18 On the Theory of 



This effect is produced in Fig. 2, Plate IV, by increasing the 

 angle of lead of the pallet AA, and diminishing that of the pallet 

 B B ; and it will be observed, that though the two angles B I C, and 

 DIE, the angles the pallets are led, are equal to one another, 

 and, consequently, that the pendulum will be led an equal angle 

 by the action of the wheel on each pallet ; yet, that the angle 

 A I C of lead as drawn of the pallet A A, is greater than the angle 

 B I C the pendulum is led, by the angle A I B, representing the dif- 

 ference between the two : and the angle D I F of lead as drawn of 

 the pallet B B, is less than the angle DIE the pendulum is led, 

 by the angle FIE the difference between the two. Consequently, 

 the. total difference between the angles of lead as drawn, is an 

 angle equal to the two angles A I B and F I E. 



A similar remark applies to Fig. 3, with this difference, that the 

 same effects take place on the reverse pallets ; the angle of lead of 

 the pallet AA is diminished, and that of the pallet B B increased ; 

 the angles B I C and DIE, the pallets are led by the wheel as in 

 the former case are equal to one another ; but the angle A I C of 

 lead of the pallet AA, is less than the angle B I C the pendulum is 

 led, by the angle A I B : and the angle D I F of lead of the pallet 

 B B, is greater than the angle DIE the pendulum is led, by the 

 angle FIE; and the difference between the two angles of lead as 

 drawn, is an angle equal to the two angles A I B and FIE. 

 This alteration of the shape of the pallets, requires a correspond- 

 ing alteration in the shape of the teeth of the wheel, which must 

 be longer and more undercut, and, consequently, weaker than 

 when the center of motion is determined as shewn by Fig. 1, 

 Plate III *. 



* Iu the case of the center being placed as in Fig. 2, and 3. Plate IV. and 

 the angle of lead of the pallets supposed to be originally drawn as represented 

 Fig. 1. Plate III., the escapement will yet perform, and the pallets lead an 

 equal angle to one another, by the action of the wheel on each pallet, by 

 only altering the angle of lead of one of the pallets, as originally drawn. This 

 is shewn Fig. 1. Plate IV., where the center of the wheel and pallets are 

 placed, and all the parts, the angles of lead of the pallets excepted, are 

 drawn as in Fi^. 2. Plate IV. ; the angle of lead of the pallet AA is drawn the 

 same as in Fig. 1. Plate II!.; buL the angle of lead of the pallet B V, is dimi- 



