Fig. 28.
Fig. 29. Note the difference in
length of arc for the same angle.
It will be seen by the diagram, [Fig. 28], that by this method the distance between the centers of motion of the pallets and that of the scape wheel takes care of itself for a given number of teeth and that it is greater when eleven and one-half teeth are to be embraced than for eight or for a less number. These short pallet arms are imagined by some workmen to be objectionable, on the supposition that it will take a heavier weight to drive the clock; but it can easily be shown that this objection is altogether imaginary. Now, bearing in mind the principles of leverage, if the distance between the pallets and escape wheel centers is very long, as in Graham’s plan, in which the pallets embraced 138° of the escape wheel, the value of the impulse received from the scape wheel and communicated through the pallets to the pendulum is no doubt greater with a proper length of verge wire, for, the lifting planes being longer, the leverage is applied to the pendulum for a longer arc of its vibration, yet we must not suppose that from this fact the clock will go with less weight, for it is easy to see that the longer the pallet arms are the greater will be the distance the teeth of the escape wheel will have to move (run) on the circular part of the pallets. [See Fig. 29]. The extra amount of friction, and the consequent extra amount of resistance offered to the pendulum, caused by the extra distance the points of the teeth run on the circular locking planes of the pallets and back again, destroys all the value of the extra amount of impulse given to the pendulum in the first instance by means of the long arms of the pallets. The escape wheel tooth resting on the locking plane of the pallet is quite variable in its effective action, and since it rests on the pallet during a part of each swing of the pendulum and the pendulum is called on to move the pallet back and forth under the tooth, any change in the friction between the tooth and pallet is felt by the pendulum and when the clock gets dirty and the friction between the tooth and pallet is increased, the rate of the clock gets slow, as the friction holds the pendulum from moving as fast as it would without friction. Now, as this friction increases by dirt and thickening of the oil, all these forms of escapements are subject to changes and so change the clock’s rate. An increase of the driving weight, or force of the mainspring, of clocks with dead-beat escapements always tends to make their rate slow, from the action mentioned.
It is for this reason that moderately short arms are used in clocks having dead-beat escapements of modern construction. Most of the first-class modern makers of astronomical clocks only embrace seven and one-half teeth, on a 30-tooth wheel, with the centers of motion of the pallets and scape wheel proportionately nearer, as it can be mathematically demonstrated that with the pallets embracing an arc of 90° the application of the power to the pendulum is at right angles to the rod and therefore is most effective.
To Draw the Escapement.—In order to make the matter clearer we show in [Fig. 30] the successive stages of drawing an escapement and also the completed work in Figs. [32] and [33] embracing different numbers of teeth. Draw a line, A B, [Fig. 30], to serve as a basis for measurements. With a compass draw from some point C on this line a circle to represent the diameter of our escape wheel. Now we shall require to know how many teeth there will be in our escape wheel. There may be 60, 40, 33, 32, 30, or any other number we desire to give it; seconds pendulums generally have 30 teeth in this wheel, because this allows the second hand to be mounted directly on the escape wheel arbor and thus avoids complications. We divide the number of degrees in a circle (360) by the number of teeth we have selected, say 30. 360 ÷ 30 = 12° for each tooth and space. One-fourth of 360° equals 90° and one-fourth of 30 teeth equals seven and one-half teeth; each tooth equaling 12 degrees, we have 12 × 7 = 84°, which gives us six degrees for drop, to ensure the safety of our actions.
