340 On. the Dead Escapement for Clocks. 
centre of motion of the axis of the verge, is sufficiently obvious. 
The line O P, Fig. 15, passing through the centres of the axis 
of the verge and the axis of the wheel, is the line the pendulum 
subtends when at rest, and the lines A R and AT, forming 
together the angle R AT, supposed of 2°, are the lines the 
pendulum will subtend, when led to the extremity of the lead 
by the action of the wheel upon each pallet. In Fig. 15, the 
pendulum is supposed to subtend the line A T. 
The following is a brief description of a method by which 
the inclined planes of the pallets are finished to the required 
angle. 
Fig. 16 represents a brass plate, about three or four inches 
in diameter, the size is not very material, and about two inches 
thick, with a groove turned in it similar to the groove A P, Fig. 1. 
The angles BAC and D A E are drawn equal to the pro- — 
posed angles of lead of the pallets, and in this case are supposed 
angles of 2°. To determine the line of the face of the inclined 
planes of the pallets, from the points G and H, where the lines 
A Band AD intersect the exterior circle of the groove, draw the 
lines G I and HK, which may be considered as chords subtend- 
ing equal arcs, intersecting the lines A C and AE, at the points 
L and M, on the inner circle of the groove; the lines G L and 
H M may, relative to the two circles of the groove, be con- 
sidered as representing the inclined planes of the pallets. Now 
supposing that portion of the original piece of brass subtended 
by the chord X Y, carefully removed, and the surface made 
perfectly flat, and at right angles to the turned face in which 
is the groove, it follows that a piece of the steel ring, Fig. 3, 
one end of which has been brought by filing very near to the re- 
quired angle, may be placed in the groove, and ground and 
finished in the most accurate manner. By this method the 
surface of the pallet will be made perfectly correct. The other 
pallet may be finished by a similar method. 
It may not be unnecessary to observe, for the preservation of 
the figure, that the principal bearings of the tool should not 
come in contact with the grinding surface during the operation. 
