20 On the Theory of 



impulses received by the pallets being unequal, the lengths of the 

 arcs of vibration of the pendulum will be unequal, and, conse- 

 quently, performed in unequal times*. 



The angles AIB and FIE, Fig. 2 and 3, Plate IV, in each 

 figure, being equal to each other, it will be found in all cases, 

 that the excess of the angle led by one pallet, above the angle of 

 lead of the same pallet as drawn ; will be equal to the excess 

 of the angle of lead, over and above the angle led by the other pallet. 



Supposing the distance between the centers of action of the 

 pallets and the scape-wheel, determined as above described, see 

 Fig. 1, Plate III, and lines drawn from the points where the teeth 

 of the wheel act upon the rests of the pallets, to the centers of 

 motion of the wheel and the pallets, they will form the one an 

 obtuse, and the other an acute angle ; and both angles will differ 

 an equal quantity, half the thickness of the pallet from a right 

 angle. Now, in principle, the most advantageous point of action 

 for the wheel upon the rests of the pallets, is at right angles to 

 the two centers of motion ; but as it is impossible that the points 

 of action on the two rests should form right angles with the 

 centers, (for were the one a right angle, the other would be the thick- 

 ness of a pallet greater or less than a right angle,) it follows, that 

 the best construction is, that in which the action of the teeth of the 

 wheel on both rests differs the least possible quantity from a right 

 angle, and is that which will have the least tendency to wear : 

 and as observed by M. Berthoud, No. 1325, " the most favour- 

 able possible." 



* This is correctly true in the case of the pendulum being supposed a beam, 

 and vibrating a short angle ; or in the case of a pendulum with a very light 

 bob suspended on a knife edge, as many of the old clocks were made : but ill 

 practice, in the case of a seconds' pendulum, and, still more, a two seconds' 

 pendulum, and a heavy bob, the power of gravity will very nearly overcome 

 the difference in the impulse : nevertheless the inequality of the impulse must, 

 in a certain degree, be prejudicial, particularly when very accurate perform- 

 ance is required. 



In the case of the anchor escapement, as applied to watches, the evil would 

 probably be greater and more felt, and cause the arcs of vibration of the 

 balance to be very unequal. 



