the Dead Escapement. 15 



D G I parallel to the two lines V W and V W, and the point I where 

 they meet will be the center of motion of the pallets, and must be 

 the same originally formed ; for a chord will always be parallel to 

 a tangent touching the same circle, when the tangent touches the 

 circle at a point equidistant between the two points where the 

 chord meets the circle ; and that is the case here, for, by the con- 

 struction of the figure, the angle XVWisa right angle, and the 

 angles VXF and VXH equal angles. The chord HF being 

 parallel to the tangent V W, it follows that the line O I, which is 

 the chord H F, prolonged, must be parallel to the same tangent 

 V"VV. A similar demonstration will apply to the chord DG. 



That there is but one proper place for the center of motion of the 

 pallets, and that it is the point found as above described, will be 

 evident when it is considered, that for the pendulum to be led an 

 equal quantity by the action of the wheel on each pallet, (the in- 

 clined planes of which must be of equal length, otherwise the action 

 will not be the same on both,) it is requisite, making no allowance 

 for drop, that at the instant the wheel has advanced a quantity 

 equal to half the space between two of its teeth, the lead of the 

 pallet should be completed, and that the tooth which has just led 

 the pallet to the extremity of the angle of lead of the pallet, should 

 quit the pallet; and, at the same instant, the other pallet should 

 present itself in such a situation, that another tooth of the wheel 

 may come into action with it ; that when that tooth shall have ad- 

 vanced the same quantity as the preceding, that it shall also have 

 led the other pallet which it has acted upon to the extremity of its 

 action of lead ; and have brought the first-mentioned pallet into a 

 situation to receive the following tooth of the wheel to that by 

 which it was previously led. 



This can only be the case when the lines I O and IP which pass 

 through the circumscribing circle, intersect it at the points which 

 determine the thickness of the pallets, which, from the construction, 

 it is evident in this case they do. By reference to the figure it will 

 be seen, that in consequence of the angles O I Q and P 1 R being 

 equal to one another, and the sides I O and I P of the same angles 

 intersecting the circumference of the circle at the points H F and 



