# The determination of precise time

This page contains the text of a lecture given by the Astronomer Royal in 1949.

THE DETERMINATION OF PRECISE TIME

Sixteenth Arthur lecture, given under the auspices of the Smithsonian Institution April 14, 1949.

By Sir Harold Spencer Jones

Astronomer Royal of Great Britain

Of the three fundamental physical units, there is an essential distinction between the unit of time and the units of mass and length. The units of mass and length are represented by material standards to which any mass or length can be related, either directly or indirectly. But the unit of time cannot be represented by any material standard. For practical purposes time can be thought of in the Newtonian sense as something which flows uniformly. The passage of time can be marked by a clock, and any simple natural phenomenon which obeys one definite law without perturbation might be used to mark off equal intervals of time and therefore to serve as a clock. The rotation of the earth provides us with a natural clock. We shall see later that it is not a perfect clock, but that it is sufficiently uniform for almost all practical purposes; it has, moreover, the great advantage of never stopping.

We can therefore define the unit of time as the period of rotation of the earth. Some reference object must be selected against which to measure the rotation. For the purposes of everyday life, time must be related to the sun, whose rising and setting gives the alternation of daytime and nighttime. The day defined by the rotation of the earth with respect to the sun is called the true solar day; it is the interval between two consecutive transits of the sun across the meridian of any place. With this unit, true solar time is obtained by dividing the true solar day into 24 hours and calling the instant of meridian passage of the sun 12 hours. The time given by a sundial is true solar time. For practical purposes, however, true solar time is not convenient; because the motion of the sun across the heavens is not uniform, the length of the solar day varies in length throughout the year. For civil purposes, therefore, a mean solar day is used, whose length is equal to the average length of the true solar days throughout the year. The time based on the mean solar day as unit is called mean solar time. The relationship between mean solar time and true solar time at some particular instant is defined by means of a convention, into the details of which I need not enter. The extreme differences between mean and true solar times range from 16½ minutes about November 3, when true noon precedes mean moon, to 14½ minutes about February 12, when true noon follows mean moon.

Astronomers, however, find it more convenient to determine time by the observation of the stars. There are many stars but only one sun and, moreover, the time of transit of a star can be determined more accurately than the time of transit of the sun. The sidereal day is defined by the rotation of the earth relative to the stars. It is about 4 minutes shorter than the solar day. If we imagine the sun and a star to be on the meridian of some particular place at the same instant, then after the lapse of one sidereal day the star will again be on the meridian; but, because of the orbital motion of the earth round the sun, the earth will have to turn a little more in order to bring the sun onto the meridian. In the course of a year the earth completes its orbit around the sun and there must consequently be exactly one more sidereal day in the year than mean solar days.

If the relative positions of a number of stars in the equatorial region of the sky have been accurately determined, we can think of them as equivalent to the graduations on the face of a clock. As the earth rotates, a telescope, fixed so as to be able to move only in the meridian, will sweep across these stars in turn, each at a definite specific instant of sidereal time. By observing the transit of stars whose positions are known, the sidereal times at the instants of meridian transit are therefore determined. The beginning of the sidereal day or, in other words, 0h. of sidereal time, is defined by the transit of the point in the sky at which the ecliptic crosses the equator from south to north; this point is called the vernal equinox or the First Point of Aries.

By defining the commencement of the sidereal day in this manner, we are provided with a means for converting from sidereal time to mean solar time, which is required for the purposes of everyday life. But it has one inconvenience. The First Point of Aries is not fixed relative to the stars. It has a slow retrograde motion, due to the precessional motion of the earth's axis, and superposed on this uniform motion is a slow to-and-fro drift, caused by the nutational or nodding motion of the axis. The nutation depends upon the relative positions and distances of the sun and moon from the earth. The principal term in the nutation has a period of about 18 years and a semi-amplitude of about 1 second of time. There is also a 6-monthly term amounting to 0.08 second and a number of short-period terms amounting to 0.020 second, of which the principal term has a period of 2 weeks. The precision of modern clocks is such that these small terms cannot be neglected. The true sidereal day, measured relative to the true position of the First Point of Aries, is therefore not absolutely uniform in length, and it is necessary to introduce the conception of mean sidereal time, measured relative to the mean position of the First Point of Aries. Actual observation of the stars provides the astronomer with true sidereal time, which he then has to correct for the nutation to obtain mean or uniform sidereal time.

The determinations of time by astronomical observations are used to control the performance of a standard clock, determining its error at a specific instant and the rate of increase or decrease of that error, the clock then being used to obtain the time at other instants. This usually involves extrapolation to some time subsequent to the latest observation. For such extrapolation to be accurate, the time determinations must not be affected by serious errors and the standard clock must be of high precision. The determination of precise time therefore involves two problems, the determination with high accuracy of the time at specific instants and the development of time-keepers of very high precision.

The sidereal time of the transit of a star across the meridian is equal to the right ascension of the star. Sidereal time can therefore be determined by observing the times of meridian transit of stars of known right ascension. The conventional method of making the observations has been to use a transit instrument. This consists of a telescope, mounted on an axis at each end of which is a cylindrical pivot. The pivots rest in fixed bearings, adjusted so that the common axis of the pivots is as nearly as possible horizontal and pointing in an east-west direction. If the axis of the pivots were exactly horizontal and in the east-west direction and if the optical and mechanical axes of the telescope coincided, the axis of the telescope would be in the meridian plane, whatever direction the telescope was pointing to. This ideal condition is never achieved and there are always small errors of level, of azimuth, and of collimation. These adjustments are liable to continual change; there are slow seasonal changes, associated with changes of temperature and possibly also with subsurface moisture; there are also more rapid changes, which are correlated with changes of circumambient temperature and with the direction of the wind. To control these changes frequent observations of level, of azimuth, and of collimation are essential, which take up a disproportionate amount of the observing time. The error of collimation can, however, be eliminated if the telescope is reversed in its bearings in the middle of each transit, half the transit being observed before reversal and the other half after reversal. It is not possible to reverse large transit instruments sufficiently quickly and it has accordingly become customary to use , which can be rapidly reversed, for the determination of time; as it is the brighter stars which are observed, a large aperture is not needed.

There are other factors which have also to be taken into consideration. The pivots will never be absolutely cylindrical; their figures have to be determined with great accuracy and appropriate corrections made to the observations. Flexure of the axis can cause troublesome systematic errors. If the horizontal axis is not equally stiff in all directions, its flexure will vary according to the direction in which the telescope is pointed. If the two halves are not equally stiff, the telescope will be twisted from the meridian by a variable amount. Personal equations between different observers are somewhat troublesome, though they do not exceed a few hundredths of a second when the so-called impersonal micrometer is used. Before its introduction, the method of observing was for the observer to press a hand-tapper at the instant the star crossed each of a number of vertical spider wires in the focal plane of the telescope; by so doing, he closed an electric circuit which sent a current to a recording chronograph, which recorded not only the signals from the telescope but also time signals, every second or alternate seconds, from the clock. The instants of the star crossing the wires could then be read off at leisure after the observations had been completed. With this method of observing, the times determined by different observers could differ by as much as half a second. The reason is easy to see; one observer might wait until he saw the star actually bisected by the wire before he pressed the tapper, with the result that, because of the time required for the message to travel from his brain to his eye and to be converted into muscular action, his signal would inevitably be late; another observer would, as it were, shoot the flying bird, gauging the rate of motion of the star so that his tap is made as nearly as possible at the instant at which the star is actually bisected. The personal equations can be determined by what are called personal equation machines; the transit of an artificial star is observed, the times at which the star is at certain positions during the transit being compared with the observed times. Although an observer will unconsciously form a fixed habit in observing so that his personal equation remains substantially constant, small variations, depending upon the physical condition of the observer, do occur.

The method of observing now almost universally employed is to have a single movable wire in the micrometer eyepiece instead of a number of fixed wires. The wire can be traveled along by the observer, who adjusts its speed so as to keep the star continually bisected by the wire. As the wire moves along, contacts are automatically made in certain positions, sending signals which are recorded on the chronograph. In order to relieve the observer of some of the strain of maintaining a uniform motion of the wire, it is now common to drive the wire mechanically at the speed appropriate to the motion of the star, using an electric motor with some form of continuously variable gearing. With this method of observing, the personal equations of different observers are very small, usually not more than two or three hundredths of a second; it is for this reason that this form of micrometer is called the “impersonal” micrometer. Small though these residual personal equations are, they remain remarkably constant and can be determined by personal equation machines. They seem to arise from two causes: there is “bisection error,” an observer systematically bisecting an image to the right or to the left of its center; this error changes sign at the zenith with instruments in which the observer changes the direction in which he faces, according to whether he is observing a north or a south star; there is also “following error,” an observer systematically setting the wire in front of or behind the center of a moving image. This error does not change sign at the zenith.

If the pivots are not exactly cylindrical, the telescope will be twisted out of the meridian by an amount varying with its position. The figures of the pivots must therefore be determined with great accuracy and appropriate corrections applied to the observed times of transit. The figures of the pivots must be determined at intervals, as they may change slowly in the course of use through wear. Other variable errors can be introduced through slight mechanical imperfections in the telescope; if there is the slightest play in the eyepiece micrometer or in the objective, errors will be introduced which will vary with the position of the telescope.

When all the possible sources of error which can affect observations with a transit instrument are borne in mind, it is rather surprising that the observations are as accurate as they are. The probable error of a single time determination is usually about two-hundredths of a second. This was quite accurate enough before the era of clocks of high precision and before there were any practical requirements for very precise time. The scatter of the observations is, however, inconveniently large for the adequate control of the performance of the modern quartz-crystal clock. For these reasons the conventional transit instrument is likely to be gradually replaced for the purpose of time determination by some other type of instrument. Several modifications of the transit instrument have been considered which eliminate or minimize some of its disadvantages. The most accurate results are given, however, by an entirely different instrument known as the photographic zenith tube. It consists of a fixed vertical telescope pointing to the zenith, which has a mercury horizon at the bottom of its tube, whose purpose is to reflect the light from a star to a focus in the plane of the second principal point of the objective. The fundamental principle of the instrument was due to Sir George Airy, who first used it for the reflex zenith tube at Greenwich: when the light is brought to a focus accurately in the plane of the second principal point of the objective, the results are unaffected by tilt of the telescope. The troublesome error of level is therefore immaterial, while any error of azimuth does not affect observations made in the zenith. The telescope is constructed so that the objective and the plate holder can be rotated through 180°, the observations being made photographically in order to eliminate personal equations and to give greater accuracy. Suppose two exposures are given on a star at times which are symmetrical about the time of meridian transit, the objective and the photographic plate being rotated through 180° between them. The two images will lie on a line exactly parallel to the meridian. If, however, the two times of exposure are not exactly symmetrical, the images will be slightly staggered; by measuring the staggering and knowing the clock times of the two exposures, the clock time of meridian transit can be inferred.

In practice an exposure of finite length is required to give a measurable image on the plate. During this exposure the plate holder is traveled along at the speed appropriate to the motion of the star, signals being sent to the chronograph at certain definite positions of the plate holder. After reversal the plate carriage retraces its path, and signals are sent during the course of the second exposure at the same positions.

With this design of instrument, collimation error does not enter, there are no pivot errors to be considered, and the various sources of error inherent in a movable instrument are avoided. At the Naval Observatory, Washington, a photographic zenith tube, designed and used by F. E. Ross originally for the determination of the variations of latitude, has been used for some years for the determination of time. An instrument on the same general principle, but differing materially in details of design, is in an advanced stage of construction for the Royal Greenwich Observatory. The errors of time determination should not exceed 2 or 3 milliseconds, which will permit a tight control of the performance of the observatory clocks.

For the purpose of time determination it is necessary to assume positions for the stars which are observed. These positions will have random errors, whose effects can be reduced by observing sufficient stars. But they may also be affected by systematic errors; if, for instance, the errors vary with right ascension they will introduce a spurious systematic variation in the derived clock error through the year. For the purpose of time determinations and in order that the times determined at different observatories can be directly compared, there is an international agreement to use the positions of the stars given in the fundamental star catalog known as the FK3. These are bright stars, whereas with the photographic zenith tube, inasmuch as observations are restricted to a narrow belt at the zenith, it is necessary to use fainter stars. Their positions must therefore be determined by transit circle observations and tied on to the FK3 system. The photographic observations will in course of time provide some measure of control over the periodic errors in right ascension of the FK3 system itself.

Until about 25 years ago, pendulum clocks of the regulator type were used as the standard clocks in observatories. A considerable improvement in precision was brought about by the invention of the free-pendulum clock. In an ordinary pendulum clock the timekeeping is impaired by the variable friction involved in driving a train of wheels to move the hands and record the actual time on a dial. An appreciably higher accuracy is to be expected if the pendulum is allowed to swing freely, except when it receives periodically impulses to maintain its swing, and is thereby relieved from all extraneous work. To achieve this had been the aim of horologists for many years, but although many attempts were made it was not really successfully accomplished until the invention by W. H. Shortt of his free-pendulum clock. The master pendulum is enclosed in an airtight case, in which the air pressure is reduced to about 1 inch of mercury and which is maintained at constant temperature and swings freely, except for small impulses, given at half-minute intervals, to maintain the amplitude at a nearly constant value. The slave clock is a normal synchronome electric clock, which is adjusted when swinging as an independent clock to lose about 6 seconds a day. The synchronizing action required from the master free pendulum is therefore a one-way action — always an accelerating action. The slave pendulum itself releases electrically the impulsing lever of the free pendulum, which falls when the free pendulum is at the midpoint of its swing. The impulse arm falls on the top of a small pivoted wheel, mounted on the free pendulum; this being a dead point, and the impulse not commencing to be given until the pendulum swings outward from the central position, the amount of the impulse does not depend upon any slight variation in the synchronization between the two pendulums which may occur.

The synchronization of the slave pendulum is effected by means of a light flexible spring carried on it. The impulse arm of the free pendulum, after it has fallen clear of the pendulum, actuates a device which closes an electric circuit and sends a current through a small electromagnet adjacent to the slave pendulum. If the slave clock has dropped sufficiently behind the master, the armature of this electromagnet will, when the electromagnet is excited, engage the bent end of the light spring on the slave pendulum. The end of the spring is then held fixed and, as the pendulum swings, the spring is flexed and the pendulum is accelerated; if, on the other hand, the slave pendulum is closely in phase with the master, the end of the spring passes under the armature before the electromagnet is excited, and nothing happens. The length and strength of the spring are so adjusted that when the synchronizing action occurs the slave pendulum is accelerated by 1/240 second. As the natural losing rate of the slave clock, 6 seconds a day, is equivalent to 1/480 second per minute, the synchronizer, which is actuated each half minute, should hit and miss alternately. For this reason it is called the "hit-and-miss" synchronizer.

The first experimental Shortt free-pendulum clock was installed at the Edinburgh Observatory in 1921. It at once proved to be such an improvement upon previous pendulum clocks that two were installed at the Greenwich Observatory in 1923 and others in subsequent years. It was the excellent performance given by these clocks that made it necessary for astronomers for the first time to introduce the conception of mean sidereal time. Previously true sidereal time had been universally used, as clocks were not good enough to be able to show up the small effects due to the short-period terms in nutation. The free-pendulum type of clock is capable of an accuracy of about one-hundredth of a second a day. Detailed investigation of their performance has shown, however, that such clocks are liable to frequent small erratic changes of rate, of the order of about 3 milliseconds a day. Small though such changes are, they cause, by integration, an irregular wandering of the clock. For sending out time signals, it is always necessary to extrapolate beyond the latest time determination; these erratic changes of rate restrict the accuracy with which the error of the clock can be extrapolated. It can, on occasion, happen that 2 weeks or more may elapse without any check on the performance of the clock being possible and the transmitted time signals may consequently be appreciably in error. Moreover, because of the errors of observation, there is a natural scatter in the derived errors of the clock. In interpolating between the observed errors there is no means of distinguishing between scatter due to errors of observation and scatter due to the irregular wandering of the clock. It is possible, of course, to attempt to reduce the effects of the wandering by using the mean of several clocks. Nevertheless, very high accuracy cannot be obtained, because residual effects due to the irregularities are always present.

A new standard of accuracy has been provided in recent years by the use of an oscillating quartz crystal, developed originally to serve as a precision standard of frequency. The quartz clock is based upon the piezoelectric property of quartz. If a plate of quartz is com- pressed, the two opposite faces become electrically charged, one positively and the other negatively. Conversely, if two opposite faces are given positive and negative charges respectively, the piece of quartz experiences a mechanical contraction or expansion. By rapidly alternating the electric charges, the quartz can be maintained in mechanical vibration. In the quartz clock an oscillating electrical circuit is used, the dimensions of the crystal being adjusted so that its natural resonance frequency is equal to the frequency of the oscillating circuit. Under these conditions a strong vibration is set up and the quartz crystal takes control and locks the frequency of the oscillating electrical circuit to its own resonance frequency. Quartz is a very stable substance and, provided it is maintained at a very uniform temperature and the drive circuit is properly designed, the frequency remains constant to a high degree of accuracy. It is usual for the crystal to be cut to give a frequency of 100,000 cycles a mean time second, the dimensions of the quartz then being conveniently small. This frequency is divided down in steps electronically, either by the use of multivibrators or by frequency subdivision until an output with a frequency of 1,000 cycles a second is obtained. The output of this frequency is used to drive a phonic motor, from which time signals can be obtained at any desired intervals.

Such clocks have many advantages over pendulum clocks. They have proved to have very high short-period stability. Their erratic changes of rate are less than half a millisecond a day, and the clocks themselves can be relied upon to about 1 millisecond a day. For extrapolating between scattered time determinations they are therefore much superior to pendulum clocks. They have, moreover, the advantage of the great flexibility inherent in dealing with 100,000 vibrations a second instead of only a single one. Electronic methods can be used for quickly and accurately determining the relative errors and rates of the clocks. For such purposes at Greenwich, decimal counter chronometers are used. This device consists of a scale-of-ten counter, and is actuated by the 100,000-cycle output per second from one of the quartz crystals. When it is switched on, it will start counting these vibrations, recording the count on five decade dials, reading, respectively, tenths, hundredths, thousandths, ten-thousandths, and hundred-thousandths of a second. To compare two quartz clocks, a seconds signal from the phonic motor driven by the one clock is used to start the count and a signal from the second clock to stop it. The time difference between the two clocks, accurate to a hundred-thousandth of a second, is thus obtained in a fraction of a second. As a check, the second clock can be used to start the count and the first clock to stop it. The difference in frequency of the two clocks is obtained by feeding the 100,000 c. p. s. outputs from the two clocks into a comparator, so that they beat against one another, and timing the beats. It is possible to obtain an accuracy of one part in 1010 in the measurement of the frequency difference.

At Greenwich, the clocks are used in groups of three, one phonic motor being provided for each group of three clocks. One of the clocks is selected to drive the phonic motor, but regular comparisons are made between each pair of clocks in the group. Automatic beat counters record the integrated time difference between each pair, A-B, B-C, C-A, the third comparison providing a check on the other two.

A further convenience of the quartz clocks is that it is not necessary to maintain separate mean-time and sidereal-time clocks as it is with pendulum clocks. By means of suitable gearing, it is possible to take sidereal seconds direct from the phonic motor which gives also mean time seconds. The ratio of the mean time second to the sidereal time second is 1.002 737 909 293. This ratio can be closely represented by a gearing of 119/114 multipled by 317/330, which is only 4 parts in 109 small. These sidereal second signals are used for recording on the chronograph during the time determinations. When the rate of the clock relative to these signals has been derived it is a simple matter to infer its rate relative to true mean time seconds. The small error in the conversion from mean time to sidereal time is, of course, eliminated.

For short-period prediction quartz clocks leave little to be desired. They have not as yet, however, reached the stage at which long-period prediction has the accuracy that is desirable. The difficulty arises from a slow drift in frequency to which they are all liable. The crystal, after cutting, appears to go through a slow ageing process; the drift in frequency is rather rapid at first, but progressively diminishes though it seems never to cease altogether. If for any reason the crystal should stop, through a tube or resistor giving out, it will not, when restarted, follow along its previous ageing curve; a new ageing cycle sets in. Any small disturbance, such as a slight temperature change, can alter the frequency drift somewhat. The effect of the frequency drift on the error of the clock increases with the square of the time so that, even though the drift may be quite small, its effects will become important with lapse of time. With the present scatter in the actual time determinations, several months' observations are needed to give a sufficiently accurate derivation of the frequency drift, but there is always the uncertainty whether during this period some small disturbance may not have caused the rate of drift to change slightly.

Moreover there are extraneous effects which can complicate the determination. During a period of several months, there will be a wide range in the right ascensions of the stars which are used for the time determinations. If there are periodic errors in the fundamental system of star places, a spurious factor will have entered into the determination of the frequency drift. The motions of the earth's poles cause further complications. The poles have an irregular motion, which is roughly circular, but with a variable radius. The extreme departures of the true poles from their mean positions are about 30 feet. The movement of the pole along the meridian causes a variation in latitude, which can be observed with a zenith telescope. The movement in the perpendicular direction causes a displacement of the meridian. The motion of the pole has two main components, with periods of a year and of about 14 months respectively. As a consequence of this motion, it would be found that if we had a perfect clock, with no rate at all, and observations which were entirely free from error, the clock would appear to have a slightly variable rate. This apparent variation of rate will affect the determination of the frequency drift and give a spurious value.

It is not possible at an observatory to measure the component of the polar motion at right angles to the meridian. At Greenwich an approximate compensation for the motion is made through the cooperation of the Naval Observatory, Washington, which sends regularly to Greenwich the observed movement of the pole along the meridian of Washington. If Washington were 90° in longitude west of Greenwich, the displacement along the meridian of Washington would also be the displacement at right angles to the meridian of Greenwich. But the longitude of Washington is only 77° west of Greenwich. However, the use of the Washington latitude-variation data does enable the greater part of the polar-motion effect to be eliminated from the Greenwich clock curves and it has been noticeable that the inferred performance of the clocks has thereby been improved.

The development of an atomic or molecular clock, in which the frequency of some selected atomic or molecular vibration will be subdivided to give a frequency closely equal to that of an oscillating quartz crystal and used to lock the vibrations of the crystal, is already foreshadowed by the work in progress at the National Bureau of Standards, Washington, in the development of an ammonia clock, in which the frequency of one particular mode of vibration of the ammonia molecule is used as the control. This work is as yet in its early stages and has not gone beyond the point of showing that the control of a quartz crystal in the way suggested is practicable. When the clock has been developed to the stage at which the accurate control of a precision quartz clock becomes possible, the crystal will be prevented from drifting in frequency. The clock error curve over a long period of time should then be represented by a straight line. Departures from a straight line could be attributed to periodic errors in the star places, to the polar motion, or to irregularities in the rate of rotation of the earth itself. Much more accurate long-term prediction would become possible, with a considerable gain in the accuracy of timekeeping.

It has been well established that the length of the day is subject to small fluctuations. It has long been known that there are discordances between the observed and the tabular positions of the moon which are not attributable to imperfections in the theory of the motion of the moon. In the development of the theory, the gravitational effects which have been neglected are far too small to amount to anything like the discordances which are observed. In more recent years it has been proved that there are similar fluctuations in the motions of Mercury, Venus, and the sun; but for these bodies the effects are much smaller than for the moon because their mean motions are much less rapid. It was the comparative smallness of the effects for these bodies which made their detection difficult. So there are, in effect, four clocks which agree together and one clock, our earth, which differs from the other four. The natural conclusion is that it is the earth which is at fault and that the length of the day, which has been adopted as the unit of time and assumed to be invariable, is actually subject to small variations.

The changes in the length of the day are found, from the analysis of the observational data, to be of two different kinds. There is a slow progressive increase in length, of the order of 1 millisecond in the length of the day in the course of a century. This progressive increase is caused by tidal friction, more particularly in the shallow sea; it acts as a brake on the earth. Though so small in amount, the effect on the mean longitudes of the moon and the planets increases with the square of the time and is large enough to make the position of the moon 20 centuries ago, if computed from its present motion in longitude, very considerably in error. The effect was actually first detected in 1679 by Halley from the early observations of eclipses. Superposed on the progressive increase of length there are also irregular changes, the day sometimes increasing in length and sometimes decreasing; these changes cannot be attributed to tidal friction, because frictional effects can cause only a slowing down and never a speeding up in the earth's rotation. These changes are due to changes in the earth's moment of inertia and could be accounted for quantitatively if the earth expanded or contracted slightly by 4 or 5 inches.

There is one essential difference between the two phenomena. A change in the moment of inertia of the earth is something that concerns the earth alone. The apparent displacements of all the other bodies are strictly proportional to their mean motions. But tidal friction is something that concerns the earth and the moon jointly; the total angular momentum of the earth-moon system is conserved, but there is interaction between the earth and the moon. The apparent displacements of Mercury, Venus, and the sun will again be proportional to their mean motions but the same will not hold for the moon; its displacement will not have the same ratio to its mean motion. It is this difference in the case of the moon which makes it possible to separate the two effects of tidal friction and of change of the moment of inertia of the earth.

Though the changes in the length of the day have been fully established by these observations, the data are not sufficiently accurate to decide whether the changes occur suddenly or whether they are spread over a few days, a few weeks, a few months, or even over a year or two. If they occur rather suddenly, they could be detected with ease by quartz clocks in their present stage of development; if spread over a few months, the larger changes could be detected, but changes of smaller amount would be likely to escape detection. Since a few years ago, when quartz clocks were adopted at Greenwich as the basis for the time service, a close watch has been kept for any evidence of a change in the earth's rotation. Once or twice small changes have been suspected but there has always been some factor which has made a definite conclusion impossible — perhaps one of the clocks has changed its rate or has stopped at the crucial time, or there has been some uncertainty in the determination of frequency drift. The evidence provided by the observations of occultations of stars by the moon is that there has been no major change in the earth's rate of rotation since about 1918. There may possibly have been small changes, but no definite conclusions are as yet possible.

It is not inconceivable that there may be small annual variations in the rate of rotation of the earth. There are seasonal displacements of matter over the earth's surface; there is, for instance, a high-pressure region over Siberia at one season of the year and a low-pressure region at another season, entailing the displacement of large atmospheric masses, with corresponding change in the moment of inertia. Such effects would be tangled up with effects due to periodic errors in star places and with the effects of the polar motion. Much more is likely to be learned about these matters when the atomic clock has reached a further stage of development, so that the frequency drift of the quartz crystal can be eliminated. Observations with photographic zenith telescopes should gradually smooth out any residual periodic errors in star places, while the information they provide about the variation of latitude will furnish basic data which can be used subsequently to separate polar motion effects from small variations in the earth's rotation. It may prove, however, that the earth itself is rather like a pendulum clock in its behavior and that its rate of rotation is liable to frequent and small irregular changes, so that we can at present merely observe their integrated effect.

The question may arise in the near future how the unit of time should be defined. Clocks are now at a stage when their stability for short periods is of a higher accuracy than the earth's rotation itself. The earth, however, has the advantage over any clock that it has no liability to a stoppage. It may be possible to develop atomic clocks to a stage at which they can be run for several years without stopping and to maintain accurate time; with a battery of such clocks, all controlled by the same atomic vibration, it would be possible to bridge over the stoppage of any single clock and thereby to maintain an accurate standard of time more or less indefinitely. There will be definite objections to using as the fundamental unit of time a unit that is known to be variable. A new unit should be absolutely invariable. A clock based fundamentally upon a length which is controlled by an atomic wave length, and upon the velocity of light, for instance, seems theoretically ideal.

Note added in proof. — Since the lecture was delivered, investigations at the Greenwich Observatory have established the existence of a fairly regular annual variation in the rate of rotation of the earth. Relative to uniform time the earth gets behind by about 60 milliseconds in May-June and ahead by a similar amount in November. The corresponding variations in the length of the day amount to somewhat more than 1 millisecond a day on either side of the mean value. H. S. J.

The lecture was published in the Annual Report of the Board of Regents of The Smithsonian Institution in 1949. Click here to view the lecture as originally published.