#### By Prof E.T. Hall, Oxford, England

##### Description of equipment
1. Clock movement
##### Impulses to the clock are provided electromagnetically every two seconds by means of a copper wire coil mounted to one side of the pendulum. Many writers on horology have decried magnetically maintained pendulums they are unreliable, they cannot be given an absolutely constant impulse etc. However if the correct design is used, they are both very reliable and, as we will see, give exceptional results as far as accuracy is concerned. In particular two points are important:
1. A constant current as opposed to voltage control must be used; this prevents changes of resistance due to temperature having an effect on the current through the coil. Modern electronics allow control of current to better than 1 ppm, if appropriate circuitry is used.
2. All electrical contacts must be eliminated for both reliability and to enable the pendulum to be 'free'.
##### Adjustment of rate. There are four methods of making such adjustments:
1. The rating nut at the bottom of the pendulum moves the bob vertically. There are 36 divisions on the top of the bob. One division movement changes the rate by ± 46 ms/Hr.
2. A small horizontal tray is carried on an extension to the pendulum about 100mm above the suspension. Addition of 1 gm to this tray will slow the clock by 30 ms/Hr.
3. A 40 turn single layer bias coil with its axis vertical is wound around the glass envelope at the height of the centre of the bob. Passing a current through this coil will cause a change of rate of 3.3 ms/Hr/ma. A current stabilised power supply with a 10 turn control provides this current.
4. A change of pressure will alter the rate. The rate coefficient for pressure is 0.77 ms/Hr/mb. However since the clock operates at < 10-5 mb, changes in this pressure region will have negligible effects on rate. However this effect should be kept in mind when initially setting up in air.

3. Associated Equipment
1. Clock readout. The pulses from the LED/diode assembly within the vacuum chamber are fed to this unit via a vacuum seal. By the use of appropriate digital counters and 25 mm high LED displays, a 12 hour clock is provided. All the required logic and drive circuitry is contained within this unit. Controls are provided on the clockface for setting time and also for setting the phase of the swing of the pendulum to coincide with the clock such that the impulse is only given when the pendulum is approaching the impulse coil
2. Clock comparator. This unit compares the time of day displayed on the clock with that time registered within the unit, driven by an oven stabilised 5 MHz quartz crystal, having a long term frequency stability better than 1 part /108/ year. The error is computed and displayed each minute to 0.1 ms. This reading is also registered by the recorder each minute and sent to the computer at the hour to a sensitivity of 0.1 ms (averaged over the hour).
3. Use of GPS frequency standard. Though time is measured by comparison with a 5 Mhz crystal with a rate of 10-2 ppm/year, the cumulative error will be 50 mS / year. It is now easy to compare the clock with UT1 using a satelite GPS (Global Positioning System). Some apparatus provides a 20 S wide pulse at the start of every second. By using a gating system and a 10 KHz crystal we have made an instrument which provides the decimal fractions of the current second on a 5 figure LED display at 4 second intervals.
4. Amplitude readout. As explained above, a shutter attached to the bottom of the pendulum swings between an LED and photodiode in such a way that light passes from the one to the other only when a 1.6 mm slot in the shutter allows it to do so. As I shall show below, the angular amplitude is directly proportional to the maximum pendulum velocity at its midpoint of swing. We can arrange that the slot is at this central point when at rest: it will also have its maximum velocity at this point when swinging. During the period that the light passes it can be arranged that an electronic gate is opened and whilst the gate is open a 1 MHz signal is allowed to pass to a counter. These counts are accumulated at each pass of the pendulum (60 times per minute). At the end of the minute the first four figures of the accumulated seven figure number are passed to the recorder and the average value of these figures is sent to the computer at the hour. This figure is inversely proportional to the amplitude. Fig. 9 illustrates this system.
5. ##### Figure 9
6. Computer and Printer. A PC computer is connected to the system. This has a number of functions:
1. At each hour the computer program passes the values of average time and average amplitude to files both on the harddisk and on the floppy. The latter can be taken (during non recording periods) to an external computer for processing the results.
2. Various parameters can be monitored and continuously recorded by being passed to the computer. Amplitude and pillar tilt are obvious examples.
3. The computer is used to stabilise the amplitude. The system works as follows. At the start of a run a value of the amplitude is chosen (this will be a 4 figure value as described above). By experience a value of the impulse coil current a little above that necessary to maintain this amplitude is also chosen and set by a potentiometer on the clock readout panel. At each minute the last measured average value of amplitude is compared to the set value and if the former indicates a higher amplitude to that set, no impulse will be given for the next minute. This procedure will continue until the measured amplitude exceeds the set value. Because the clock operates in a high Q regime some -'hunting' may occur for several hours until the system stabilises.
4. The printer is used to continuously monitor the time and amplitude drift on paper.
7. Pressure measurement. A commercial Pirani gauge is used to monitor the backing pump pressure. The clock case pressure is measured by a cold cathode ionisation gauge which uses a strong permanent magnet. It has been thought wise to remove this magnet as far away as convenient so as to obviate changes of clock rate due to drifts of the associated magnetic field. In fact it is mounted on a 500 mm long 50 mm diam. aluminium tube. Whilst on this subject, it is worth mentioning the importance of removing any potentially disturbing magnetic objects or fields; this particularly concerns those which might get moved after setting up the equipment, e.g. metal chairs or pieces of apparatus.
8. Standby power and alarm. It is most important that long runs of results should be protected and that continuity should be preserved. Since all results are recorded every hour in two places protection is secure. It is important that the following devices do not stop on a mains failure; backing pump, turbo pump, computer, amplitude monitor (which also provides power to the clock and impulse system) and rate adjustment bias coil supply. All these units are mains powered from inverters, which convert 24 volts DC to 230 2 volts AC . The 24V DC is provided by two 12V car batteries in series; they have a capacity of 150 AH. The batteries are kept charged by AC operated power supplies with a capacity of 25 amps. If the mains fail, the battery/inverter system will maintain accurate time for at least 4 hours. At the same time an alarm will sound, which will signal 'panic stations'; it is hoped that this time interval will allow emergency steps to be taken. A standby 1.5 kW petrol driven generator is on site and, by means of a simple changeover switch, can take over from the mains until repairs are effected.
9. Pendulum tilt detector. As has been stated above, the whole clock assembly is firmly fixed to a cast concrete pillar. Although it is hoped that this pillar is completely stable, we cannot be sure that it is so and how can we verify this? When setting up the clock, we adjusted the left/right jacks to allow the pendulum to swing centrally by eye. We have now incorporated a more scientific method for both setting the central swing and also so as to check the stability of the swing amplitude.
##### The counter readings, as displayed, are transfered to the analogue recorder via the computer so that a trace is available to show the trends of the tilt of the pillar during changes of weather etc. See 3(e) below for calibration of these readings.
4. Design Features.
1. Amplitude calculations.
##### Or a change of 1 unit of A, represents a change of 0.15" of φ.
3. Calculation of Q.
##### The drag coefficient (CD) of a cylindrical pendulum is a function of the Reynolds number (R) only and this will vary with the gas pressure and in particular as to which regime (laminar, low R or turbulent, high R) is prevalent.1 The science of Reynolds numbers is complex, but, as far as we are concerned, it is only the principle which matters; actual calculations are not provided here.
5. Calculation of energy requirements.
##### For example by experiment we find the following:
 Pressure (Mb) Time ( sec) Q LPE Watts Ergs/sec 1000 4545 10300 11.13 2.4 * 10-7 2.4 1 * 10-5 530000 1.2 * 106 11.13 2.1 * 10-9 2.1 * 10-2
##### Since the slit width is 1.6 mm, the pulse width should be 0.16 / 2.12 secs or 75 ms: this is in reasonable agreement with that measured below.
7. Amplitude 'lock' facility and impulse current.
##### The values, found by experiment at a pressure of 10-5 mb, are approximately:
• Impulse coil resistance = 910 ohms
• Pulse current peak value = 900 μa
• Pulse width = 70 ms
• Repetition rate ( averaged over 1 hr) = 0.25 Hz
9. Calibration of pendulum tilt detector.
10. ##### Let us assume
• Half angle of swing = θ degrees
• Angular misalignment of pillar = φ degrees
• Linear misalignment of pillar over pendulum length = L mm
• Then φ= R * θ / 2* 500000
• If 0 = 0.25 and R = 1, then φ = 2.5 * 10-7 degrees or approx. 10-3 arc seconds
• If the pendulum length (between suspension and slot) = 1120 mm
• then L = 1120 * Tan φ
• or using the above conditions, L = 5 * 10-6 mm = 5 * 10-3 μ M
##### In practice it has been found, over a long period, that the recorder shows a maximum deflection of about ± 10 mm, representing some ± 0.25 arc seconds of tilt.
5. RESULTS
1. Amplitude stability.
##### However since amplitude changes will be plus and minus, the average figure will be much less. Indeed the computer shows that the average hourly amplitude does not change by more than ± 2 units, showing a rate change of some 1ms/day as a more likely figure.
3. Time stability.
##### Figure 8 - Drift
5. Allan variation.4
##### We can calculate the gradient of the Allan curve as follows:
• If, from Fig. 6, the interval and dF/F at any particular time are I1 and F1 etc., the Allan gradient will be (log F2 - log F1) / (log H2 - log H1)
• Using this formula with the figures in Fig. 6, we find that the gradient is -0.5 ± 0.05
• This result is described as "ideal" in Ref.4 p.364.