TIME, MEASUREMENT OF. Time is measured by successive phenomena recurring at regular intervals. The 'only astronomical phenomenon which rigorously fulfils this condition, and the most striking one, - the apparent daily revolution of the celestial sphere caused by the rotation of the earth, - has from the remotest antiquity been employed as a measure of time. The interval between two successive returns of a fixed point on the sphere to the meridian is called the sidereal day; and sidereal time is reckoned from the moment when the "first point of Aries" (the vernal equinox) passes the meridian, the hours being counted from 0 to 24. Clocks and chronometers regulated to sidereal time are only used by astronomers, to whom they are indispensable, as the sidereal time at any moment is equal to the right ascension of any star just then passing the meridian. For ordinary -purposes solar time is used. In the article ASTRONOMY (vol. ii. p. 771) it is shown that the solar day, as defined by the successive returns of the sun to the meridian, does not furnish a uniform measure of time, owing to the slightly variable velocity of the sun's motion and the inclination of its orbit to the equator, so that it becomes necessary to introduce an imaginary mean sun moving in the equator with uniform velocity. The equation of time (ioc. cit., pp. 772-773) is the difference between apparent (or true) solar time and mean solar time. The latter is tronorny, i. p. 25.
that shown by clocks and watches used for ordinary purposes. Mean time is converted into apparent time by applying the equation of time with its proper sign, as given in the Nautical Almanac and other ephemerides for every day at noon. As the equation varies from day to day, it is necessary to take this into account, if the apparent time is required for any moment different from noon. The ephemerides also give the sidereal time at mean noon, from which it is easy to find the sidereal time at any moment, as 24 hours of mean solar time are equal to 24" 3m 56o5554 of sidereal time. About 21st March of each year a sidereal clock agrees with a mean-time clock, but it gains on the latter 3a 56'o5 every day, so that in the course of a year it has gained a whole day. For a place not on the meridian of Greenwich the sidereal time at noon must be corrected by the addition or subtraction of 9'o8565 for each hour of longitude, according as the place is west or east of Greenwich.
While it has for obvious reasons become customary in all civilized countries to commence the ordinary or civil day at midnight, astronomers count the day from noon, being the transit of the mean sun across the meridian, in strict conformity with the rule as to the beginning of the sidereal day. The hours of the astronomical day are also counted from 0 to 24. An international conference which met in the autumn of 1884 at Washington, to consider the question of introducing a universal day (see below), has recommended that the astronomical day should commence at midnight, to make it coincide with the civil day. The great majority of American and Continental astronomers have, however, expressed themselves very strongly against this change ; and, even if it should be made in the British Nautical Almanac, it appears very doubtful whether the other great ephemerides will adopt it, the more so as astronomers have hitherto felt no inconvenience from the difference between the astronomical and the civil day.
Determination of Time. - The problem of determining the exact time at any moment is practically identical with that of determining the apparent position of any known point on the celestial sphere with regard to one of the fixed (imaginary) great circles appertaining to the observer's station, the meridian or the horizon. The point selected is either the sun or one of the standard stars, the places of which are accurately determined and given for every tenth day in the modern ephemerides. The time thus determined furnishes the error of the clock, chronometer, or watch employed, and a second determination of time after an interval gives a new value of the error and thereby the rate of the timekeeper.
The ancient astronomers, although they have left us very ample information about their dials, water or sand clocks (clepsydra?), and similar timekeepers, are very reticent as to how these were controlled. Ptolemy, in his Almagest, states nothing whatever as to how the time was -found when the numerous astronomical phenomena which he records took place ; but Hipparchus in the only book we possess from his band gives a list of forty-four stars scattered over the sky at intervals of right ascension equal to exactly one hour, so that one or more of them would be on the meridian at the commencement of every sidereal hour. In a very valuable paper t Schjellerup has shown that the right ascensions assumed by Hipparchus agree within about 15' or one minute of time with those calculated back to the year 140 B.C. from modern star-places and proper motions. The accuracy which, it thus appears, could be attained by the ancients in their determinations of time was far beyond what they seem to have considered necessary, as they only record astronomical phenomena (e.g., eclipses, occultations) as having occurred "towards the middle of the third hour," or "about 8i hours of the night," without ever giving minutes.' The Arabians had a clearer perception of the importance of knowing the accurate time of phenomena, and in the year 829 we find it stated that at the commencement of the solar eclipse on 30th November the altitude of the sun was 7° and at the end 24°, as observed at Baghdad by Ahmed ibn Abdallah, called Habash.2 This seems to be the earliest determination of time by an altitude ; and this method then came into general use among the Arabians, who on observing lunar eclipses never failed to measure the altitude of some bright star at the beginning and end of the eclipse. In Europe this method was adopted by Purbach and Regiomontanus, apparently for the first time in 1457. Bernhard Walther, a pupil of the latter, seems to have been the first to use for scientific purposes clocks driven by weights : he states that on 16th January 1484 he observed the rising of the planet Mercury and immediately attached the weight to a clock having an hour-wheel with fifty-six teeth; at sunrise one hour and thiity-five teeth had passed, so that the interval was an hour and thirty-seven minutes. For nearly two hundred years, until the application of the pendulum to clocks became general, astronomers could place little or no reliance on their clocks, and consequently it was always necessary to fix the moment of an observation by a simultaneous time determination. For this purpose Tycho Brahe employed altitudes observed with quadrants ; but he remarks that they are not always of value, for if the star is taken too near the meridian the altitude varies too slowly, and if too near the horizon the refraction (which at that time was very imperfectly known) introduces an element of uncertainty. He therefore preferred azimuths, or with the large "armillary spheres" which played so important a part among his instruments he measured hour-angles or distances from the meridian along the equators Transits of stars across the meridian were also observed with the meridian quadrant, an instrument which is alluded to by Ptolemy and was certainly in use at the Mardgha (Persia) observatory in the 13th century, but of which Tycho was the first to make extensive use. It appears, however, that he chiefly employed it for determining star-places, having obtained the clock error by the methods already described.
In addition to these methods, that of "equal altitudes" was much in use during the 17th century. That equal distances east and west of the meridian correspond to equal altitudes had of course been known as long as sun-dials had been used ; but, now that quadrants, cross-staves, and parallactic rules 4 were commonly employed for measuring altitudes more accurately, the idea naturally suggested itself to determine the time of a star's or the sun's meridian passage by noting the moments when it reached any particular altitude on both sides of the meridian. But Tycho's plan of an instrument fixed in the meridian was not forgotten, and from the end of the 17th century, when Roemer invented the transit instrument, the observation of transits across the meridian became the principal means of determining time at fixed observatories, while the observation of altitudes, first by portable quadrants, afterwards by reflecting sextants, and during the 19th century by portable alt-azimuths or theodolites, has been used on journeys.
During the last fifty years the small transit instrument, with what is known as a "broken telescope," has also been much employed on scientific expeditions; but great caution is necessary in using it, as the difficulties of getting a perfectly rigid mounting for the prism or mirror which reflects the rays from the object-glass through the axis to the eyepiece appear to be very great, for strange discrepancies in the results have often been noticed. The gradual development of astronomical instruments has been accompanied by a corresponding development in timekeepers. 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 trustworthy timekeeper in the hands of travellers.
We shall now give a sketch of the principal methods of determining time.
In the spherical triangle ZPS between the zenith, the pole, and a star the side ZP= 90° - cp (0 being the latitude), PS=90° - 8 (8 being the declination), and ZS or Z=90° minus the observed altitude. The angle ZPS=t is the star's hour-angle or, in time, the interval between the moment of observation and the meridian passage of the star. We have then cos 95 cos S which formula can be made more convenient for the use of logarithms by putting Z+ + 8=2S, which gives tan, it _ sin (S - .0) sin (S - 8) cos S cos(3 - Z) o According as the star was observed west or east of the meridian, t will be positive or negative. If a be the right ascension of the star, the sidereal time =t+a, a as well as 8 being taken from an ephemeris. If the sun had been observed, the hour-angle I would be the apparent solar time. The altitude observed must be corrected for refraction, and in the case of the sun also for parallax, while the sun's semi-diameter must be added or subtracted, according as the lower or upper limb was observed. The declination of the sun being variable, and being given in the ephemerides for noon of each day, allowance must be made for this by interpolating with an approximate value of the time. As the altitude changes very slowly near the meridian, this method is most advantageous if the star be taken near the prime vertical, while it is also easy to see that the greater the latitude the more uncertain the result. If a number of altitudes of the same object are observed, it is not necessary to deduce the clock error separately from each observation, but a correction may be applied to the mean of the zenith distances. Supposing n observations to be taken at the moments T1, T2, To, ..., the mean of all being To,o and calling the z corresponding to this Z, we have dZ 1 el2Z z1=Z+--dt(T1 - 71t2(T5 - Tor ; and so on, t being the hour-angle answering to To. As 1(T - To) =0, these equations give But, if in the above-mentioned triangle we designate the angles at Z and S by 180° - A and p, we have sin z sin A =cos 8 sin I ; sin z cos A= - cos o75 sin 8+ sing:. cos 8 cos t ; and by differentiation d2Z cos cos S cos A cosp dt2 sin Z in which A and p are determined by sin I sin t sin _A= sin Z cos and sinp =sin Z cos q.
With this corrected mean of the observed zenith distances the hour-angle and time are determined, and by comparison with To the error of the timekeeper.
o The method of equal altitudes gives very simply the clock error equal to the right ascension minus half the sum of the clock times corresponding to the observed equal altitudes on both sides of the meridian. When the sun is observed, a correction hasto be applied for the change of declination in the interval between the observations. Calling this interval 2t, the correction to the apparent noon
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