the Dead Escapement. 7 



angle of 5° to have the inclined plane, draw the line db passing- 

 through the points d and b where the straight lines a /and ag 

 which form the angle g a f intersect the portions of circles ds 

 and b t." 



1330. " To draw the inclined plane c e, it is to be observed, that 

 as the pallet d b is drawn 5° within the circle of the wheel, it 

 follows that the pallet c must be situated without the same circle, 

 and ready to come into action as the other pallet escapes from the 

 wheel. Prolong the line a c to h, and draw the angle h a i of 5°, 

 which will determine the measure of the inclined plane c e; it only 

 then remains to draw the line ce, which passes through the points 

 c and e, where the straight lines a h and a i intersect the portions 

 of circles cp and eq: thus will be given the inclined plane which 

 is to terminate the pallet, and so situated, that when the tooth 

 C shall have led the pallet without the circle of the wheel, a quan- 

 tity equal to an angle of 5°, the pallet c e shall also be led an angle 

 of 5°, and within the wheel ; consequently, when the tooth r shall 

 have led the pallet to escape, the pallet c will have described an 

 angle of 5°, whence it follows, that the total lead of the escape- 

 ment will be 10°* ". 



* This is a mistake ; the total quantity the pendulum is led being an angle 

 equal to the angle of lead of either of the pallets ; (it is supposed that the 

 angles of the two pallets are equal to one another, as they ought to be,) and 

 the pendulum is led nearly an equal angle, ascending and descending on each 

 side of zero, (or the perpendicular line on the degree plate,) by each pallet 

 alternately; but the advance of the wheel, and consequently the friction 

 upon the inclined planes of the pallets, is not uniform during the ascending 

 and descending of the pendulum at each vibration, but exists upon a greater 

 proportion of, and is consequently greater upon, the pallets as the pendulum 

 ascends than as it descends ; for, supposing the inclined planes of the pallets 

 divided at that point which the extremity of the tooth of the scape wheel 

 has reached when the pendulum is perpendicular, the portion of the inclined 

 planes the tooth of the wheel acts upon, as the pendulum descends, is less 

 than the portion acted upon as the pendulum ascends. 



It is possible to make the inclined planes of the pallets so long, that the 

 angle of the total vibration of the pendulum will not exceed the angle of lead 

 of the pallets, in which case it will be visible that the total angle the pen- 

 dulum is led is only equal to the angle of one of the pallets. 



M. Berthoud has fallen into the same error at No. 300. To 



