lves to the graphic plan, considering it preferable. In the
practical detail drawing we advise the employment of the scale given,
i.e., delineating an escape wheel 10" in diameter. The drawings which
accompany the description are one-fourth of this size, for the sake of
convenience in copying.

With an escape wheel of fifteen teeth the impulse arc is exactly
twenty-four degrees, and of course the periphery of the impulse roller
must intersect the periphery of the escape wheel for this arc (24 deg.).
The circles _A B_, Fig. 139, represent the peripheries of these two
mobiles, and the problem in hand is to locate and define the position of
the two centers _a c_. These, of course, are not separated, the sum of
the two radii, i.e., 5" + 21/2" (in the large drawing), as these
circles intersect, as shown at _d_. Arithmetically considered, the
problem is quite difficult, but graphically, simple enough. After we
have swept the circle _A_ with a radius of 5", we draw the radial line
_a f_, said line extending beyond the circle _A_.

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
(1