When we talk of detached escapements, or any escapement applied to a pendulum, it is necessary to bear in mind that there is always one-third at the least of the pendulum’s vibration during which the arc of escapement is intimately mixed up with the vibration, either in locking, unlocking, or in giving impulse; therefore, whatever inherent faults any escapement may possess are constantly mixed up in the result; the words “detached escapement” can hardly be applied when the entire arc of vibration is only two degrees; or, in other words, what part of the vibration is left without the influence of the escapement?—at most one degree. In chronometers the arc of vibration is from ten to fifteen times greater than the arc of escapement.
The dead-beat escapement has been accused of interfering with the natural isochronism of the pendulum by its extreme friction on the circular rests, crutch, and difficulty of unlocking, etc., all of which we shall show is only so when improperly made.
When the dead-beat escapement has been mathematically constructed, and is strictly correct in all its bearings, its vibrations are found to be isochronous for arcs of different extent from 0.75 of a degree to 2.50 degrees; injurious friction does not then exist; the run up on the locking has no influence, nor is there any friction at the crutch; oil is not absolutely necessary, except at the pivots; and there is no unlocking resistance nor any inclination to repel or attract the wheel at its lockings.
The general mode of making this escapement is very defective and indefinite, and entirely destroys the naturally isochronous vibration of the pendulum.
The following is the usual rate of the same pendulum’s performance in the different arcs of vibration with an escapement as generally constructed after empirical rules:
| Arc of vibration | 3° | rate per diem 9.0 seconds. |
| Arc of vibration | 2½° | rate per diem 6.0 seconds. |
| Arc of vibration | 2° | rate per diem 3.5 seconds. |
| Arc of vibration | 1½° | rate per diem 1.5 seconds. |
| Arc of vibration | 1° | rate per diem 0.0 seconds. |
Thus for a change of vibration of 1°, we have a daily error of 3.5. No change of suspending spring will alter inherent mechanical errors destructive of the laws of motion. With clocks made in the usual manner, whether you apply a long or short spring, strong or weak, broad or narrow, you will not remove one fraction of the error; so the sooner the fallacy of relying upon the suspending spring to cure mechanical errors is exploded the better.
That the suspending spring plays a most important part must be admitted, since, when suspended by a spring, a pendulum is kept in motion by a few grains only, whereas, if supported on ordinary pivots, 200 lbs. weight would not drive it 2′ beyond its arc of escapement, so great would be the friction at the point of suspension.
The conditions on which alone the vibrations of the pendulum will be isochronous are the following:
1. That the pendulum be at time with and without the clock, in which state it is isochronous “suspended by a spring.”