Astronomical clock

“ A good clock is also a necessary adjunct for astronomical observations, and the astronomical clocks and chronometers now in use record the time with almost perfect accuracy. The improvement in telescopes, the use of micrometers, etc., have greatly facilitated observations. In the transit clock we have a most useful timekeeper, for the ordinary clocks are not sufficiently accurate for very close observations. The sidereal time differs from solar time, and the twenty-four hours’ period is calculated from the moment a star passes the meridian until it passes it again. ”

“ In the first place, every observatory is, of course, provided with what is known as an astronomical clock. This instrument, from the astronomer's point of view, is something very different from the ordinary popular idea. To the average person an astronomical clock is a complicated and elaborate affair, giving the date, day of the week, phases of the moon, and other miscellaneous information. ”

“ We have now given a description of the astronomical clock—the modern astronomical instrument which it was our duty to consider. There is another time-keeper—the chronometer—which we have to dwell upon. In the chronometer, instead of using the pendulum, we have a balance, the vibration of which is governed by a spiral spring, instead of by gravity, as the pendulum is. By such means we keep almost as accurate time as we do by employing a pendulum, the balance being corrected for temperature on principles, one of which we shall describe. ”

“ It seems to follow that the extent to which astronomical clocks can be made accurate, viz. to 1/30 of a second average variation from their mean daily rate, or one two-and-a-half millionth of 24 hours, is a degree of accuracy sufficient for present purposes, and it seems rather doubtful whether mechanical science will in the case of clocks be likely to reach a much higher figure. ”

“ Something better is obtainable from the very best astronomical clocks, which, indeed, are found to keep a uniform rate, from which they will vary only three or four hundredths of a second daily. But astronomical clocks, as is well known, are not required to indicate the exact time, mean or sidereal, but only to go at a uniform rate, which, if it be found to be practically invariable, is corrected at the time of the observation in which it is employed. The most accurately running large clock in the world, which has been regulated to keep diurnal time, is the Westminster clock in England. ”

“ Likewise, the moon in the heavens will be in eclipse if, at the time of opposition, the pointers of the little index (which we mentioned before) situated below the center of the clock are so far away from the belly of the dragon that they are forced to lie under the two smaller segments of the circle which, in all full moons, are always to be moved from the index of the synodic moon to the region of that little index. As a matter of fact, the closer the little pointers approach to the middle of the segments, the more obscured it will be. ”

“ Motion from clock to polar axis is transmitted by means of a set of bevel gears and worm and worm wheel. The worm wheel is held by friction to the polar axis so that the telescope can be moved without loosening any screw and without affecting the clock. The clock will give steady and accurate motion to the telescope and with ordinary care it will keep in good repair for years. A slow motion adjustment independent of the clock is fitted to the polar axis.
With the instrument are furnished three celestial eye pieces giving a magnifying power of about 50, 100 and 150 diameters respectively. ”

“ Yet clockmakers (artifices horologiorum) are trying to make a wheel (circulum) which will make one complete revolution for every one of the equinoctial circle, but they cannot quite perfect their work. But if they could, it would be a really accurate clock (horologium verax valde) and worth more than an astrolabe or other astronomical instrument for reckoning the hours, if one knew how to do this according to the method aforesaid. The method of making such a clock would be this, that a man make a disc (circulum) of uniform weight in every part so far as could possibly be done. ”

“ On the basis of such evidence I have suggested elsewhere9 that the clock is "nought but a fallen angel from the world of astronomy." The first great clocks of medieval Europe were designed as astronomical showpieces, full of complicated gearing and dials to show the motions of the Sun, Moon and planets, to exhibit eclipses, and to carry through the involved computations of the ecclesiastical calendar. ”

“ Of the three indices which revolve from the left, the uppermost completes its cycle within 12 hours, just as the hour index. The middle one with two pointers on diametrically opposite sides, carries the marks of conjunction and opposition of the luminous bodies, with a movement equal to the course of the sun from lunar apogee or perigee. The lowest index, fitted with a single pointer, indicates the motion of the moon from its apogee or perigee. ”

“ From being very untrustworthy, astronomical clocks are now made to great perfection by the application of the pendulum and by its compensation, while the invention of chronometers has placed a portable and equally trust worthy timekeeper in the hands of travellers. ”

“ The stellar day, that is the time from one transit of a star to the next, is shorter than a solar day by 3m. 56s., so what is called sidereal time, regulated by the transits of well-known stars, in the manner we shall presently explain, by no means runs parallel with mean time so far as the clock indications go. Indeed when we look at a sidereal clock, we see something different to the clock we are generally accustomed to see. In the first place, we have twenty-four hours instead of twelve, and then generally there is one dial for hours, another for minutes, and another for seconds. ”

“ With the general introduction of clocks and watches into use about a century ago this kind of solar time went out of common use, since no well-regulated clock could keep the time correctly. The earth in its orbital motion around the sun goes faster in some parts of its orbit than in others, and in consequence the sun appears to move more rapidly among the stars in winter than in summer ”

“ Accordingly, now that the pendulum clock affords astronomers the means of determining time exactly, a measurement of the Right Ascensions of heavenly bodies by means of a clock and a transit instrument, is a part of the regular business of an observatory. If the sidereal clock be so adjusted that it marks the beginning of its scale of time when the first point of Right Ascension is upon the visible meridian of our observatory, the point of the scale at which the clock points when any other star is in our meridian, will truly represent the Right Ascension of the star. ”

“ The observatory clock having been once set right by observations of the sky, its error can be re-determined every few days quite easily. Thus even the small irregularities of its nearly perfect mechanism can be prevented from accumulating until they might reach a harmful magnitude. ”

“ In the equatorial mounting, clockwork is introduced, and after the instrument has been pointed to any particular star or celestial body, the clock is clamped to the circle moving round the polar axis, and so made to drive it round in exactly the time the earth takes to make a rotation. ”

“ The astronomer’s clock, for instance, is no standard of the efflux of time; it serves but to subdivide, with approximate accuracy, the interval of successive passages of a star across the meridian, which it may effect perhaps to the tenth part of a second, or 1/864000 part of the whole. The moving globe itself is the real standard clock, and the transit instrument the finger of the clock, while the stars are the hour, minute, and second marks, none the less accurate because they are disposed at unequal intervals. ”

“ But if one star is lost by cloud, there are many others, and the chance is by no means utterly gone. Beside, the sun enables us to tell the time only at noon; the stars enable us to find it at various times throughout the entire night; indeed, throughout both day and [160] night, since the brighter stars can be observed in a large telescope even during the day.
There are two great standard clocks at the Observatory: the mean solar clock and the sidereal clock. The latter registers twenty-four hours in the precise time that the earth rotates on its axis. ”

“ The lunar clock has, so-to-speak, a more varied and mysterious mechanism than the solar, and it certainly has impressed itself to a great extent in folklore, a fact to which Dr. Rivers has drawn the attention of the Society. [5] Finally, the sidereal clock, by the rising and setting of stars and constellations with its annual periodicity, gives the precise information that is required, thus the agricultural and other operations are generally regulated by the very backward peoples by the movements of stars. ”

“ Hence it is evident that if we indicate the exact interval of time between the culmination of the sun and that of one particular star, or name the star with which the sun precisely culminates, we can determine the day of the solar year. This is the principle of one method of computing time which was very common among ancient and primitive peoples, but has entirely dropped out of use in modern times owing to our paper calendar. The stars are so to speak the stationary ciphers on the clock-face and the sun is the hand. ”

“ We are constantly correcting their errors and never entirely succeed in getting them to run accurately to periods of time which exist entirely outside of such little things as men and clocks. So a clock is better as it approximates or bears a regular relation to some motion in nature. The sidereal clock of the astronomer does run to a regular motion; but our 24-hour clocks do not, as we shall see later. Now consider the year, or the sun's apparent motion in the Zodiac, from any given star around to the same one again. ”

“ A space-space representation is developed for nonrelativistic wave mechanics as was done for classical mechanics, by adding to the system a rotating body to serve as a clock, and applying the time-independent forms of the equations of motion. ”

“ The behavior of clocks during travel in the curved space-time of the general theory of relativity is discussed, and effects observable in journeys in the solar system or on earth satellites are examined. ”

“ Until machines for accurately measuring time were invented, apparent time—time, that is to say, given by the sun itself, as by a sun-dial—was the only time about which men knew or cared. But when reasonably good clocks and watches were made, it was very soon seen that at different times in the year there was a marked difference between sun-dial time and that shown by the clock, the reason being simply that the apparent rate of motion of the sun across the sky was not always quite the same, whilst the movement of the clock was, of course, as regular as it could be made. ”

“ Current interest in the possibilities of space flight and the prediction that atomic clocks in earth satellites may be utilized to check Einstein's theory have focused attention on the clock problem in relativity, or the so-called time-traveler paradox and its implication. General theory holds that a precise clock will run more slowly at extreme altitudes than an earthbound clock because of differences in gravitational fields. ”

“ In view of the paucity of experimental tests for the general theory of relativity, it is desirable to consider the uses to which a satellite vehicle could be put. The advance of the perigee is calculated similarly to the perihelion advance of Mercury; it amounts to only 15 seconds of the arc per year. However, the effect on a satellite clock is large and could be measured. With respect to an earth clock it is calculated to be a "red shift" for low-altitude orbits, zero shift for an orbit of one-half the earth's radius, and a "violet shift" for higher altitudes, where it approaches 7 x 10-10. ”

“ Fractions are left out of these lengths as they would only confuse the explanations. At the Naval observatory in Washington, D. C., the standard clocks have seconds pendulums, the rods of which are nickel steel, called “Invar,” which is little influenced by changes of temperature. These clocks are kept in a special basement, so they stand on the solid earth. The clock room is kept at a nearly uniform temperature and each clock is in a glass cylinder exhausted to about half an atmosphere. ”

“ The whole skill of the clockmaker is devoted to the object of giving stability to the going of the clock for the period, whether long or short, during which it is to go. To gain this object, he contrives a pendulum by which the disturbances of the temperature may be compensated. He cannot prevent the expansion of metals, but he can so balance, by the expansion of different metals, the disturbances produced, that the result is invariable motion. This is precisely what is done in the solar system. ”

“ The seconds beat of a clock sympathetic with the solar standard, rings out loud and clear above the insect-like chatter of the ticking of the hundreds of chronometers, and wherever the assistant stands, he has but to lift his eyes to see straight before him, if not a complete clock-face, at least a seconds dial moving in exact accordance with the solar standard. ”