the Dead Escapement. 13 



case with the angle of lead of both the pallets, entirely within the 

 periphery of the circle of the wheel. 



I apprehend a very general and correct rule, and one easy of 

 application, for determining the distance at which the center of 

 action of the pallets ought to be placed from the center of the 

 scape wheel, and for drawing the lines of the dead escapement, may 

 be given. 



Having determined the diameter of the wheel, the number of its 

 teeth, and the number of the teeth of the wheel the pallets are to 

 take over, draw a circle circumscribing the points of the teeth of 

 the wheel, and upon this circle at the proper places as determined 

 by the opening of the pallets, mark the thickness of the pallets, 

 which, making no allowance for drops, should always be half the 

 space between two points of the teeth for each pallet ; that done, 

 draw two straight lines between the points that mark the thickness 

 of the pallets upon the circumscribing circle ; these lines will be 

 chords to the portions of the circle they subtend ; prolong these 

 two lines until they intersect each other; the point where they 

 meet will be the proper center of motion for the pallets. Next, to 

 describe the circular faces of the pallets; from the center of motion 

 as above determined, draw portions of two circles that shall in- 

 tersect the circle circumscribing the wheel at the four points which 

 mark the place and thickness of the pallets. The angle of lead 

 which is quite optional must then be determined — this is done by 

 drawing two lines from the center of action of the pallets ; the one 

 within and the other without the lines by which the said center 

 was found, and forming with those lines two equal angles : the 

 angle of lead determined, it now only remains to draw the inclined 

 planes or acting faces of the pallets ; this is done by drawing two 

 diagonal lines from the upper to the lower points of intersection of 

 the lines forming the sides of the two angles of lead, by the circular 

 faces of the pallets. 



To illustrate this further, suppose ABC, Fig. 1, Plate III, a 

 scape wheel of six teeth, to which it is required to apply a pair of 

 dead-beat pallets, which are to take over two teeth, or what ia the 

 tame tiling, occupy the portion of the circle contained between 



