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## LOCATING THE CENTER OF THE BALANCE STAFF.

Somewhere on this line is located the center of the
balance staff, and it is the problem in hand to locate
or establish this center. Now, it is known the
circles which define the peripheries of the escape
wheel and the impulse roller intersect at *e e^2*.
We can establish on our circle *A* where these
intersections take place by laying off twelve degrees,
one-half of the impulse arc on each side of the line
of centers *a f* on this circle and establishing
the points *e e^2*. These points *e e^2*
being located at the intersection of the circles *A*
and *B*, must be at the respective distances
of 5” and 21/2” distance from the center
of the circles *A B*; consequently, if we set
our dividers at 21/2” and place one leg at *e*
and sweep the short arc *g^2*, and repeat this
process when one leg of the dividers is set at *e^2*,
the intersection of the short arcs *g* and *g^2*
will locate the center of our balance staff.
We have now our two centers established, whose peripheries
are in the relation of 2 to 1.

To know, in the chronometer which we are supposed
to be constructing, the exact distance apart at which
to plant the hole jewels for our two mobiles, *i.e*.,
escape wheel and balance staff, we measure carefully
on our drawing the distance from *a* to *c*
(the latter we having just established) and make our
statement in the rule of three, as follows: As
(10) the diameter of drawn escape wheel is to our real
escape wheel so is the measured distance on our drawing
to the real distance in the chronometer we are constructing.

It is well to use great care in the large drawing
to obtain great accuracy, and make said large drawing
on a sheet of metal. This course is justified
by the degree of perfection to which measuring tools
have arrived in this day. It will be found on
measurement of the arc of the circle *B*, embraced
between the intersections *e e^2*, that it is
about forty-eight degrees. How much of this we
can utilize in our escapement will depend very much
on the perfection and accuracy of construction.

[Illustration: Fig. 139]

We show at Fig. 140 three teeth of an escape wheel,
together with the locking jewel *E* and impulse
jewel *D*. Now, while theoretically we could
commence the impulse as soon as the impulse jewel *D*
was inside of the circle representing the periphery
of the escape wheel, still, in practical construction,
we must allow for contingencies. Before it is
safe for the escape wheel to attack the impulse jewel,
said jewel must be safely inside of said escape wheel
periphery, in order that the attacking tooth shall
act with certainty and its full effect. A good
deal of thought and study can be bestowed to great
advantage on the “action” of a chronometer
escapement. Let us examine the conditions involved.