d _B f_ embrace five degrees of
angular motion of the pallet. Now, the impulse plane of the pallet
occupies four of these five degrees. We do not draw a radial line from
_B_ inside of the line _B e_ to show where the outer angle of the
impulse plane commences, but the reader will see that the impulse plane
is drawn one degree on the arc _p_ below the line _B e_. We continue the
line _h h_ to represent the impulse face of the tooth, and measure the
angle _B n h_ and find it to be twenty-seven degrees. Now suppose we
wish to delineate the entrance pallet as if not in contact with the
escape-wheel tooth--for illustration, say, we wish the inner angle of
the pallet to be at the point _v_ on the arc _s_. We draw the radial
line _B l_ through _v_; and if we draw another line so it passes through
the point _v_ at an angle of twenty-seven degrees to _B l_, and continue
said line so it crosses the arc _p_, we delineate the impulse face of
our pallet.

We measure the angle _i n B_, Fig. 92, and find it to be seventy-four
degrees; we draw the line _v t_ to the same angle with _v B_, and we
define the inner face of our pallet in the new position. We draw a line
parallel with _v t_ from the intersection of the line _v y_ with the arc
_p_, and we define our locking face. If now we revolve the lines we have
just drawn on the center _B_ until the line _l B_ coincides with the
line _f B_, we will find the line _y y_ to coincide with _h h_, and the
line _v v'_ with _n i_.

HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.

We have now instructed the reader how to delineate either tooth or
pallet in any conceivable position in which they can be related to each
other. Probably nothing has afforded more efficient aid to practical
mechanics than has been afforded by the graphic solution of abstruce
mathematical problems; and if we add to this the means of correction by
mathematical calculations which do not involve the highest mathematical
acquirements, we have approached pretty close to the actual requirements
of the practical watchmaker.

[Illustration: Fig. 93]

To better explain what we mean, we refer the reader to Fig. 93, where we
show preliminary drawings for delineating a lever escapement. We wish to
ascertain by the graphic method the distance between the centers of
action of the escape wheel and the pallet staff. We make our drawing
very carefully to a given scale, as, for instance, the radius of the arc
_a_ is 5". After