koning from the center _p_) of twelve degrees,
and be arrested by the inside of the arc _l_ at _e_. If we now should
reverse the motion and turn the arc _l_ backward, the tooth at _e_
would, in turn, be released and the tooth following after _D_ (but not
shown) would engage _l_ at _f_. By supplying motive to revolve the
escape wheel (_E_) represented by the circle _n_, and causing the arc
_l_ to oscillate back and forth in exact intervals of time, we should
have, in effect, a perfect escapement. To accomplish automatically such
oscillations is the problem we have now on hand.

HOW MOTION IS OBTAINED.

In clocks, the back-and-forth movement, or oscillating motion, is
obtained by employing a pendulum; in a movable timepiece we make use of
an equally-poised wheel of some weight on a pivoted axle, which device
we term a balance; the vibrations or oscillations being obtained by
applying a coiled spring, which was first called a "pendulum spring,"
then a "balance spring," and finally, from its diminutive size and coil
form, a "hairspring." We are all aware that for the motive power for
keeping up the oscillations of the escaping circle _l_ we must contrive
to employ power derived from the teeth _D_ of the escape wheel. About
the most available means of conveying power from the escape wheel to the
oscillating arc _l_ is to provide the lip of said arc with an inclined
plane, along which the tooth which is disengaged from _l_ at _f_ to
slide and move said arc _l_ through--in the present instance an arc of
eight and one-half degrees, during the time the tooth _D_ is passing
through ten and one-half degrees. This angular motion of the arc _l_ is
represented by the radial lines _k f'_ and _k r_, Fig. 8. We desire to
impress on the reader's mind the idea that each of these angular motions
is not only required to be made, but the motion of one mobile must
convey power to another mobile.

In this case the power conveyed from the mainspring to the escape wheel
is to be conveyed to the lever, and by the lever transmitted to the
balance. We know it is the usual plan adopted by text-books to lay down
a certain formula for drawing an escapement, leaving the pupil to work
and reason out the principles involved in the action. In the plan we
have adopted we propose to induct the reader into the why and how, and
point out to him the rules and methods of analysis of the problem, so
that he can, if required, calculate mathematically exactly