THE BELL SYSTEM

SOME of the earliest documents in human history relate to man’s interest in timekeeping. This interest arose partly because of his curiosity about the visible world around him, and partly because the art of time measurement became an increasingly important part of living as the need for cooperation between the members of expanding groups increased. There are still in existence devices believed to have been made by the Egyptians six thousand years ago for the purpose of telling time from the stars, and there is good reason to believe that they were in quite general use by the better educated people of that period.1 Since that period there has been a continuous use and improvement of timekeeping methods and devices, following sometimes quite independent lines, but developing through a long series of new ideas and refinements into the very precise means at our disposal today.

The art of timekeeping and time measurement is of very great value, both from its direct social use in permitting time tables and schedules to be made, and in its relation to other arts and the sciences in which the measurement of rate and duration assume ever increasing importance. The early history of timekeeping was concerned almost entirely with the first of these and for many centuries the chief purpose of timekeeping devices was to provide means for the approximate subdivision of the day, particularly of the daylight hours.

The most obvious events marking the passage of time were the rising and setting of the sun and its continuous apparent motion from east to west through the sky. The first practical measure of the position of the sun of which any record is known was the position or the length of shadows of fixed objects, resulting through a long period of development in the well-known sundial in its many forms. But the sundial was in no sense an instrument of precision and in no sense could be considered as a time keeping device. Even after the development which resulted in mounting the gnomon parallel with the axis of the earth, the largest, most elaborate, and most carefully made instruments could at best indicate local solar time. Furthermore, the sundial has value only in daylight hours and then only on days when the sun shines clearly enough to cast a shadow. These shortcomings became more and more important with advances in society and, for measuring duration, man soon began inventing timekeeping means that would work without benefit of the sun.

The evolution of timekeeping devices may be divided into three main periods, each employing a specific type of method, although overlapping to some degree in their applications, and characterized by increasing orders of accuracy.

A graphical representation of this evolution, indicating these three periods of development, and showing the relation between some of the major contributions to time keeping and the resulting accuracy of time measurement, is shown in Fig. 1. The methods employed chiefly during these three periods may be classified broadly as CONTINUOUS FLOW from the beginning up until about 1000 A.D., as APERIODIC CONTROL from then until about 1675 A.D. and as RESONANCE CONTROL from that time up to the present. Keeping in mind the logarithmic nature of the time and accuracy scales used in this graph, it can be seen readily that most of the advancement has been made in a very small part of the total time, corresponding to the resonance control epoch.

Fig. 1 - The accuracy of timekeeping through history.

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* The subject matter of this paper was given before the British Horological Institute in London on the occasion of the presentation of the Horological Institute's Gold Metal for 1947 to Mr. Marrison in consideration of his contribution toward the development of the quartz crystal clock. The present text is substantially as published in the Horological Journal.

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THE EPOCH OF CONTINUOUS FLOW

Perhaps due to a feeling that the passage of time was like the flow of some medium, the first time measuring devices were those depending on the flow of water into or out of suitable basins.

It was recognized that, with an orifice properly chosen, the time required to fill or empty a given basin should be about the same on repetition, and hence was born the first reliable means for measuring time at night or on overcast days. A great variety of devices operating on this principle were constructed and used, some of the earliest having been made by the Babylonians and the Egyptians 3500 years ago.

Some of these water clocks, or clepsydra as they were called, had floats or other indicators which were intended to subdivide a unit of time into substantially uniform divisions. Others were constructed so that successive fillings of the basin would be counted or would operate a stepping device, associated with a dial or other indicator. Through the centuries great numbers of such devices were constructed, with some of the later ones having elaborate mechanisms for striking the hours or for animating figures of people or animals.

For use in places where water was not readily available and where sand was plentiful, clepsydra were developed that would operate with the flow of sand in much the same way as with the flow of water. The basic ideas were not greatly different, the substitution being merely one of expedience.

The hour glass, and its smaller counterparts, is one of the most convenient forms of this device and until quite recent times served a useful purpose where accuracy was of no great importance. The hour glass shown in Fig. 2 was used by a pastor in the early eighteen hundreds to determine the length of his sermons. The average variation among a set of ten one-hour determinations made recently with this glass was 3 minutes, or about 5 per cent.

The clepsydra that were designed to repeat and totalize an endless succession of cycles were especially adaptable to the measurement of extended intervals of time, although with very poor accuracy as we now think of it.

Fig. 2 - Hour glass.

By suitable design any desired number of cycles could be made equal to the natural large unit, the day, so that any fraction of a day within the accuracy of a given instrument could be determined simply by counting off the number of cycles from a particular starting point such as sunrise, sunset, or high noon. It was possible with these devices to operate without calibration over periods of several days, although the cumulative error inevitably was very large.

An error of a few hours was of small importance in the days when the speed of communication and travel alike depended on pack animals or the caprices of the wind. And so, in spite of the inaccuracies of the water clocks and sand clocks, they served their purpose well through many centuries. In fact, it was not until the tenth century A.D. that any really novel effort was made to improve upon them as timekeepers. The first efforts to improve upon them, making use of falling weights for motive power and various frictional devices to control the rate of fall, were not very successful because no satisfactory means were known to keep a friction-controlled device sufficiently constant for the job. Clocks so constructed were no better timekeepers on the whole than the traditional clepsydra. They had, however, the hope of compactness, and much ingenuity was exercised in their design over several centuries.

Also in the category of continuous flow devices should be mentioned the methods depending on the rate of burning, such as in time candles, time lamps and their numerous variations. Such timekeepers are not very accurate but are thoroughly reliable in dry, quiet places, even providing their own illumination at night. Such timekeepers are known to have been used before the tenth century A.D. and certain variations still are used by a few isolated tribes, especially in the tropics.

THE EPOCH OF APERIODIC CONTROL

In or about the year 1360 the invention of an escapement mechanism for controlling an alternating motion from a steady motive power, such as a suspended weight, was the first really important step in the history of precision clock development, and marks the beginning of the second major epoch in timekeeping evolution. The escapement in one form or another was soon applied in practically all timekeepers, the most outstanding example of an early application being a clock constructed by Henry De Vick for Charles V of France in or about the year 1360 A.D. and still in use—with extensive modifications—in the Palais de Justice in Paris.

This invention was important, not because De Vick's clock, or any of its immediate successors, were good timekeepers, but because this was the first time that vibratory motion in a mechanism was used deliberately to control the rate of a time-measuring device. All precision clocks depend in one way or another on using energy to produce vibratory motion, and on using the rate of that motion to regulate suitable dials and other mechanisms.

No simple improvement on De Vick's clock could ever have produced a precision clock in the modern sense, however, because the essential rate-controlling feature was still lacking. His invention consisted of the use of a verge escapement which produced oscillatory motion in a dynamically balanced member, known as a foliot balance, having essentially only moment of inertia and friction. The rate of oscillation, therefore, depended to a large extent on the applied force exerted by the falling weight through a train of wheels, and upon the friction of the escapement parts and of the oscillating member itself.

This sort of operation is known sometimes as relaxation oscillation and appears in many forms. In the clock, the rate-controlling feature depends upon the length of time it takes a member having a given moment of inertia to move from one angular position to another under a given applied torque. Thus, the rate depends to first order on the applied torque.

Although De Vick's clock was one of the most famous in all history, it was not because of its good record of timekeeping. In its original form, it is said that it often varied as much as two hours a day from true time. Outwardly, this clock on the Palais de Justice appears about the same as it did originally, but the "works" have been modernized and it keeps much better time now.

The history of timekeeping during the next three hundred years consisted mainly in improvements and in a great variety of applications of the principles contained in De Vick's clock. During this period great numbers of clocks of all sizes, from tower clocks to portable table clocks were made, controlled by various forms of the crown wheel, verge and foliot balance. All of these timekeepers belong to the class that we have just called aperiodic. Their accuracy, in general, was still poor and the indicator on their dials consisted of but one hand—the hour hand. It was not until the invention and application of the pendulum that the next major improvement was born in timekeeping.

THE EPOCH OF RESONANT CONTROL

All that has been said so far is a prelude to the shortest but by far the most productive epoch in timekeeping, that of resonant control. The heart of every precision clock is an oscillatory device which depends upon resonance for its constancy of rate. The history of precision clock development consists largely of the choice and design of stable resonant elements and of devising means for using them so that as far as possible their inherent properties alone control their rates of oscillation. Once in stable oscillation, it is only necessary to control the indicating of dials and other suitable mechanisms in order to constitute a complete clock.* Presumably this can always be done, but in some cases it is more convenient to do than in others, as will appear.

The resonant element may be any of a wide variety of forms, mechanical or electrical, all characterized by the single property that, if deformed from a rest condition and released, the stored energy is transformed back and forth from potential to kinetic at a rate depending chiefly on the effective mass and the effective stiffness, or other like properties, a small proportion of the energy being lost in internal friction at each oscillation. Some resonant elements which have been used in timekeepers are illustrated in Fig. 3.

Fig. 3 - Typical resonant elements used in timekeeping.

The simplest appearing of all these is that of a mass, M, supported by a spring with stiffness, S. From the equation of motion

the period of oscillation may be derived simply and is found to be

Similarly for the simple electrical resonant circuit where current flowing in an inductance, L, behaves like a mass, and current flowing in a condenser, C, behaves like the reciprocal of a stiffness, the period may be written.

* Encycl. Brit. 14th Ed. "A clock consists of a train of wheels, actuated by a spring or weight or other means, and provided with an oscillating governing device which so regulates the speed as to render it uniform." Similar expressions are derivable for the periods of oscillation of all simple oscillating systems, including the pendulum for which the period (for small amplitudes) is given by

where and are respectively the length and gravity expressed in the same system of units, for example, the c.g.s. system.

When any such resonant element is strained from its rest condition, and released, it will oscillate with gradually decreasing amplitude until all of the stored energy has been dissipated in internal friction or resistance, and in the friction or resistance of the coupling with the supports. In general, the resulting amplitude of free oscillation may be given as

the graph of which is a damped sine wave. The rate of free oscillation, , is dependent chiefly on the effective mass and stiffness and to a small degree on the effective resistance of the element, while the rate of loss of amplitude, that is, the logarithmic decrement, , is dependent on the ratio of effective resistance to effective mass.

If the resistance could be made exactly zero, such a motion once started would continue forever and its rate would be controlled wholly by the effective mass and stiffness of the resonant element. Actually, of course, such a condition cannot be realized in practice but, by the selection of suitable materials and environment, and by special control means, it is possible to approach very closely to the ideal condition by causing the oscillation to be maintained almost as though there were no damping.

The evolution of precision timekeeping, whether consciously or not, has centered around the study and development of these two ideas: to discover resonant elements whose rate-determining properties are inherently stable, and to discover means for sustaining them in oscillation as though they had no effective resistance; or in employing means to circumvent or to compensate for any such resistance. The high precision of rate control that can now be obtained has been the result largely of developments in these two categories.

The Pendulum

The gravity pendulum was the first truly resonant element to be used to regulate the rate of a clock and for nearly three centuries maintained the supremacy for precision measurements of time. The pendulum was more a discovery than an invention, the popular story of its origin being that, while still a youth of seventeen years, Gallileo Galilei chanced to notice that a hanging lamp in the Cathedral of Pisa seemed to swing at the same rate regardless of amplitude. This he confirmed approximately by comparison with his pulse, and later made an extensive study of the isochronism of swinging bodies. These studies were in progress as early as 1583. Nearly sixty years later Gallileo described to his son Vincenzio how a pendulum could be used to control a clock, but no concrete result of this advice is known to have been made at that time. A working model of this clock, made subsequently from the original drawings, is on exhibition in the South Kensington Science Museum, London. The first authentic record of the actual use of a pendulum in a clock is attributed to the great Dutch scientist, Christian Huygens, who produced his first pendulum clock in 1657. This was described by him in the Horologium in 1658.2

The performance of pendulum clocks was so good that almost immediately clocks of all other types were modified to include a pendulum. So complete was this transformation that very few unmodified clocks are now in existence which antedate the first application of the pendulum to timekeeping. This, as a matter of fact, is one of the major reasons that so little is known about the actual mechanisms used in mechanical clocks that were made before the introduction of the pendulum.

The subsequent history of pendulum clock development is well described in numerous books and papers and covers a wide field. Only those factors that relate the pendulum to other means of rate control will be discussed in the following.

The properties of a pendulum which make it such a good timekeeper are easily seen from a study of the forces on the bob as illustrated in Fig. 3. Since these forces must be in equilibrium at all times we may write (assuming no friction)

The nearly isochronous property of the pendulum is contained in this relationship since the period, on solution, is

where q is the maximum semi-amplitude of swing expressed in radians. When this arc is small the period approaches a minimum. For small angles the natural period depends almost wholly on the ratio of to and the stability of depends chiefly upon the constancy of and . Figure 4 shows the relation between period and the arc of swing, expressed as seconds per day departure from the theoretical rate for zero arc.

Fig. 4 - Relation between arc and rate of pendulum.

The sum of all the terms that depend upon powers of sin /2 is known as the circular error, relating to the fact that the bob is constrained to move on the arc of a circle. It was shown theoretically by Christian Huygens3 that if the bob could be constrained to move on the arc of an epicycloid it would be truly isochronous, that is, the period would be completely independent of its amplitude of motion. It is of interest to note at this point that in no other resonator used for precision timekeeping is there the direct counterpart of circular error, for in all other cases the restoring force varies linearly with displacement in the region of operation and not as a sine function of it.

In the early stages of pendulum clock development it was not necessary to consider the arc error because other errors were of greater magnitude. But it is by no means a negligible factor, and in all precision timing by pendulums it must be accounted for, either by allowing for an arc correction, as is done commonly in geodetic survey work, or by keeping the arc small and precisely controlling it. According to F. Hope-Jones4, referring to the master pendulum in the famous Synchronome free-pendulum clock: "A variation of only 0.01 mm. in the excursion of the bob or 2 secs. of arc will by circular error alter the rate by 0.00145 sec. per day, - and if it arose unperceived and was steadily maintained, it would produce an accumulated error of half a second in a year, so the necessity for this close observation is obvious."

The control of arc has almost invariably been accomplished by keeping constant the amount of energy applied per swing so that the actual amplitude obtained is that value for which all of the applied energy is dissipated in the pendulum system. In a sense this method of control of arc puts a penalty on improvements in design that would reduce the friction, because the better a pendulum becomes in this respect the less stable becomes the arc control. Since even the best pendulums develop unexplainable small changes in arc, it has been common practice in some observatories to record the arc frequently and to make allowance for changes in it when making the most precise time determinations.

The inherent constancy of rate of a pendulum, with small or constant amplitude of swing, depends to the one-half power on the stability of /. The changes in and are quite independent of each other and so can be treated separately. Other factors that will be described also affect the rate, and it is the object in every precision clock design to reduce such variable effects to the absolute minimum.

Some control can be exercised over every factor except , which remains a property of space and is dependent only on the proximity of matter and on acceleration. As is well known, the value of varies over the surface of the earth due chiefly to its deviation from spherical shape, and because of the uneven distribution of matter. It also varies with vertical displacement or tides at any location to such an extent that a gravity clock that keeps accurate time at ground level will lose a second a day or more in a tall building. Actually, it is now possible to chart variations in with high precision through measurement of the rate of a pendulum clock against a standard whose rate does not depend upon gravity.

Most of the factors that can affect have been studied critically and means have been found to reduce them to very small effects. The chief source of variation was at first the temperature coefficient of the pendulum rod. With ordinary metals the rod expands from 10 to 16 parts in a million per degree C, causing a proportionate change in rate of half this amount, corresponding to from one-half to two-thirds of a second per day. Many ingenious means were developed to reduce this effect, starting with George Graham's mercury-filled bob in 1721, followed by John Harrison's grid-iron pendulum in 1726, and a great number of variations on these ideas, all depending on the differential coefficient of expansion of dissimilar materials.

About the year 1895, Charles Edouard Guillaume of Paris developed an alloy, consisting chiefly of nickel and iron, which he called Invar, because it had a very small temperature coefficient of expansion, from which pendulum rods could be made. The use of this material made it unnecessary to resort to complex compensated pendulums with their own inherent instabilities, and the accuracy of timekeeping was increased another step. The residual temperature effects could be measured readily, and compensated if desired, by the use of a small bar of aluminum attached to the bob.

Some other important factors that affect the working length of a pendulum are the aging of the supporting rod, the "knife edge" or spring used for the suspension, the nature of the main supporting column or frame, and some atmospheric effects caused by changing temperature and pressure. In the most accurate pendulum clocks, the atmospheric effects are greatly reduced by mounting the pendulum in partially evacuated, hermetically sealed enclosures which can be temperature controlled. All of these factors and many others are discussed in every good treatise on accurate pendulum clocks. They are mentioned here chiefly for the purpose of comparison with like factors in the quartz crystal clock and to show how in many cases the difficulties introduced by such factors may be more easily and more positively controlled.

In every primary clock mechanism the resonant governing device must be sustained in oscillation, and the manner in which this is done has a strong bearing on its rate regardless of the quality of the governing element. The basic requirements are the same for any kind of oscillator, whether a pendulum, an electrically resonant circuit comprising inductance and capacitance, a steel tuning fork, or a quartz crystal resonator. The requirements were first stated for the case of the pendulum by Sir George Airy in 1827 and it has always been the aim in the design of every good pendulum driving means to satisfy Airy's condition.

This condition is conveniently illustrated by the diagram of Fig. 5 which shows the two most familiar representations of damped sinusoidal motion. In order to provide a convenient scale in the drawing an impractically large damping is represented, corresponding to a Q of 20. The Q of a resonant circuit is related to the logarithmic decrement, d , by the relation Qd = p . The factor d is the logarithm, to base e = 2.718..., of the ratio of the amplitudes at any two successive periods. It should be noted that the Q of a good electrically resonant circuit is in the order of 200, that of a good pendulum from 10,000 to 100,000 and that of a good quartz resonator from 100,000 to 5,000,000. The significance of these higher values of Q will be evident from the following discussion.

Fig. 5—Amplitude-phase diagram for resonant element.

In Fig. 5 the damped sine wave shown corresponds, point by point, to the phase diagram, which is simply a logarithmic spiral. By suitable choice of scale the spiral can be interpreted to represent either the amplitude or the velocity—in which case the real amplitude is vertical and the real velocity horizontal. In this representation the velocity is shown maximum when the amplitude is zero, which is a very close approximation to fact for all practicable values of Q. The discussion will center on the velocity spiral.

Let us assume that the pendulum is sustained in oscillation by a succession of short impulses, one for each swing applied at some phase angle j ₁. If the impulse is really short, the velocity will be increased to the value that the pendulum had when it occupied the same position during the last swing. This change of condition is represented by the short horizontal path on the velocity-phase diagram and, as indicated, is accompanied by an advance in phase D j ₁. This can be interpreted as meaning that the period of a pendulum sustained in oscillation in this way is reduced from its natural period in the ratio of It is obvious from the diagram that becomes smaller and that this ratio approaches unity as the phase of the applied impulse approaches that of the maximum velocity—that is, when the pendulum is in the center of its swing; and this is Airy's condition. It is clear also that if the impulse is applied after (instead of before) the instant of maximum velocity, the period will be correspondingly increased. From the geometry of the figure, it can be seen that, in the neighborhood of the optimum condition, the deviation from natural period is very closely proportional to the amount of the phase departure.

The closeness of spacing of the turns of the spiral depends directly on the Q of the resonant element. For a Q of 200, the turns will be packed ten times closer than shown, and the corresponding will be only one tenth as great, other conditions being comparable. For a Q of a million or more, becomes very small indeed, especially when j is properly chosen—and the variation in , which is a measure of the variation in rate due to the driving means, may be made vanishingly small.

The importance of the above properties to timekeeping depends upon how well conditions can be set up to realize them. At first wholly mechanical means were employed and, with the advent of the dead-beat and detached escapements and by careful design and operation, quite remarkable performance was obtained.

A new approach in timekeeping methods was introduced by Alexander Bain5 in 1840 when he first used electrical means for sustaining a pendulum in oscillation. The importance of Bain's invention of the electric clock is indicated by a long controversy over the priority of the invention with Charles Wheatstone, who was working along similar lines at the same time as a by-product of his extensive researches on the electrical telegraph. A brief story of this controversy entitled "The First Electric Clock" was written for the one-hundredth anniversary of Bain's invention6. The first electric pendulum clocks could not compare in accuracy with the best mechanically driven pendulums of the period but, in spite of a great deal of initial skepticism on the part of those brought up in the mechanical tradition, electrical maintenance and control has been applied in the most accurate pendulums in the world.

The free-pendulum clock makes use of the idea, first proposed by Rudd, of allowing a master pendulum to swing free of all sustaining or other mechanism for a considerable number of periods and of imparting to it, after each group of free swings, a single impulse large enough to maintain the next equal number. The advantage is that no friction effects of driving mechanism are coupled to the pendulum except during that minimum time required to impart energy to it. Actually, in theory, the phase error introduced by one large impulse after n free swings is exactly the same as the sum of the phase errors for n small impulses. That can be deduced from the phase diagram of Fig. 5. But experience has shown that a pendulum is actually more stable when the sustaining mechanism is detached from it the greater part of the time.

The Synchronome free-pendulum clock includes also the basic idea of the gravity remontoir first applied by Lord Grimthorp (then Sir Edmund Beckett Denison) in the design of the mechanism of Big Ben, London, constructed in 1854—and still in continuous operation. The ingenious application of these principles and the electrical means devised by F. Hope-Jones and W. H. Shortt for its accomplishment have resulted in the construction of the most accurate pendulum clocks in the world by the Synchronome Clock Company of London. The history and development of the free-pendulum clock is elegantly described by F. Hope-Jones in his book on Electric Clocks7.

The predominant characteristics of a pendulum resonator, as used in a clock, have just been discussed in order to show the parallel between them and the properties of other resonant systems. It will be shown how some of the factors that have been troublesome in the development of pendulums have been rather easily taken account of in other types of control devices and in particular in the quartz crystal clock.

THE EVOLUTION OF ELECTRIC OSCILLATOR CLOCKS

It almost never happens that a result of any considerable value is obtained at a single stroke or comes through the efforts of a single person. More often even the most important advances come as the climax of a long series of ideas which have accumulated over a period of years until the next step becomes almost self-evident and is accomplished either through the necessity for a new result or as a logical next step.

This was preeminently the case in the crystal clock development and involved the putting together of a considerable number of ideas that had been accumulating through a century or more of related activity. The chain of events which led eventually to the crystal clock followed a course quite independent of pendulum clock development, although parallel with it, and meeting it from time to time on the way. From the start, it involved the use of resonant elements whose frequencies do not depend upon gravity for controlling the frequency of oscillations in a positive feedback amplifier. From a rather simple beginning, taking advantage of a series of discoveries and inventions through about a century of progress, there has evolved a clock whose stability is comparable with that of astronomical time itself, as heretofore defined in terms of the earth's rotation, and having a versatility far exceeding all other existing means for the precision measurement of time.

Electric Oscillators

The first recorded experiments that relate directly to this development were those of Jules Lissajouss8 who, in 1857, showed that a tuning fork can be sustained in vibration indefinitely by electrical means, using an electromagnet and an interrupter supported by one of the prongs. The idea of using an interrupter to sustain vibration was not new with Lissajous, but had been invented by C. G. Page9 and described by him as early as April 1837, to obtain a regularly interrupted electric current. Credit for this important invention is often given to Golding Bird10 or Neeff11 who evidently were working along similar lines concurrently although quite independently of each other. Page, Golding Bird and Neeff were all medical doctors and evidently were interested in their devices more for their therapeutic interest than for the general scientific value, since "galvanic" electricity was attributed at that time with marvelous healing powers.

Lissajous was probably the first to make use of the idea for accurate measurements of rate, being a prolific experimenter in mechanics and acoustics, and the originator of the famous method bearing his name for the study of periodic motions. Indeed, the electrically operated fork was developed especially for use as a standard to be used in studying the rates of other vibrators. In principle, the electrically operated fork is like the pendulum drive of Alexander Bain, except that the rate of vibration in this case is not a function of gravity but for the most part is controlled by the effective mass and elastic stiffness of the vibrating member.

The tuning fork itself was invented in 1711 by John Shore, a trumpeter in Handel's orchestra12, and was developed to a high state of perfection by the great instrument maker and physicist of Paris, Rudolph König. To establish an accurate standard of pitch for calibrating these forks König developed what he termed an "absolute" method for the determination of frequency. This consisted of a tuning fork having a frequency of 64 vibrations per second, with delicate mechanical means, similar to a clock escapement, for sustaining the fork in vibration and for counting the number of vibrations over any desired interval of time. For this purpose, the escapement mechanism was geared to the hands of a clock, so that when the fork had its nominal frequency the clock would keep correct time. Dr. König credits the invention of the fork-clock to N. Niaudet13 in these words:

"Cette disposition avait été realisée pour la première fois dans l'horloge à diapason que N. Niaudet fit présenter à l'Académie des Sciences le 10 décembre 1866, et que à figuré aux expositions universelles de Paris 1861 et de Vienne 1873."*

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* "This apparatus was realized for the first time in the fork-clock which N. Niaudet described at the Academy of Sciences on December 10, 1866, and which was shown at the expositions of the University of Paris in 1867 and the University of Vienna in 1873."

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Thus, as early as 1866, the essential elements had been developed separately from which a clock of the electric oscillator type could have been constructed. But it was not until more than half a century later, when there was more apparent need for such a clock, that it was actually realized. It was chiefly for the purpose of studying temperature coefficients and like properties of tuning forks that König constructed and used his famous mechanical fork-clock. There is no evidence that there was at that time any idea of using a fork-clock as a timekeeper.

It was for the purpose of making still more precise studies of the properties of tuning forks that H. M. Dadourian14 in 1919 made use of the phonic wheel motor for the first time for counting the number of cycles executed by a fork over an extended period of time to measure its rate. By means of a chronograph the time interval corresponding to the total of a very large number of periods could be measured precisely in terms of a standard clock, thus providing a direct "absolute" measure of fork rate. For this he found already invented for him all of the essential component parts, including the fork with electromagnetic drive, and the phonic wheel motor.

The phonic wheel motor, which in some modified form is an essential part of nearly all oscillator clocks, was invented by two investigators, apparently quite independently and for entirely different purposes. The first published reports of each appeared in 1878.

The first of these is an American patent that was granted on May 7, 1878 to Poul La Cour15, a Danish telegraph engineer. The application was filed in Washington on April 9 of the same year, and described a fork-controlled impulse motor similar to those still used in many modern synchronous clocks. The other publication was a report in Nature for May 23 of the March 30 Physical Society Meeting. In this, Lord Rayleigh described a motor which he developed to measure the frequency of sound by a stroboscopic method.16 Both of these original disclosures indicated a considerable amount of previous study, even including the fluid-filled flywheel to reduce hunting. It may be impossible at this time to know who actually put in motion the first phonic wheel motor.

Difficulties inherent to contact-controlled devices prevented the development of highly accurate fork standards of this type, and there is no evidence so far that any thought had been given to the use of a tuning fork as a timekeeper.

The method of using a microphone instead of a contact was proposed by A. and V. Guillet17, in 1900 and has been used considerably in frequency standards of moderate accuracy, but that too had limitations which made it impossible to utilize fully the inherent stability of a good tuning fork.

The Use of Vacuum Tubes

The first opportunity for really precise control of the frequency of a mechanical vibrating system, and the next step in the oscillator clock; evolution, came with the invention of the thermionic vacuum tube at the turn of the century. The development of the vacuum tube has been a more or less continuous process18 starting with the studies of electrical conduction in the neighborhood of hot bodies by Elster and Geitel, Edison, and Fleming, and later developed into the first practical devices by Fleming19 and DeForest20 in England and America respectively. The first patent for such a device, a two-element tube, was issued to J. A. Fleming in 1904.21 The first patent on a tube containing three elements and suitable for use as an amplifier was issued to Lee DeForest in 1907.22

The vacuum tube as an amplifier found almost immediate and widespread application in telephony and, next to the basic telephone elements, was the most important single factor contributing to long distance communication. For this purpose large amounts of amplification were required. Very often in the operation of early amplifiers, enough signal from the output would somehow get coupled into the input circuit to make the entire circuit break into oscillation on its own account at some frequency for which the amplifier and feedback circuit were particularly efficient.

Although this was very annoying in an amplifier, it led naturally in 1912 to the invention of the vacuum tube oscillator, consisting essentially of an amplifier with coupling between the output and the input and some definite means for regulating the frequency of oscillation. The first to seek patent protection in vacuum tube oscillators were Siegmund Strauss23 in Austria, Marconi Company in England24, A. Meissner in Germany, and Irving Langmuir, E. H. Armstrong and Lee DeForest25 in America. Many specific forms have since been invented and widely used, some of the more familiar types being associated with the names of Colpitts, Hartley and Meissner.

With the vacuum tube oscillator controlled by electric circuit elements, it would have been possible immediately to operate a clock by means of a phonic wheel motor. Even if this had been done, however, the accuracy would not have compared very favorably with that of good mechanical clocks of the period. This is because the rate-controlling element of such oscillators was subject to large changes due to temperature and aging, and because means were not yet known for avoiding the effects of tube and other variables on the resulting frequency.

The next important step in our evolution was the use of the vacuum tube to sustain the vibration of a tuning fork. This may be considered either as an improvement on the contact-driven fork by the substitution of a vacuum tube relay device instead of the contact, or as an improvement on the vacuum tube oscillator by the substitution of a mechanical resonator for the electrical resonant element. This achievement was first announced by Professor W. H. Eccles26 in April or May, 1919, and was followed on June 20 by a note by Eccles and Jordan27 in the London Electrician. Meanwhile, on June 16 of the same year, a similar announcement appeared in Comptes Rendus by Henri Abraham and Eugene Block28, showing that parallel developments were in progress in both England and France. However, Eccles and Jordan in discussing their work at the National Physical Laboratory stated: "Several instruments of this kind have been set up and used during the past 18 months." From this, we may imply that they had vacuum tube driven forks in operation early in 1918.

One of the chief advantages of the use of the vacuum tube to sustain oscillations in a mechanical system is that the variable friction of the contact mechanism is avoided. Previously this had been one of the main causes of instability. With the new method it became possible to operate in a wide frequency range, continuously, and at small amplitude, and to deliver alternating currents of approximately sine wave form and having more constant frequency than heretofore had been possible. The judicious use of a vacuum tube in delivering power to sustain the vibration of a resonator is analogous to the ideal of the so-called free pendulum but may be utilized more effectively in freeing the resonator from disturbing influences associated with the driving means.

Another important advantage, which, however, was not realized immediately, is the ease with which the phase of the driving force applied to a mechanical vibrator can be adjusted for greatest frequency stability. In a manner analogous to the pendulum, in which it was shown that the rate is least affected when the driving impulse is applied at the instant of maximum velocity, the current delivered to the driving electromagnet and hence the force applied to the vibrating element, should be in phase with the velocity of that element. In the vacuum tube oscillator, it is a relatively simple matter to design the feedback circuits to meet this condition very accurately.

In 1921 and 1922 Eckhardt, Karcher and Keiser29,30 described the development of a precise fork and vacuum tube driving means, pointing out the following uses: "As a sound source; as a small scale time standard; as a current interrupter; as a synchronizer." The chief emphasis seems to have been on the second item because in the same year Eckhardt described a high-speed oscillograph camera using the same fork as a precise timing device. The study and improvement of the tuning fork oscillator were carried on continuously and soon such oscillators were used in several national physical laboratories and commercial research institutions as standards of frequency and time interval.

The next two reports of progress appeared in 1923, one by D. W. Dye of the National Physical Laboratory in Teddington, and the other by J. W. Horton, N. H. Ricker and W. A. Marrison of Bell Telephone Laboratories, New York City. Both of these papers disclosed work done over a period of two or three years and described apparatus that had been in operation for a considerable period. Dr. Dye employed a 1000-cycle steel tuning fork and a phonic wheel motor operating synchronously from it with a gear reduction and cam to produce periodic electrical signals which he compared with a clock by means of a chronograph31. Horton, Ricker, and Marrison used a 100-cycle steel fork, a synchronous motor with a gear reduction to produce electrical impulses at one-second intervals, and a clock mechanism operating directly from these signals32. This appears to be the first time that a vacuum tube-controlled oscillator was ever used to operate a complete clock mechanism. Shortly thereafter, a clock was built in which the 100-cycle motor was geared directly to the clock mechanism instead of operating through a stepping device. A contacting device was retained, however, for the purpose of making precise time measurements.

For precise measurements of rate over long time intervals, means were provided to compare the seconds pulses controlled by the synchronous motor directly with time signals received by radio from the Naval Observatory. To facilitate these comparisons, a two-pen siphon recorder was built by means of which the time marks were laid down side by side on a moving strip of paper in such a way that accurate subdivisions of a second could be made on any part of the record.

This same two-pen recorder and 100-cycle fork time standard was used during the total solar eclipse of January 24, 1925 to time the progress of the moon's shadow as observed at a number of stations in the path which were all connected by a round-robin telegraph circuit, through the Bell Telephone Laboratories’ headquarters in New York City33,34. A photograph of the original records is reproduced in Fig. 6. This is believed to be the first time that a vacuum tube oscillator type of time standard was ever used in the service of astronomy.

Fig. 6--Timing records of total solar eclipse of January 24, 1925.

During the following ten years a great number of improvements were made in tuning fork oscillators and they became widely used as precise frequency standards. The Bell Laboratories' 100-cycle fork standard was mounted in a container which could be sealed at constant pressure or vacuum. It was carefully temperature controlled and provision was made to keep the amplitude within prescribed limits. In describing this improved standard35, comprising a synchronous motor geared directly to a clock mechanism, the authors Horton and Marrison made the following statement:

"During tests on this frequency standard, it was found that it constituted a far more reliable timekeeper than the electrically maintained pendulum clock which was used to obtain the data already published. The pendulum clock was, therefore, dispensed with and all measurements of the rate of the fork are now made by direct comparison with the mean solar day as defined by the radio time signals sent out by the U. S. Naval Observatory."

In all fairness to the pendulum clock in question, it should be stated that the laboratory was situated on the seventh floor of a building adjoining a busy street and so was continually subject to vibration from traffic, wind, and other changing conditions. Disturbances of this sort have little or no effect on standards of the electric oscillator type but seriously impair the performance of most high precision pendulum clocks. The relative immunity of the oscillator standard to change of position and shock has an important bearing on its value in many applications.

Probably the most precise tuning fork controlled time and frequency standards ever constructed were those developed in the National Physical Laboratory at Teddington, as a continuation of the work begun there by Professor Eccles and carried forward by Dr. Dye and his staff. A report by D. W. Dye and L. Essen in the Royal Society Proceedings in 193436 described a number of refinements in the fork and method of use some of which had been suggested by Dr. Dye as a result of his studies ten years earlier. Among these was the use of elinvar in the construction of the forks in order to reduce the effect of variable temperature on the frequency. Elinvar is a nickel steel containing about twelve per cent of chromium, which on proper treatment has a small or zero temperature coefficient of elasticity. It was invented by Charles Edouard Guillaume37,38 and was further studied by P. Chevenard39,40. The excellence of the N.P.L. fork standard can be appreciated readily from the conclusion of the 1934 report which states in part:

"The frequency of the fork in comparison with the N.P.I. Shortt clock can be measured at any time with an accuracy of 5 parts in 10⁸. It is necessary to apply a correction for the rate of the Shortt clock, and the ultimate accuracy with which the absolute value of frequency is known depends on the accuracy of the time signals which are used to determine the rate of the clock. The final frequency can, however, usually be ascertained with an accuracy of ± 1.5 parts in 10⁷. In its present condition the turning fork maintains a frequency stability of the order of 3 parts in 10⁷ over periods of a week or more."

A considerable amount of effort has been devoted to the improvement of tuning forks, directed mostly toward stabilizing the fork itself. Patents issued to H.H. Hagland41, August Karolus42 and Bert Eisenhour43 have been concerned with the reduction of temperature coefficient by various methods of compensation in the alloy or in the mechanical structure of the fork. In recent years, alloys have been produced from which forks with a zero coefficient of frequency can be machined. These alloys have neither a zero expansion coefficient nor a zero elastic coefficient, but the two coefficients are so balanced that their effects cancel as they concern the frequency of a tuning fork.

One of the largest residual sources of error in a good fork is that caused by the coupling through the mounting. A fork which is efficient is a producer of sound by coupling through the base would be quite useless as a precise standard of rate due to the losses introduced in this manner. It has been shown by S.E. Michaels44 that the tines of well-balanced fork can be so shaped that practically no energy at fundamental frequency is transmitted through the base.

By making use of all that is known about materials, shapes and mountings for tuning forks, and all that is known about stabilized vacuum tube circuits for driving them, it is quite possible that considerable further improvement could now be obtained in such a standard. But another line of development has shown greater promise in this field and the ultimate accuracy of tuning fork oscillators has never been pursued.

The Quartz Resonator

During the same ten years that the greatest advances were being made in the tuning fork art, the striking properties of the quartz crystal resonator were reviewed and first applied in the construction of frequency and time standards. Its use in primary standards for the most exacting measurements of frequency and time is now almost universal in national and industrial laboratories throughout the world.

Quartz crystal is the most abundant crystalline form of silicon dioxide, occurring, in some parts of the world, in large single crystals from which mechanical resonators of useful dimensions can readily be formed. The physical properties that make it eminently suitable for use in a standard of rate or time are its great mechanical and chemical stability. Having a hardness nearly equal to that of ruby and sapphire, and a rigidity of structure such that it cannot be deformed beyond its elastic limit without fracture, it might be expected to remain in a given shape indefinitely under ordinary conditions of use. Because of its great chemical stability, its composition is not easily modified by any ordinary environment.

In addition to its inherent physical and chemical stability, the elastic hysteresis in quartz is extremely small. For this reason, it requires only a very small amount of energy to sustain oscillation and the period is only very slightly affected by variable external conditions in the means for driving it.

A striking illustration of the importance of this property is indicated by the number of periods that a resonant element will execute freely, that is, without any sustaining forces whatever, during the time required for the amplitude to decrease to one-half of some prescribed value. For a good electrical circuit consisting of an air core inductance and an air condenser, this number is about 100; for a good tuning fork in vacuum, it is about 2000. For a good cavity resonator under standard conditions of temperature and pressure, the number may be as high as 10,000. The best gravity pendulums will swing freely from 2,000 to 20,000 times before they reach half amplitude. The effect is most striking of all in quartz crystal, in which the internal losses are extremely low. Professor Van Dyke has measured the rate of decay of oscillations under a wide range of conditions45 and has found that, as ordinarily mounted, nearly all of the losses are in the mounting or in the surrounding atmosphere, if any, or in surface effects. Extremely small amounts of surface contamination will more than double the decrement. Recently46 Maynard Waltz and K. S. Van Dyke have measured the decrement of one out of the first set of four zero coefficient ring crystals ever made47 and found that, vibrating freely in vacuum and favorably mounted, it would execute more than a million vibrations before falling to half amplitude.

The advantage of this property is immediately obvious because of the relatively small amount of energy that must be supplied at each oscillation to keep the resonator in motion. As already discussed in relation to the pendulum, the amount that the rate of oscillation may be disturbed in a given structure is proportional to this energy and, to first order, on the departure from the ideal phase condition of the applied driving force.

The properties just enumerated are sufficient to assure the superiority of quartz crystal for the control element in a rate standard; no other vibrating system known at the present time is so sharply resonant or so stable. However, one more property, its piezoelectric activity, has added greatly to the convenience of its use in vacuum tube devices.

The piezoelectric effect was discovered by the Curie brothers in 1880,48and in the years following was studied extensively by them49,50. They found that when quartz and certain other crystals are stressed, an electric potential is induced in nearby conductors and, conversely, that when such crystals are placed in an electric field, they are deformed a small amount proportional to the strength and polarity of that field. The first of these effects is known as the direct piezoelectric effect and the latter as the inverse effect. The amount of such deformation in quartz is extremely minute, a static potential gradient of 1 esu (300 volts) per centimeter causing a maximum extension or contraction, depending on the polarity, of only 6.8 X 10^-8 cm per cm. If a crystal resonator is subjected to an alternating electric field having the frequency for which the crystal is resonant, the amplitude of motion will, of course, be multiplied many times. In practice, however, the actual amplitudes of motion are kept so small, by limiting the applied electric field that even with the largest crystals used they can be observed only under a high powered microscope. This, in conjunction with means for precise amplitude control, is one of the reasons for the remarkable frequency stability of quartz crystal oscillators.

In practice, a quartz resonator is mounted between conducting electrodes which now most often consist of thin metallic coatings deposited on the surface of the crystal by evaporation, chemical deposition or other suitable means. Electrical connection is made to these coatings through leads which also support the crystal mechanically. The resonators with which we are chiefly concerned in this discussion have only two electrodes.

If such a two-terminal resonator is connected into any circuit, it will behave there as though it consisted of wholly electrical circuit elements, usually of such low loss as can not be realized by other means. The equivalent electric circuit for a quartz crystal resonator was first described51 by K. S. Van Dyke in 1925 and, for some significant cases, is illustrated in Fig. 7. The part of such an equivalent circuit which in many cases cannot be duplicated by any ordinary means is the inductance element containing so little resistance. It is as though an electric resonator could be made and utilized constructed of some supra-conducting material.

Fig. 7.--Equivalent electrical circuits for typical quartz crystal resonators.

Among the first serious efforts to utilize the piezoelectric effect in electrical circuits were those of Alexander McLean Nicolson who used rochelle salt crystal in the construction of devices for the conversion of electrical energy into sound and vice versa. He constructed loudspeakers and microphones during several years of study prior to the publication of his work52 in 1919 - ideas now being used extensively in phonograph pickups, microphones and sound producers. Nicolson also was the first to use a piezo-active crystal to control the frequency of an oscillator. His patent53, applied for in 1918, shows a circuit which he operated successfully in 1917. The first actual use of resonators of quartz is attributed to P. Langevin54,55, who drove large crystals in resonance in order to generate high-frequency sound waves in water for submarine signaling and depth sounding.

The Quartz Crystal Controlled Oscillator

The first comprehensive study of the use of quartz crystal resonators to control the frequency of vacuum tube oscillators was made by Walter G. Cady in 1921 and published by him in April, 192256. This was the step which initiated a most extensive and intensive research of the properties of quartz crystal and into methods for its use in numerous fields requiring a stable frequency characteristic.

The extent and importance of this research are well indicated by the number of investigators and published contributions of the art. Among these, a paper by A. Scheibe57 in 1926 lists 28 articles on the subject, along with a description of his own extensive studies. Two years later Cady published a bibliography58 on the subject, including 229 separate references to papers and books and 84 patents in various countries. R. Bechmann in 1936 published a review of the quartz oscillator59 including 26 references to other original contributions in that field alone. More recently there comes at the end of Cady's 1946 book60 on "Piezoelectricity", a bibliography of 57 books and 602 separate published articles on this subject. By any measure this represents a great amount of detailed effort for a single subject in so short a time—just about a quarter of a century. Of this great amount of material, it is feasible to review only a small number of the outstanding ideas relative to the evolution of the quartz crystal clock.

The first published quartz-controlled oscillator circuit is reproduced in Fig. 8A from Cady's 1922 article. In this oscillator the "direct" and "inverse" piezoelectric effects were employed separately, making use of two separate pairs of electrodes. The output of a three-stage amplifier was used to drive a rod-shaped crystal at its natural frequency through one pair of electrodes making use of the "inverse" effect, while the input to the amplifier was provided through the "direct" effect from the other pair. The feedback to sustain oscillations in the electrical circuit could be obtained only through the vibration of the quartz rod and hence was precisely controlled by it. Cady’s results were received with widespread interest and were duplicated and continued in many laboratories, which soon resulted in many new discoveries and inventions.

Fig. 8--Typical quartz oscillator circuits.

Important contributions were made by G. W. Pierce, who, showed in the following year that plates of quartz cut in a certain way could be made to vibrate so as to control frequencies proportional to their thickness61. He also proposed somewhat simplified circuits for their use which soon found very general application in the construction of wavemeter standards and later for oscillators used to control the frequency of broadcasting stations and for many other purposes. In 1924, the General Radio Company of Cambridge, Massachusetts, produced a commercial instrument based on these studies.

The significance of the unusually stable properties of quartz crystal — which at times were viewed with a sort of awe and a tendency at first to expect too much62^*__was soon recognized in relation to precise standards of frequency and time, and many laboratories made experiments directed toward these applications.

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*In 1929, M.G. Siadbei wrote "Nous pensons que le quartz piécoélectrique peut trouver un nouvel emploi dans la chronometrie, étant donnée la conservation rigoureusement constant de ses oscillations."

"La seul cause de variation de la période d’oscillation résulte en effect du changement de la temperature..’

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For some years these efforts usually took one of two forms: either that of a quartz-controlled oscillator used as a comparison standard by various means63, or that of using the quartz resonator itself as a portable standard, the high-frequency counterpart of an isolated tuning fork. Probably the most convenient standards of the latter sort were the luminous resonators first described in 1925 by Giebe and Scheibe64. The following year they proposed the use of such luminous resonators as frequency standards65 and, shortly following, portable frequency indicators of this sort were made available for general use. The use of such a luminous resonator for the international comparison of frequency standards was reported by S. Jimbo, in 1930.66 The first international comparison of frequency standards making use of piezo resonators as isolated standards was carried out by Walter G. Cady in 1923, who by means of a set of early type resonators compared the existing standards at Rome, Livorno, Paris, Teddington, Farnborough, Washington, and Cruft Laboratory at Harvard University67. In the following year the U. S. Bureau of Standards carried out a similar international frequency comparison, but of greater accuracy, employing portable quartz crystal oscillators. This comparison and other important related studies were described by J. H. Dellinger in 1928—"The Status of Frequency Standardization"68.

It was soon recognized that quartz oscillators could be built with a stability far greater than that of any other known type and that they possess qualities very desirable for a combined time and frequency standard. However, all early quartz oscillators had frequencies far too high to operate any synchronous motor and it was not immediately obvious how a clock could be operated thereby.

The Frequency Divider

The illustration in Fig. 9 from the author's notebook for November, 1924 is believed to be among the earliest means proposed to accomplish this. In brief, the proposal was to control the speed of a motor driving a high-frequency generator so that a harmonic of the generator output, say the tenth, would have a frequency of the same order as that of the crystal but differing from it by a relatively low frequency, f₁. This low frequency, derived from the modulator was to be used to drive the synchronous motor.

Fig. 9—Early suggestion of means to control a rotating device such as a clock from a high frequency.

The shaft speed of the motor-generator would, therefore, be integrally related to the crystal frequency and hence any mechanism geared to the shaft, such as a clock, would indicate time as dictated by the crystal. This method could have been carried through readily by a combination of means already developed for other purposes, and the construction of an apparatus based on this suggestion was soon begun. However a simpler method69, not involving a rotating machine in the control system, was suggested and the first quartz crystal clock was constructed using the simpler means. This apparatus was described by Horton and Marrison70 before the International Union of Scientific Radio Telegraphy in October, 1927: The resonator in its mounting that was used in this first model is shown in Fig. 10. It consisted of a rectangular block of crystal, cut in the manner usually called X-cut, and of such size as to oscillate at a frequency of 50,000 cycles per second in the direction of its length. The temperature coefficient of this resonator was approximately 4 parts in a million per degree C at the temperature of operation, which was controlled at a value in the neighborhood of 40 degrees C.

Fig. 10--50,000-Cycle quartz resonator, in original mounting, used in first quartz clock--1927.

The method for frequency subdivision used in this first quartz crystal clock is illustrated in Fig. 11. The inductance element of an electric circuit oscillator, designed to operate at the desired low frequency, has a core of variable permeability so that the frequency can be adjusted over a narrow range through the control of direct current in an auxiliary winding. A harmonic of this low frequency, generated in the tube following the oscillator, is compared with the incoming high frequency in the vacuum tube modulator. The harmonic chosen has nominally the same frequency as that of the control, or crystal oscillator, so that one output of the modulator is a direct current whose magnitude and sign vary with the phase relation between the inputs to the modulator. The use of this method to regulate the low-frequency oscillator insures that the low frequency is some exact simple fraction of the high frequency. If, therefore, a synchronous motor is operated from the low frequency thus produced, its rate represents accurately that of the high-frequency source as though it had been possible to use that source directly.

Fig. 11—Submultiple controlled frequency generator used in first quartz clock

Several other electrical circuits were proposed around 1927 for the subdivision of high frequencies. The method in most general use at present is an adaptation of the "multivibrator" first used by Henri Abraham and Eugene Block in 1919 for the measurement of high frequencies71. They used their circuit to produce a wave rich in harmonics and having a fundamental that could be compared directly with that of a tuning fork standard. By various means now well known the high frequency could be compared with one of the harmonics of this special oscillator.

This procedure was reversed by Hull and Clapp72, who discovered that the fundamental frequency could be controlled by coupling the high-frequency source directly into the circuit of the multivibrator. This, in fact, is a general property of any oscillator in which the operating cycle involves a non-linear current-voltage characteristic, being most pronounced in those of the relaxation type. Van der Pol and Van der Mark in 1927 reported on some experiments on "frequency demultiplication" using gas tube relaxation oscillators73. The multivibrator is, in effect, a relatively stable relaxation oscillator74, and with slight modification has been used extensively as the frequency-reducing element in quartz-controlled time and frequency standards throughout the world.

One serious difficulty with the multivibrator type of submultiple generator has been that, if the input fails or falls below a critical level, it will continue to deliver an output which, of course, will not hen have the expected frequency. Certain variables in the circuit, such as tube aging, may cause a similar result. With this in view, a general method for frequency conversion has been developed by R. L. Miller75, in which the existence of an output depends directly on the presence of the control input. The basic, idea involved in this, now known as regenerative modulation, was anticipated by J. W. Horton in 191976 but had not been developed prior to Miller's investigations. The circuit of a regenerative modulator in its simplest form as a frequency divider of ratio "two" is shown in Fig. 12.

Fig. 12--Frequency divider for ratio TWO employing regenerative modulation.

Soon after the announcement in 1927 of the first quartz crystal controlled clock,⁷⁰ the idea was studied and applied in many places notably in America and Germany, and at the present time it forms the basis for precise measurements of time and frequency in many government physical laboratories as well as in many astronomical observatories and industrial and university laboratories throughout the world.

Although the first results were quite satisfying, it was the immediate interest of all concerned to find out what improvements could be made, and these were not long in coming. As in the case of the pendulum already discussed, or with any other oscillator, the constancy of rate obtainable depends on two kinds of properties: those which concern the inherent stability of the governing device itself, and those concerned with the means for sustaining it in oscillation. Some of the factors in the two groups are interrelated and must be considered together.

The improvements in quartz oscillator stability therefore have been concerned with two main endeavors, namely that of cutting and mounting the resonator so as to realize effectively the unusually stable properties of quartz crystal itself, and that of coupling it to the electrical circuit in such a way as to avoid the effects of such variables as power voltage variation, aging of vacuum tubes, and the like, on the controlled frequency. The latter effects were not obvious at first because the temperature coefficient and the effects of friction and change of position in the mounting caused variations of considerably larger magnitude. It was natural, then, to see what could be done about these effects.

Zero Temperature Coefficient of Frequency

With the knowledge that X-cut resonators had negative coefficients, frequently as large as thirty parts in a million per degree C, and that Y-cut resonators in general had positive coefficients, often in excess of a hundred parts in a million per degree, the author undertook to make resonators of such shape that the oscillations would occur in both modes simultaneously, and so combine the coefficients, in the hope that the resultant could be made zero.77

The first experiments, made on two series of resonators both yielded encouraging results. The first was a series of rectangular X-cut plates of varying thickness shown in Fig. 13. The second was a series of three circular discs of different diameters, all being cut with the large surfaces in the plane of the Y and Z axes. The three discs were made from the same material, each smaller one being trepanned from the previous one after complete measurements had been made upon it. The set of circular crystals remaining after these tests were completed is shown in Fig. 14 and the slab from which they were cut is shown assembled with the original large crystal in Fig. 15.

Fig. 13--Set of rectangular quartz resonators made for zero temperature coefficient study.

Fig. 14--Circular pieces remaining after temperature coefficient study of quartz discs and rings.

Fig. 15--Large crystal and slab from which low coefficient studies were made.

Subsequent tests showed that the annular pieces could be designed for a low or zero coefficient and such a shape shown in Fig. 16 was employed for a number of years in the Bell System Frequency Standard in New York City78. As described in this reference, the reason for using the ring in preference to the solid disc or rectangular plate was in the convenience of mounting. The rings were formed with a ridge in the central plane of the hole so that they could be supported on a horizontal pin thus providing a one-point support at a position where the vibration is very small. The rings used in this first application of zero coefficient quartz resonators have been called "doughnut" crystals for obvious reasons. In Fig. 17, George Hecht is shown making a final adjustment, by "lapping" with fine abrasive, on one of the four original zero-coefficient ring crystals. Mr. Hecht made all four of these resonators, as well as many others of various shapes and sizes used in the early experiments in this work.

Fig. 16--100-Kilocycle quartz ring resonator with zero temperature coefficient.

Fig. 17--George Hecht finishing the first set of zero-coefficient quartz rings.

Supported as described, the rings hang in a vertical plane and, as first used, they were supported freely between solid electrodes rather closely spaced to the flat surfaces. The small amount of free motion relative to the electrodes, inherent in this sort of mounting, caused occasional changes in frequency if the support were disturbed, which at times would be as large as one part in ten million. To avoid this difficulty, other ring crystals were constructed with a sort of narrow shelf at the central plane that could be mounted in a horizontal plane on pin supports. The two methods of supporting the ring resonators are illustrated in Fig. 18. Such resonators were used in the Bell System Frequency Standard until 1937 when they were replaced by an entirely different type that will be described later.

Fig. 18--Methods of mounting quartz ring resonators.

The rings were adjusted to oscillate at 100,000 vibrations per second, the frequency which has been adopted in nearly all oscillators of extremely constant rate. All of these rings were constructed to have a zero frequency temperature coefficient at a temperature in the neighborhood of 40 degrees C, the frequency being a maximum at that point on an approximately parabolic characteristic. The zero temperature coefficient makes it possible to practically eliminate frequency changes caused by ambient temperature changes since, by relatively simple means, it is possible to control the resonator within ± 0.01 degree C, at the temperature for which the effect is substantially nil. The reduction of the effect of temperature, and the stabilization of the mounting, increased the stability of frequency control and oscillator-clock rate beyond anything that had ever been obtained before. Subsequent improvements that will be described later produced even greater stability.

The Crystal Clock

The striking stability of the crystal oscillator clock led the author to propose the general use of this type of clock for precision timekeeping, the chief emphasis having been previously on the derivation of constant frequency. A paper entitled "The Crystal Clock,"79 presented before the National Academy of Sciences in April, 1930, described such a clock and pointed out some of its properties and likely uses.

Chief among these properties, of course, is its inherent stability and relative freedom from extraneous effects. The quartz crystal clock is not dependent on gravity and, without any compensating adjustment, will operate at the same rate in any latitude and at any altitude. This property already has been useful in the measurement of gravity and gravity gradient by measuring the rates of pendulums on land and at sea.80,81

The crystal clock is practically immune to variations in level and shock and can be used as, an instrument of precision under conditions entirely unsuitable to pendulum clocks. For this reason it performs satisfactorily in practically any location, including earthquake zones, and may be used in transit as in a submarine, in an airplane or on the railroad.

Some of the outstanding properties of the quartz oscillator clock were discussed in 1932 by A. L. Loomis and W. A. Marrison82, in relation to a series of experiments comparing the performance of quartz clocks at Bell Telephone Laboratories in New York and a set of synchronome free-pendulum clocks operating in the Loomis Laboratory in Tuxedo Park, about fifty miles away. The comparison was effected through a circuit maintained between the two laboratories over which a 1,000-cycle current controlled by a crystal in New York was used to drive the Loomis Chronograph83 in Tuxedo Park. During part of the time, signals from the clocks were sent back over the same circuit and recorded on the Bell Laboratories' Spark Chronograph84.

The quartz oscillator assembly at the Bell Telephone Laboratories at the time of these experiments is shown in Fig. 19. The four ring crystals in their individual temperature-controlled 'ovens' are mounted under hermetically sealed bell jars to avoid the effects of ambient temperature and atmospheric pressure changes. The vacuum tube oscillator circuits are immediately below the bell jars; and the control, monitoring and power supply equipment in the remainder of the space.

Fig. 19 - Bell System Frequency Standard, 1930.

One of the most interesting results of these cooperative experiments was the measurement of a periodic variation in the rate of the pendulum clocks in phase with the lunar daily cycle. The amount of this daily variation is very small, being only a few tenths of a millisecond, but readily observable in comparison with a stable rate standard that does not vary with gravity.

Further Refinements in Quartz Clocks

The spectacular results from the use of the quartz crystal clock up to this time, about 1932, were due in part to its novelty and in part to the fact that it is quite independent of some of the variable factors that affect conventional precision clocks, including gravity itself upon which the rate of all pendulum clocks depends. The remarkable stability of present day quartz oscillators and clocks is the result of a series of developments and refinements extending over a number of years.

As mentioned previously, the factors that cause departure from constant rate in the completed operating device fall into two distinct classes, namely those which concern the inherent or natural frequency of the resonator itself, and those which concern the means for driving it at that inherent rate.

The first class comprises all those properties of the mounted resonator which tend to relate its inherent rate to ambient conditions such as temperature, atmospheric pressure, change of position and vibration, and to the passage of time—that is, aging. Since the final stability cannot exceed the inherent stability of the mounted resonator itself, its study is of prime importance.

The second class comprises properties of the means for sustaining oscillations in such a resonator which relate the resulting actual rate to variations in the electrical circuits, in the power voltages, in vacuum tubes and other like effects. In the limit, it is the hope that the net result of all such effects can be eliminated so that the stability of the quartz crystal alone will remain the sole governing factor. This is the goal, and the inherent stability of the substance, quartz crystal, is the limit toward which the stability of the quartz crystal clock will approach but cannot exceed.

The development of the quartz resonator and its mounting for numerous applications is described in some detail by Raymond A. Heising and his collaborators85 in their recent book, "Quartz Crystals for Electrical Circuits". Of all the types of resonator described in this work the one having the most extensive use at the present time, for quartz clock installations and for other applications of comparable accuracy, is the GT crystal resonator developed by W. P. Mason86. This resonator is cut from quartz crystal in such a way that the positive and negative coefficients are effectively neutralized over a range of about 100 degrees C, so that in any part of this range the resulting temperature coefficient of frequency is not more than one part in a million per degree C. With suitable precautions in manufacture, the tangent at the point of inflection in the frequency-temperature curve may be made horizontal, which means that the temperature coefficient may be made substantially zero over a considerable range of temperature.

The GT crystal resonator therefore introduces two significant advantages in timekeeping, namely that greater accuracy of rate may be obtained with a given accuracy of temperature control arid that the value at which the temperature is controlled may be chosen in a considerable range. In fact, without any temperature control at all, the rate of a clock regulated by such a crystal may be accurate to a tenth of a second a day over an ambient range of 100 degrees C. Among the many quartz clock installations now using the GT resonator; all or in part, are the Royal Observatory at Greenwich, the British Post Office, the U. S. Naval Observatory and the U.S. Bureau of Standards.

One of the chief sources of variation in rate of quartz oscillators, in the early stages of their development, was in the means for mounting and in the electrical circuit connections. As mentioned previously any variation in the effective resistance or in the effective mass or stiffness of a resonator has a direct effect upon its rate of oscillation. The problem reduces to that of supporting the resonator so that the frictional losses are small and constant and so that the coupling to the electrical circuit is as nearly as possible invariable.

The mounting of quartz crystal units is discussed at length by R. M. C. Greenidge in Chapter XIII of Mr. Heising's book referred to above.⁸⁵ The most satisfactory means by far that has been found for mounting crystals of the GT type is that of actually soldering them to thin supporting wires by means of small discs of silver deposited on the crystal at its nodes. This method serves the double role of supporting the crystal and of providing electrical connection to metal electrodes plated on the crystal. Resonators so supported may be made almost immune to mechanical shock and will continue in satisfactory operation through accelerations of several times . Nearly all crystals which vibrate in a long dimension are now mounted in this way. One manufacturer produced about 10,000,000 crystals of a single type so mounted in a three-year period during World War II. Prior to the use of wire supports, such crystals were "pressure mounted" by means of small metal jaws which clamped from opposite sides at the nodes. A GT crystal mounted in this way is shown in Fig. 20. Crystals so mounted are still in use in the Bell System Frequency Standard, being the first of the GT crystals to go into actual service. This type of mounting is not quite so stable as the wire mounting and is somewhat more difficult to manufacture. One of the wire-mounted crystals such as developed for LORAN and other Oscillators of comparable accuracy is shown in Fig. 21.

Fig. 20—Pressure-mounted GT crystal for sealing in a metal envelope.

Fig. 21—Wire-supported GT crystal sealed in a glass envelope.

Fig. 22—Frequency-temperature characteristics for three types of quartz resonators.

The plating of electrodes on the crystal surface has led to increased stability of frequency control, chiefly because the coupling to the electrical circuit may be kept more nearly constant thereby. When separate electrodes were employed, the variation in spacing was always found to be a source of instability, as mentioned previously in relation to the use of the first ring crystals. Plating of crystals is not a new idea but the application to quartz resonators of high Q requires a great amount of technical skill in order to obtain coatings which are mechanically and chemically stable and which utilize the minimum of added material. The use of too much metal will, of course, impair the resonator by increasing its rate of energy dissipation and probably its aging rate. The metal most often used for electrodes is silver, although gold and aluminum have been used in special cases. Evaporation in vacuum has been found to be the most satisfactory method for the actual plating, giving very adherent coatings and being subject to precise manufacturing control. The art of plating quartz resonators is discussed in detail by H. W. Weinhart and H. G. Wehe in Mr. Heising's book.

Several other factors have had an important bearing on the final stability of quartz resonators. One of the most important of these is the care that must be exercised during fabrication in order to avoid setting up stresses in the material that subsequently can be relieved only slowly. By slow grinding with adequately fine abrasive such effects can be kept very small. Etching with hydrofluoric acid has resulted in much further improve melt through the removal of stressed surface material and all potentially loose material which, formerly, often caused anomalous aging effects. Artificial aging by heating, and thorough cleaning before and after plating, have also contributed greatly to the final stability of the crystal unit. The resonator finally is mounted in high vacuum in a glass envelope in order to eliminate losses due to sound radiation and friction, and to protect it from surface contamination and chemical action.

Even the most perfect quartz resonator, in an ideal mounting, is unable to keep time unless it is maintained in oscillation; and, like a pendulum, its rate will depend in large part on the manner in which it is driven. The same general principles apply to both cases, except that usually a pendulum is driven by impulses which should be applied when the velocity is maximum, while a quartz resonator is usually driven by a sinusoidal force arising through the piezoelectric coupling, and so phased that the maximum force occurs when the velocity is maximum. This, in fact, is a required condition for maximum rate stability. The graphical analysis of Fig. 5 applies equally for the case of sine wave drive, since the sine wave can be considered as the summation of an impulse at its peak and of sets of pairs of impulses symmetrically disposed with respect to it. Obviously, the phase errors for each such pair of impulses cancel, bringing us back to Airy's condition, but with the broader view that, for the feedback or driving wave to have minimum effect on the rate of an oscillator, the force wave must be in phase with the velocity of the resonator.

Numerous vacuum tube circuits have been proposed and used for maintaining quartz resonators in oscillation, some of which are illustrated in Fig. 8. The one among these which at present most nearly approaches the ideal is that developed by L. A. Meacham, known as the Bridge Stabilized Oscillator.87 This oscillator, in its original form or with slight modifications, is now used almost universally in England and America where the maximum stability of rate control is required.

In the bridge stabilized oscillator, the feedback path is through a Wheatstone bridge with the crystal in one arm and with resistances in the other three. The frequency of oscillation becomes that for which the reactance of the crystal approaches zero; the bridge can only be balanced when the crystal behaves electrically like a resistance. The unbalance voltage from the bridge is fed back into the amplifier, which should provide a relatively high gain, as will appear. The great frequency stability of this oscillator depends upon the fact that, in the neighborhood of balance, a small phase shift in the resonant elements causes an enormously larger phase shift in the unbalance voltage. But the actual amount of this unbalance phase shift is limited by the fact that it must be equal and opposite to that in the amplifier in order for oscillations to be sustained. This insures that at all times the phase shift in the crystal is much smaller than that occurring in the amplifier which itself can be made small by suitable design. The ratio of the phase shift of the bridge output to that of its input increases as balance is approached, making it possible to practically eliminate the effect of phase shift in the amplifier simply by increasing the amplifier gain. Most of the variable factors in the amplifier of an oscillator circuit affect the controlled frequency through the phase shifts caused by them. It is evident, then, that the bridge circuit, which permits only a small fraction of such phase shifts to become effective at the resonant element, will substantially free the resonator from variable effects in the amplifier and allow it to control a rate determined almost wholly by its own properties.

When the above condition is attained and the crystal resonator, when oscillating, acts in the circuit like an electrical resistance, it acts that way because the velocity is in phase with the applied mechanical force, which, as has been stated, is the condition for most stable rate control. In the crystal oscillator, this ideal condition is obtained simply by the automatic balancing of a bridge circuit, accomplishing in a most elegant manner the equivalent, in the case of a pendulum, of applying driving pulses at the exact center of swing.

The bridge-stabilized oscillator includes also an automatic control of amplitude. The variation of frequency with amplitude is very small and in no way comparable with the "circular error" of an ordinary pendulum, but in the quest for the highest attainable stability it must be taken into account.

The control of amplitude is obtained by the use of a resistance with positive temperature coefficient in the bridge arm conjugate to the crystal, chosen so as to have exactly the right value to balance the resistance of the crystal when a specified current is flowing in the bridge. If larger than normal current flows momentarily the resistance is increased, which decreases the feedback, thus stabilizing the amplitude at some predetermined value. For the highest stability it has been found advantageous to operate the crystal at a very small fraction of the amplitude that normally would be used in a power oscillator. In power oscillators the crystal sometimes is subjected to strains near .the fracture point, which is not a favorable condition for precision control. The actual amplitude of motion of the crystal is of course extremely small. In the GT crystal, as currently used, the maximum change of dimensions during oscillation amounts to only about +0.0006 per cent.

The improvements in quartz resonators, and in their driving circuits, have resulted in the construction of quartz crystal clocks that will keep time with an accuracy better than 0.001 second a day, so that measurements of time of great interest and value to astronomers and geophysicists can now be made with an accuracy hitherto unattainable.

Facility of Precise Time Measurement

In making such precise measurements of time it is of importance, second only to the inherent accuracy of the standards themselves, to have available means whereby they can be carried out with facility and within a reasonable time interval. The ease with which precise time measurements, and precise rate comparisons, can be made is an outstanding feature of the quartz crystal clock and already has an important bearing on the use of this type of clock in astronomical observatories. This facility depends chiefly on two properties of the oscillator clock: first, that continuous rotation of controlling and measuring devices can be produced having the stability of the primary control element; and, second, that the period of the control element, and therefore of alternating current controlled by it, is of very short duration.

The first of these, through simple devices controlled directly from the electrical output of the crystal oscillator, with suitable frequency reducing equipment, permits of ready comparison between any time phenomena in the form of electric or light signals, and of the derivation of precisely controlled time signals for radio transmission and for laboratory experiments.

Of prime importance among these comes the means for rating crystal clocks in terms of stellar observations using meridian transits or the photographic zenith tube88. It is possible to control a mechanism in the time-star observing equipment so that the difference between a star position predicted from the clock rate, and the actual star position, can be observed directly or recorded photographically with great accuracy. The difference thus observed, after allowing as well as possible for known systematic errors, is the best known single check on the time indication of a clock. A series of such observations constitutes the best known measure of the rate of a clock. The great value of the method is that the comparisons are made directly without the need of any intermediate mechanism thus eliminating a large part of the "personal error" of observation. The probable error of observation as derived from a number of such measurements on a good night may be as small as one or two milliseconds89. The average rate of a clock thus determined depends on the number of days over which the rate is computed and in a two-week period may be compared with the rate of the earth, that is, with astronomical time, with an accuracy of one part in one hundred million or about a third of a second a year. All this, of course, is contingent on the stability of the quartz clock, which, except for long-time effects, may be demonstrated independently.

A rotating mechanism controlled directly from a crystal clock is admirably adaptable to the transmission of precise time signals. Rhythmic signals of any desired structure can be produced readily by means of cams, special generators, or interrupted light beams, and the timing of those signals can be adjusted as precisely as the clock time is known by simply advancing or retarding the signal generators. Such adjustment is attained readily by means of differential gearing in the mechanical system, or by means of continuous phase shifters in the electrical driving circuit. The use of electrical phase shifters for this purpose was first proposed in "The Crystal Clock" paper⁷⁹ previously mentioned. Figure 23, taken from that paper, illustrates the manner of using the phase shifter with one type of time signal generator. Extremely fine control of timing is possible by rneans of the electrical phase shifter since it can he included in the circuit at any stage of frequency subdivision. If, for example, it is used at the lowest frequency, assumed to be 1,000 cycles, one complete turn of the phase shifter dial will cause a progressive time adjustment of one millisecond. When used at a higher frequency, the precision of adjustment is increased correspondingly. Continuous phase shifters suitable for such purposes were proposed as early as 1925.90The idea of utilizing continuous phase shifters for the purpose of making controllable changes in the frequency or indicated time in a standard time and frequency system91 was first disclosed in a comprehensive patent filed in 1934 and issued to Warren A. Marrison in 1937. The most elegant type of phase shifting element suitable for such purposes was developed by Larned A. Meacham.92 This has been used in many transmission systems requiring continuous variation of phase such as in variable direction radio beam systems93 and LORAN.

Fig. 23--The use of an electrical phase shifter to adjust the timing of a signal. (From "The Crystal Clock", 1930)

The conversion between mean solar time and sidereal time, or for that matter between any time systems, may be accomplished very easily with the quartz clock. Having a rotating device, such as a dial or commutator, whose rate corresponds to mean solar time, it is only necessary to apply a gearing or the equivalent to obtain another rate corresponding to sidereal time. It has been shown by F. Hope-Jones94, Ernest Esclangon95 and others how any desired ratio, such as the ratio of the rates of mean solar and sidereal clocks, can be obtained with any required accuracy by gearing. A combined mechanical and electrical method was proposed in the "Crystal Clock" paper by means of which this ratio can be realized with an accuracy of one part in 10¹¹ using simple gearing and a continuous phase shifter.

The potential value of the factors just (discussed in precision time studies was realized early in the crystal clock development. This was indicated in the "Crystal Clock" paper written in 1930 which closed with the following paragraph:

"It would thus be possible to combine, in a single system mean solar and sidereal time indicating mechanisms, means for rating the clocks in terms of time star observations and means for transmitting time and frequency signals with the absolute accuracy of the time determinations."

It is of some interest to compare this predication with the present trend of development. In describing the quartz clock installation in the Royal Observatory in Greenwich, Sir Harold Spencer Jones stated89in 1945:

"The quartz clocks being installed at the Royal Observatory are all adjusted to give a frequency of approximately 100,000 per mean time second. By suitable gearing, the synchronous motor can give impulses every sidereal second and tenths of a second. Thus, the same clock can be made to serve both as a mean time and as a sidereal time standard. All time signals are, of course, sent out according to mean time; the sidereal time is required only for the actual time determination so that it is not necessary for all the clocks to have the gearing to give