In order to realize any power from our escape-wheel tooth, we must provide an impulse face to the pallets faced at f e; and the problem before us is to delineate these pallets so that the lever will be propelled through an arc of eight and one-half degrees, while the escape wheel is moving through an arc of ten and one-half degrees.  We make the arc of fork action eight and one-half degrees for two reasons—­(1) because most text-books have selected ten degrees of fork-and-pallet action; (2) because most of the finer lever escapements of recent construction have a lever action of less than ten degrees.

LAYING OUT ESCAPE-WHEEL TEETH.

To “lay out” or delineate our escape-wheel teeth, we continue our drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8.  With our dividers set at five inches, we sweep the short arc a a’ from f as a center.  It is to be borne in mind that at the point f is located the extreme point of an escape-wheel tooth.  On the arc a a we lay off from p twenty-four degrees, and establish the point b; at twelve degrees beyond b we establish the point c.  From f we draw the lines f b and f c; these lines establishing the form and thickness of the tooth D.  To get the length of the tooth, we take in our dividers one-half a tooth space, and on the radial line p f establish the point d and draw circle d’ d’.

To facilitate the drawing of the other teeth, we draw the circles d’ c’, to which the lines f b and f c are tangent, as shown.  We divide the circle n n, representing the periphery of our escape wheel, into fifteen spaces, to represent teeth, commencing at f and continued as shown at o o until the entire wheel is divided.  We only show four teeth complete, but the same methods as produced these will produce them all.  To briefly recapitulate the instructions for drawing the teeth for the ratchet-tooth lever escapement:  We draw the face of the teeth at an angle of twenty-four degrees to a radial line; the back of the tooth at an angle of thirty-six degrees to the same radial line; and make teeth half a tooth-space deep or long.

[Illustration:  Fig. 8]

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