We now come to the consideration of the pallets and how to delineate them. To this we shall add a careful analysis of their action. Let us, before proceeding further, "think a little" over some of the factors involved. To aid in this thinking or reasoning on the matter, let us draw the heavy arc l extending from a little inside of the circle n at f to the circle n at e. If now we imagine our escape wheel to be pressed forward in the direction of the arrow j, the tooth D would press on the arc l and be held. If, however, we should revolve the arc l on the center k in the direction 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.
We have spoken of paper being employed for drawings, but for very accurate delineations we would recommend the horological student to make drawings on a flat metal plate, after perfectly smoothing the surface and blackening it by oxidizing.
PALLET-AND-FORK ACTION.
By adopting eight and one-half degrees pallet-and-fork action we can utilize ten and one-half degrees of escape-wheel action. We show at A A', Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half; that is, the original drawing was made for an escape wheel ten inches in diameter. We shall make a radical departure from the usual practice in making cuts on an enlarged scale, for only such parts as we are talking about. To explain, we show at Fig. 10 about one-half of an escape wheel one eighth the size of our large drawing; and when we wish to show some portion of such drawing on a larger scale we will designate such enlargement by saying one-fourth, one-half or full size.
At Fig. 9 we show at half size that portion of our escapement embraced by the dotted lines d, Fig. 10. This plan enables us to show very minutely such parts as we have under consideration, and yet occupy but little space. The arc a, Fig. 9, represents the periphery of the escape wheel. On this line, ten and one-half degrees from the point of the tooth A, we establish the point c and draw the radial line c c'. It is to be borne in mind that the arc embraced between the points b and c represents the duration of contact between the tooth A and the entrance pallet of the lever. The space or short arc c n represents the "drop" of the tooth.
This arc of one and one-half degrees of escape-wheel movement is a complete loss of six and one-fourth per cent. of the entire power of the mainspring, as brought down to the escapement; still, up to the present time, no remedy has been devised to overcome it. All the other escapements, including the chronometer, duplex and cylinder, are quite as wasteful of power, if not more so. It is usual to construct ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel action; but we shall show that half a degree more can be utilized by adopting the eight and one-half degree fork action and employing a double-roller safety action to prevent over-banking.
From the point e, which represents the center of the pallet staff, we draw through b the line e f. At one degree below e f we draw the line e g, and seven and one-half degrees below the line e g we draw the line e h. For delineating the lines e g, etc., correctly, we employ a degree-arc; that is, on the large drawing we are making we first draw the line e b f, Fig. 10, and then, with our dividers set at five inches, sweep the short arc i, and on this lay off first one degree from the intersection of f e with the arc i, and through this point draw the line e g.
From the intersection of the line f e with the arc i we lay off eight and one-half degrees, and through this point draw the line e h. Bear in mind that we are drawing the pallet at B to represent one with eight and one-half degrees fork-and-pallet action, and with equidistant lockings. If we reason on the matter under consideration, we will see the tooth A and the pallet B, against which it acts, part or separate when the tooth arrives at the point c; that is, after the escape wheel has moved through ten and one-half degrees of angular motion, the tooth drops from the impulse face of the pallet and falls through one and one-half degrees of arc, when the tooth A'', Fig. 10, is arrested by the exit pallet.
To locate the position of the inner angle of the pallet B, sweep the short arc l by setting the dividers so one point or leg rests at the center e and the other at the point c. Somewhere on this arc l is to be located the inner angle of our pallet. In delineating this angle, Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement," makes an error, in Plate III of large