We produce the vertical line m passing through the center p of the circle n.  From the intersection of the circle n with the line m at i we lay off thirty degrees on each side, and establish the points e f; and from the center p, through these points, draw the radial lines p e’ and p f’.  The points f e, Fig. 6, are, of course, just sixty degrees apart and represent the extent of two and one-half teeth of the escape wheel.  There are two systems on which pallets for lever escapements are made, viz., equidistant lockings and circular pallets.  The advantages claimed for each system will be discussed subsequently.  For the first and present illustration we will assume we are to employ circular pallets and one of the teeth of the escape wheel resting on the pallet at the point f; and the escape wheel turning in the direction of the arrow j.  If we imagine a tooth as indicated at the dotted outline at D, Fig. 6, pressing against a surface which coincides with the radial line p f, the action would be in the direction of the line f h and at right angles to p f.  If we reason on the action of the tooth D, as it presses against a pallet placed at f, we see the action is neutral.

[Illustration:  Fig. 6]

ESTABLISHING THE CENTER OF PALLET STAFF.

[Illustration:  Fig. 7]

With a fifteen-tooth escape wheel each tooth occupies twenty-four degrees, and from the point f to e would be two and one-half tooth-spaces.  We show the dotted points of four teeth at D D’ D’’D’’’.  To establish the center of the pallet staff we draw a line at right angles to the line p e’ from the point e so it intersects the line f h at k.  For drawing a line at right angles to another line, as we have just done, a hard-rubber triangle, shaped as shown at C, Fig. 7, can be employed.  To use such a triangle, we place it so the right, or ninety-degrees angle, rests at e, as shown at the dotted triangle C, Fig. 6, and the long side coincides with the radial line p e’.  If the short side of the hard-rubber triangle is too short, as indicated, we place a short ruler so it rests against the edge, as shown at the dotted line g e, Fig. 7, and while holding it securely down on the drawing we remove the triangle, and with a fine-pointed pencil draw the line e g, Fig. 6, by the short rule.  Let us imagine a flat surface placed at e so its face was at right angles to the line g e, which would arrest the tooth D’’ after the tooth D resting on f had been released and passed through an arc of twelve degrees.  A tooth resting on a flat surface, as imagined above, would also rest dead.  As stated previously, the pallets we are considering have equidistant locking faces and correspond to the arc l l, Fig. 6.