The Modern Clock / A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair

by Ward L. Goodrich

2. That the crutch and pallets shall each travel at the same precise angular velocity as the pendulum, which can only happen when the arc each is to describe is in direct proportion to its distance from the center of motion, that is, from the pallet axis.

3. That the angular force communicated by the crutch to the pendulum shall be equal on both sides of the quiescent point; or, in other words, that the lead of each pallet shall be of the same precise amount.

4. That any number of degrees marked by the crutch or pallets shall correspond with the same number of degrees shown by the lead of the pendulum, as marked by the index on the degree plate.

5. That the various vibrations of the pendulum be driven by a motive weight in strict accordance with the theoretical law; that is, if a 5-lb. weight cause the pendulum to double its arc of escapement of 1°, and consequently drive it 2°, all the intermediate arcs of vibration shall in practice accord with the theory of increasing or diminishing their arcs in the ratio of the square roots of the motive weight.

To accomplish the foregoing conditions, there is but one fixed point or line of distance between the axis of the escape wheel and that of the pallet, and that depends upon the number of teeth embraced by the pallets and only one point in which the pallet axis can be placed from which the several lines of the escapement can be correctly traced and properly constructed with equal angles, and equal rectangular lockings on both sides, so that each part travels with the same degree of angular velocity, which are the three essential points of the escapement.

Much difference of opinion has been expressed upon the construction of the pallets, as to whether the lockings or circular rests should be at equal distances from the pallet axis, with arms and impulse planes of unequal length, or at unequal distances from the pallet axis, with arms and impulse planes of equal length. In the latter case the locking on one side is three degrees above, and on the other three degrees below the rectangle, whereas in the former the tooth on both sides reposes at right angles to the line of pressure; but the length of the impulse planes is unequal. When an escapement is correctly made upon either plan, the results are very similar.

It is possible to obtain equal angles by a false center of motion or pallet axis; but then the arcs of repose will not be equal. This, however, is not of so much consequence as that of having destroyed the conditions Nos. 2, 3, 4; for even at correct centers, if the angles are not drawn off correctly by the protractor, and precisely equal to each other, the isochronous vibrations of the pendulum will be destroyed, and unequal arcs will no longer be performed in equal times; the quiescent point is not the center of the vibration, except when the driving forces are equal on both sides of the natural quiescent point of the pendulum at rest.

Now this is the very pith of the subject, and which few would be inclined to look for with any hope of finding in it the solution of this important question, the isochronism of the pendulum.

One would naturally suppose that unequal arcs on the two sides of the vertical lines would not seriously affect the rate of the clock, but would be equal and contrary, and consequently a balance of errors, and so they probably are for the same fixed vibration, but not for any other; because different angles are driven with different velocities, the short angle has a quicker rate of motion than the long. Five pounds motive weight will multiply three times the pendulum’s vibration over an arc of escapement of 0.75°; but the same pendulum, with an arc of escapement of 1°, would require 11.20 lbs. to treble its vibration; the times of the vibration vary in the same ratio as the sum of the squares of the differences of the angles of each pallet, compared with the spaces passed over.

From this it will be seen that the exact bending point of the pendulum spring should be opposite the axis of the fork arbor when regulating the clock and this may have to be determined by trial, raising or lowering the plates by screws in the arms of the suspending brackets until the proper position is found, when the movement may be clamped firmly in position by the binding screws, [see Fig. 158].