6 On the Theory of 



other point of the compasses to the other side, and see if it will 

 reach the back of the point of another tooth at c: if it does not, 

 the opening of the compasses must be varied until it reaches from 

 the center a, at the same opening the points of the two teeth, the 

 nearest to the points c and b: draw the portions of circles bt, cp, 

 which will represent two of the circular faces of the pallets*". 



1327. " To find the other two circular faces, the opening of the 

 compasses must be altered in such a manner, that the teeth of the 

 wheel having advanced a quantity equal to half the interval be- 

 tween them, they pass a second portion of a circle drawn from the 

 same center a, and intersecting the circle of the wheel ; but as 

 that may equally be done by opening or closing the compasses, a 

 quantity equal to the space between two teeth, it is preferable to 

 use that of the two openings which will occasion the distance of the 

 lines from the center to vary the least from the points c and b, 

 which points are to be varied from as little as possible. That done, 

 trace the other two faces of the pallets ds and eg-f, which are 

 here by preference drawn within the others, to diminish the space 

 the anchor has to move, and, consequently, the friction of the 

 pallets. In this manner are described the four circular faces of 

 the two pallets, placed in such a manner, as to let the teeth of the 

 wheel alternately escape as the pallets approach and recede from 

 the center of the wheel by the action of the pendulum." 



1328. " The length of the pallets is regulated by the quantity of 

 the ano-le of lead that is to be given to the escapement, which we 

 will here suppose of 5° on each side, or thereabouts." 



1329. (This part is very much abridged in the translation.) 

 " To describe the angle of escapement, prolong the line a b, to f. 

 See Fig. 3, Plate I, and draw the angle fa g of 5°, the point d, 

 where the line a g intersects the inner circular face of the pallet, 

 determines the length of the pallet ; for the wheel in passing the 

 pallet, causes it by its action on the inclined plane, to describe an 



# This is not correct, because c p, Fig. 3. Plate I., is not a face of the 

 pallet. 



f This again is incorrect ; d S, Fig. 3. Plate I, is not a face of the pallet, 

 and cannot be considered as such. 



