aced off on
each side of the line of centers, forming the angles _m_ A _k_ of
10 1/4deg. Placing our dividers on A B the center distance of 'scape
wheel and pallets, we plant them on A and construct _c c_; thus we will
have the acting length of fork and its path. We saw in our analysis that
the impulse angle should be as small as possible. We will use one of
28deg. in our draft of the double roller; we might however remark that
this angle should vary with the construction of the escapements in
different watches; if too small, the balance may be stopped when the
escapement is locked, while if too great it can be stopped during the
lift; both these defects are to be avoided. The angles being
respectively 10 1/4deg. and 28deg. it follows they are of the following
proportions: 28deg. / 10.25 = 2.7316. The impulse radius therefore bears
this relation (but in the inverse ratio to the angles), to the acting
length of fork.

We will put it in the following proportion; let A_c_ equal acting length
of fork, and _x_ the unknown quantity; 28:10.25 :: A_c_:_x_; the answer
will be the theoretical impulse radius. Having found the required radius
we plant one jaw of our measuring instrument on the point of
intersection of _c c_ with _k_ A or _m_ A and locate the other jaw on
the line of centers; we thus obtain A' the balance center. Through the
points of intersection before designated we will draft X A' and Y A'
forming the impulse angle X A' Y of 28deg. At the intersection of this
angle with the fork angle _k_ A' _m_, we draw _i i_ from the center A;
this gives us the theoretical impulse circle. The total lock being
1 3/4deg. it follows that the angle described by the balance in
unlocking = 1 3/4 x 2.7316 = 4.788deg. According to the specifications
the width of slot is to be 5 1/8deg.; placing the center of the
protractor on A we construct half of this angle on each side of _k_ A,
which passes through the center of the fork when it rests against the
bank; this gives us the angle _s_ A _n_ of 5 1/8deg. If the disengaging
pallet were shown locked then _m_ A would represent the center of the
fork. The slot is to be made of sufficient depth so there will be no
possibility of the ruby pin touching the bottom of it. The ruby pin is
to have 1 1/4deg. freedom in passing the acting edge of the fork; from
the center A we construct the angle _t_ A _n_ of 1 1/4deg.; at the point
of intersection of _t_ A with _c c_ the acting radius of the fork, w