12 On the Theory of 



from the center of the wheel considerably less than a quantity equal 

 to one diameter of the wheel ; and that when the pallets take over 

 twelve teeth, the distance is considerably greater than one diameter 

 of the wheel. Also by reference to Fig. 5, that when the pallets 

 take over eleven teeth, the distance is exactly (or very nearly so) 

 one diameter ; and when they take over thirteen teeth, a little more 

 than one and a half diameter of the wheel. It is unnecessary 

 to make any remarks on the continuation of the description of 

 " Graham's dead beat," with regard to Berthoud's rule, after the 

 notice that has been taken of Berthoud's account of the dead es- 

 capement at the beginning of this paper. In the representation of 

 Graham's Escapement, in Rees, Plate XXXII. Fig. 4, before men- 

 tioned, the center of the pallets is placed at one diameter of the 

 wheel from the center of the wheel, and the pallets take over 

 eleven teeth. In the representation of the anchor escapement, 

 Fio-. 3, the pallets take over ten teeth, and their center of motion 

 is less than one diameter of the wheel from the center of the wheel. 

 It may be considered requisite, in reference to the subject, that 

 some notice should be taken of the escapement under the denomi- 

 nation of " Modification of the dead beat, by Grinion," described 

 immediately after Graham's dead beat. I shall content myself with 

 observing that Mr. Grinion describes his dead escapement as con- 

 structed on the same principle as I. A. Lepautre states Graham to 

 have made his, (see page 10, and Fig. 2, Plate II.,) with the rests 

 of the pallets at equal distance from their center of motion, and 

 with the center of the pallets placed at the distance of one diameter 

 of the scape wheel from the center of the wheel. In the figure (see 

 Fi°\ 5, Plate XXXII., Rees' plates,) the pallets are represented 

 with the angle of lead of both pallets entirely within the periphery 

 of the circle of the wheel ; with the pallets so constructed, the 

 point of the tooth of the wheel would drop on the rest of the pallets 

 at a very considerable distance from the inclined plane, and, con- 

 sequently, the friction be very much increased ; and, moreover, 

 the pendulum must vibrate a very long arc, to enable the 

 pallets to escape at all. 



" Bennet's dead beat," represented Fig. 7, is also in the same 



