the Dead Escapement. 3 



expresses himself : " 397. The distance between the center of 

 the anchor of the escapement and the center of the wheel, depends 

 upon the arc the pendulum is required to vibrate * ; if it is to 

 describe large arcs of 10°, for example, then the center of the 

 anchor must be at B." See Fig. 1, Plate I. (Berthoud, Fig. 8, 

 Plate XV.) 



398. " But if, on the contrary, it is to describe a short arc, of 1° 

 for example, the center must be at a. See Fig. 2, Plate I. (Ber- 

 thoud, Fig. 10, Plate XV.) at the distance of about a diameter and 

 a half of the wheel A from the center of the wheel f ; observing in 



* This is not perfectly well expressed, as by the arc the pendulum is re- 

 quired to vibrate, might in this case mean the arc the pendulum must describe 

 to enable the pallets to escape ; or, in other words, the quantity the pendulum 

 is led by the action of the wheel upon the inclined planes of the pallets, and 

 not the total arc of the vibration of the pendulum ; (at Nos. 399 and 400, 

 M. Berthoud describes the difference between the total arc of vibration of 

 the pendulum, and the arc led by the action of the wheel upon the pallets,) 

 neither is this a correct statement, for the quantity the pendulum is led by 

 the action o( the wheel upon the pallets, depends upon the angle of lead of 

 the pallets, or the length of their inclined planes ; as well as upon the distance 

 between the center of action of the pallets and center of the wheel, and con- 

 sequent number of teeth the pallets take over. In illustration of this, (see 

 Fig. 3. Plate II.) to the same wheel are applied two pairs of pallets, which, 

 taking over a different number of teeth of the Wheel, are consequently at 

 different distances from the center of the wheel ; and yet from the difference 

 of the angle of lead of the pallets, the pendulum will be led an equal quan- 

 tity of the action of the wheel upon either pair of pallets ; the difference be- 

 tween the angles of lead of the pallets compensating for the difference between 

 the distances at which each pair of pallets is placed from the wheel. 



In the figure the four triangles, B A C, DAE, FW G, and H W I, which 

 express the angles of lead of the pallets, are drawn equal to one another, and 

 equal to the triangles KAL and NVVM, also equal to one another, which 

 shew the quantity the pendulum is led by the action of the two pair of pallets, 

 on each side of the perpendicular line AX. 



f I believe that Mr. Graham, Mr. Shelton, who worked with him, and 

 most of the clock-makers of that period, who trod in the footsteps of 

 Mr. Graham in the construction of their seconds pendulum clocks, (the scape 

 wheels of which were necessarily cut into thirty teeth,) made their pallets take 

 over eleven, twelve and thirteen teeth of the wheel ; and the distance between 

 B 2 



