is equal to 540deg. a fork angle of 10deg. and a proportion of 2.75 for the
impulse angle which would be equal to 10 x 2.75 = 27.5deg. The _free_
vibration of the balance, or as this is called, "the supplemental arc,"
is equal to 540deg. - 27.5deg. = 512.50deg., while with a proportion of
5 to 1, making an impulse angle of 50deg., it would be equal to 490deg.
To sum up, the finer the watch the lower the proportion, the closer the
action to the line of centers, the smaller the friction. On account of
leverage the more difficult the unlocking but the more energetic the
impu