FROM THE PASTFROM THE PASTAU FIL DES ANSAU FIL DES ANSTHE LENGTH OF THE YEARThe following note arose from inquiries over the telephone which revealed that considerable confusion prevails in the use of the termyear. Perhaps the writer may be pardoned for an attempt to elucidate the matter here.The two chief units of time are the day and the year. The former is the rotation-period of the Earth on its axis; the latter, itsrevolution-period round the Sun.At the instant when the centre of the Sun is on the meridian we say it is solar noon, and the interval between two successivesuch noons is a solar day. The lengths of such intervals are not all equal, and their average length is a mean solar day. This is the dayin common use; it contains 86,400 seconds as ticked off by your watch.How shall we determine the length of the year? While we are persuaded that the Earth revolves about the Sun, to us the Sunappears to move, in the course of the year, about the sky in a circle which we call the ecliptic, and which intersects the celestialequator in two points. When the Sun is at one of these points as it is moving from the south side to the north side of the celestialequator, it is the spring equinox (March 21); when at the other, it is the autumn equinox (September 23). The interval from one springequinox to the next one is a tropical year, or a year of the seasons. By it our lives are governed. Such years vary in length considerably,and their average length is 365d. 5h. 48m. 46s. (approximately).It may be interesting to give the actual length of some of these tropical years. In the Observer’s Handbook is stated each yearthe date of the spring equinox, correct to one minute, and by writing down these dates for a series of years one can calculate thelength of the tropical year elapsing from one equinox to the next. In this way the following table was prepared for years 1928-45.Year Equinox Length of Yeard h m d h m1928 Mar. 20 15 45 … . ..1929 Mar. 20 21 35 365 5 501930 Mar. 21 03 30 365 5 551931 Mar. 21 09 07 365 5 411932 Mar. 20 14 54 365 5 471933 Mar. 20 20 43 365 5 491934 Mar. 21 02 28 365 5 451935 Mar. 21 08 18 365 5 501936 Mar. 20 13 58 365 5 401937 Mar. 20 19 45 365 5 471938 Mar. 21 01 43 365 5 581939 Mar. 21 07 29 365 5 461940 Mar. 20 13 24 365 5 551941 Mar. 20 19 21 365 5 571942 Mar. 21 01 11 365 5 501943 Mar. 21 07 03 365 5 521944 Mar. 20 12 49 365 5 461945 Mar. 20 18 38 365 5 49It will be seen that the year 1931 was 17m. shorter than the year 1938.The cause of this variation lies partly in the attraction of the other planets, particularly the massive Jupiter and Saturn, upon theearth, helping it forward at some parts of its orbit and holding it back at others.The remainder of the variation is due to changes in the position of the equinoxes themselves; this is known as nutation, and isproduced by varying lunar attractions.by C. A. Chant,from Journal, Vol. 39, pp. 30–31, January, 1945.234 JRASCDecember/ décembre 2000
Second Light“Of Pale Kings and Pyramids”by Leslie J. Sage (l.sage@naturedc.com)When I was a child, I likedEgyptian mummies almost asmuch as I liked stars, and theEgyptian galleries at the Royal OntarioMuseum were a favourite place. Thirtyyears later, it gives me great pleasure towrite about stars and mummies. Althoughthe subject of this column is somewhatdifferent than usual, I hope that my readerswill enjoy the topic as much as I do.It is a commonly held, but erroneous,view that people living in ancient timeswere not as intellectually sophisticatedas we are today. In fact, given thetechnological and engineering limitationsof the times, they often came up withextremely elegant solutions to practicalproblems. Aficionados of astronomy knowthat the ancient Greeks proved that theEarth is a sphere orbited by the Moon,and that the Moon shines by reflectedsunlight. Less well known is that someof the pyramids of ancient Egypt arealigned with rather uncanny precisionto true north. Writing in the journalNature, Egyptologist Kate Spence, of theUniversity of Cambridge, has recentlyshown, however, just how simply thisalignment was possibly achieved 4500years ago, during the Old Kingdom.The precision in the pyramidalignments is uncanny because at thattime there was no north star to act as aheavenly marker. The nearest relativelybright star to the celestial pole around2600 bc was about 2 degrees from truenorth, while the alignment of the GreatPyramid at Giza is only 3 arcminutes fromnorth. Even today, using Polaris, pyramidbuilders would not be able to achieve theprecise alignment realized around 2550bc, because Polaris is almost a degreeaway from the north celestial pole.“The precision in the pyramid alignments isuncanny because at that time there was nonorth star to act as a heavenly marker. Thenearest relatively bright star to the celestialpole around 2600 BC was about 2 degrees fromtrue north, while the alignment of the GreatPyramid at Giza is only 3 arcminutes from north.”You might imagine that the Egyptianscould have used the transit of the noonhour Sun, then turned to face the oppositedirection, to find north. But the Sun isabout half a degree across, and the sourceof considerable heat — which disturbsthe seeing — so the errors in alignmentwould most probably be randomly scatteredover at least a degree. Using the transitof the Moon or a single star might producebetter results, although the size of thefull Moon is also about half a degree onthe sky.But the curious thing about thealignments of the pyramids is that theprecision does not vary randomly with aGaussian (or bell curve) distribution, asone would expect if the measurementshad been made using transits of the Moonor single stars. In fact, the alignmentsduring the Old Kingdom start off relativelybadly (about 20 arcminutes from north),get better over the space of about 50 years,then get worse again for another hundredyears. You would think that if the Egyptianshad worked out an absolute system ofdetermining north, they could continueto apply it with equal precision over thespace of several hundred years, given thattheir civilization lasted several thousandyears.Spence has found a technique withvariable accuracy that fits very well withthe observed precision of the alignments.She proposes that the Egyptians used thesimultaneous transit of two relativelybright circumpolar stars to determinenorth; one star would be at its uppermostpoint, heading west, the other would beat its lowermost point, heading east. Atthe time of the transits, surveyors coulddrop a plumb line against the lineconnecting the two stars to lay out thewestern edge of the pyramid. This isintrinsically much more accurate thanusing the transit of a single circumpolarstar. And, because of the precession ofthe Earth’s orbit, the technique is variablein time.By definition, if the transits aresimultaneous, the line connecting thetwo stars in the sky passes through thenorth celestial pole. But that will be trueonly for a relatively brief period of time(a year or so, in fact). At other times, onestar will transit slightly ahead of the other,and a vertical line connecting them —December / décembre 2000 JRASC235