of the arrow i, the tooth D would escape from the edge of l and the tooth D’’ would pass through an arc (reckoning 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 how many grains of force the fork exerts on the jewel pin, and also how much (or, rather, what percentage) of the motive power is lost in various “power leaks,” like “drop” and lost motion.  In the present case the mechanical result we desire to obtain is to cause our lever pivoted at k to vibrate back and forth through an arc of eight and one-half degrees; this lever not only to vibrate back and forth, but also to lock and hold the escape wheel during a certain period of time; that is, through the period of time the balance is performing its excursion and the jewel pin free and detached from the fork.