4 On the Theory of 



both cases, that the opening of the compass that describes the rests, 

 or circular faces of the pallets, is such that drawing a line from the 

 point 5, Fig. 1, Plate I, through the center B of the anchor, and 

 drawing upon its extremity 5 a line z A that shall pass through 

 the center A, of the wheel ; these lines are so situated that the 

 line z A shall be perpendicular to the line 5 B * ; and by the same 

 rule, if the anchor is placed at g, the pallets, or inclined planes, of 

 the anchor should act upon the wheel at the points ef; this un- 

 derstood, the portions of the circles 1 C, 3 D, Fig. 2, Plate I. (M. 

 Berthoud tranfers his description to Fig. 10 of his work,) must be 

 drawn of the same radius a C; and in the same manner 2, 5, and 

 6, 4, taking care that the space, or thickness, C 5, 6 D, between 

 these portions of circles, is a little less than half the interval be- 

 tween the teeth of the wheel." 



" Now, to determine the inclination of the planes, from the 

 center a, Fig. 2, draw the straight lines af and a g, forming the 

 angle/ a g, being half the angle the pendulum is required to be 

 ledf ; through the points 2 and 1, where these lines intersect the 

 arcs 2, 5, and 1, C, draw the straight line 2, 1, which gives the in- 

 clined plane 2, 1, by a similar operation the inclined plane of the 



the centers was one diameter of the wheel in the case of taking over eleven 

 teeth ; about one and a half diameter in the case of taking over thirteen 

 teeth ; and between one diameter and one diameter and a half in the case of 

 taking over twelve teeth. The French clock-makers, who copied Graham's 

 escapement, followed nearly the same rule. 



* (See Fig. I. Plate I.) In the case of the anchor, whose center of motion 

 is at B, M. Berthoud determines the center of action of his pallets by the 

 intersection of two tangents drawn from the points where the circle of the 

 inner rest of the pallets prolonged intersects the circle that circumscribes the 

 wheel. By this mode the two centers are nearer together than they would 

 have been, had he determined their distance by tangents diawn from the 

 points where the circle of the outer rest intersects the same circle. 



That the points found by the intersection uf tangents drawn from either of 

 these points is not the proper center of action of the pallets, will be shewn 

 hereafter, — in the oue case the centers are too far apart ; in the other case 

 they are too near together. 



f See note, page 3. 



