adius of that circle and must be multiplied by two in order to
get the diameter. The acting length of fork = 4.5 mm., what is the
amount of shake when the ruby pin passes the acting corner?
4.5 x 2 x 3.1416 / 360deg. = .0785 x 1.25 = .0992 mm. The shake of the ruby
pin in the slot of the fork must be as slight as possible, consistent
with perfect freedom of action. It varies from 1/4deg. to 1/2deg.,
according to length of fork and shape of ruby pin. A square ruby pin
requires more shake than any other kind; it enters the fork and receives
the impulse in a diagonal direction on the jewel, in which position it
is illustrated at Z, Fig. 20. This ruby pin acts on a knife edge, but
for all that the engaging friction during the unlocking action is
considerable.

Our reasoning tells us it matters not if a ruby pin be wide or narrow,
it must have _the same_ freedom in passing the acting edge of the fork,
therefore, to have the impulse radius on the point of intersection of
A'X with AW, Fig. 17, we would require a _very_ narrow ruby pin. With
1deg. of freedom at the edge, and 1/2deg. in the slot, we could only
have a ruby pin of a width of 1 1/2deg. Applying it to the preceding
example it would only have an actual width of .0785 x 1.5 = .1178 mm.,
or the size of an ordinary balance pivot. At _n_, Fig. 17, we illustrate
such a ruby pin; the theoretical and real impulse radius coincide with
one another. The intersection of the circle _ii_ and _cc_ is very
slight, while the friction in unlocking begins within 1deg. of half the
total movement of the fork from the line of centers; to illustrate, if
the angular motion is 11deg. the ruby pin under discussion will begin
action 4 1/2deg. before the line of centers, being an engaging, or
"uphill" friction of considerable magnitude.

[Illustration: Fig. 17.]

[Illustration: Fig. 18.]

[Illustration: Fig. 19.]

[Illustration: Fig. 20.]

The intersection with the fork is also much less than with the wider
ruby pin, making the impulse action very delicate. On the other hand the
widest ruby pin for which there is any occasion is one beginning the
unlocking action on the line of centers, Fig. 17; this entails a width
of slot equal to the angular motion of the fork. We see here the
advantage of a wide ruby pin over a narrow one in the unlocking action.
Let us now examine the question from the standpoint of the impulse
action.

Fig. 18 illustrates the moment the impulse is transmitted; t