CHAPTER III

THE MEASUREMENT OF TIME: THE KALENDAR

AND THE CYCLE OF THE SEASONS

Declination of a star-the angular elevation above or below the equator, the complement of the polar distance. Right Ascension-the angular distance of the polar circle through the star measured west to east along the equator from the first point of Aries.

Angular velocity of the earth's rotation, 360° in one sidereal day, 72.92 × 10-" radians per second.

Mean sidereal day, 23-93447 mean solar hours.

Mean solar day, 24 mean solar hours.

True solar day varies from maxima of 24-0036 hours and 24-0083 hours on June 19-20 and December 22-23 to minima of 23-9949 hours and 23.9940 hours on March 26-27 and September 18-19.

One mean solar hour corresponds with rotation through 15° of longitude.

The length of "day" for a sun or star in hours from sunrise to sunset, allowing for refraction, is n/15, where /sin {45° +} (6 −8 +r)}. sin {45° − } (6 −8 −r)} ̧

n sin 4

cos .cos &

is the latitude, & the northerly declination of the sun or star, r the apparent elevation due to refraction, about 34′ Mean obliquity of the ecliptic, 23° 26′ 56′′·55 (1925).

Mean synodic lunar month, 29-53059 days, varying to the extent of 13 hours in the course of the year.
Mean solar or tropical year, 365-2422166 mean solar days.

Perihelion (1924), January 2, 2 h. Sun's distance, 91,341,000 miles.

Aphelion (1924), July 3, afternoon. Sun's distance, 94,495,000 miles.

Precession of the equinox, 50-2564′′ +0·02220′′ t per annum, t being the time reckoned from 1900 in centuries. Annual increase of declination of a star in consequence of precession, 20" cos a, where a is the Right Ascension. Vernal equinox, March 20 or 21; Summer solstice, June 21 or 22.

Autumnal equinox, September 23 or 24; Winter solstice, December 22 or 23.

Commencement of quarters of the May Year: May 6, August 8, November 8, February 4.

1st Olympiad of 4 years commences 776 B.C. 293rd Olympiad of 4 years commences A.D. 393. Lustrum of 5 solar years 6 Romulian years.

IN the summaries of observations which represent the climates of the Mediterranean the data have been grouped according to what is conventionally called a year, and further according to "kalendar months." The year therein indicated is in reality a group of 365 days, or 366 days for leap year, taken as an approximation to the mean solar or tropical year of 365.2422166 days. The kalendar months are twelve in number, of unequal lengths adjusted arbitrarily to make up 365 or 366 days. That is the ordinary vogue in dealing with the representations of climate and it has thousands of years of history behind it; but it was not the common practice of the ancients. The kalendar as a practical system of recording the time of events was only brought into something like order by Julius Caesar and the months, as we know them, date only from an edict of Augustus. The latter, in making the final adjustments, introduced an unnecessary complication by claiming the maximum allowance of thirty-one days for the month of his own name as well as that of his great-uncle Julius, which used to have the more appropriate names of Quinctilis and Sextilis.

SPECIFICATION OF SEASONS BY THE STARS

There was always the day with its alternation of light and darkness, and the year with its regular variation of the sun's times and position of rising and setting and the consequent cycle of the seasons, but there was no acceptable method of marking the position of an event within the year by counting the days. The gradual march of the sun during the year through the twelve constellations of the Zodiac was made out by the Babylonians1, and the moon with its regularly recurring phases must always have been within the cognisance of the dwellers in those countries where the sky is proverbially clear, and where night is the most suitable time for making land-journeys. But to identify the times or seasons for making voyages by sea, or for the operations of agriculture on land, it was apparently not the number of moons from the commencement of the year that was remembered but the face of the sky about sunrise or sunset. The conspicuous features of the sky, the prominent stars and constellations were recognised and the seasons were identified by the stars that rose just before, or set just after, the sun: the so-called "heliacal rising and setting" of the stars just visible when the sun itself was perhaps 10° below the horizon.

DAY AND NIGHT. THE HOUR

Before we enter into further details of the use of the stars for the identification of the seasons we must devote some attention to the general question of the rising and setting of the sun, moon or stars, the length of the day and of the night and its variations with the seasons.

The length of the true solar day is the period of rotation of the earth with respect to the sun. It is the actual interval between two consecutive passages of the actual sun, the true sun as the astronomers call it, over any meridian of the earth, as established by setting up a true North and South line and watching "apparent" successive passages of the sun across the vertical plane of the meridian. The actual interval between two consecutive transits varies at different times of the year from 24.0083 hours on December 22-23 to 23.9940 hours on September 18-19.

But the transits of a star are subject to no such variation within the year; apart from the variation due to very slow alterations in the position of the earth's polar axis among the stars, which causes a gradual change in the star's declination, any star rises always at the same point on the horizon, sets at the same point and remains above the horizon always for the same length of time. The duration of its day at a selected point on the earth's surface is given by the equation which is set out at the head of this chapter: when the latitude of the place and the declination of the star are duly inserted.

The length of time that the sun is above the horizon is no fixed quantity as

1 From 2330 B.C. the Babylonians used a regular kalendar with a week of seven days and a year of twelve months, named after the zodiacal signs. Their year was of 360 days which probably suggested the division of the circle into degrees which we have derived from them. Chambers's Encyclopædia, s.v. Chronology.

in the case of a star. The fact that the earth moves in its orbit so as to complete the circumnavigation of the sun in a year adds one complete sidereal revolution to the year and gives 366 complete sidereal days within the year; and the elliptical shape of the orbit causes the variation in the length of the solar day that has been already referred to. Further than that, the inclination of the polar axis or of the plane of the earth's equator to the plane of its orbit, the ecliptic, causes the sun to vary its declination during the year from its maximum of 231° above the equatorial plane at the summer solstice (June 21 or 22) to 2310 below the equatorial plane at the winter solstice (December 22 or 23), passing through the equinoctial points in the upward direction on March 20-21, and in the downward direction on September 23-24, when the sun is in the plane of the equator.

THE TOWER OF THE WINDS

All these variations can be traced upon sun-dials, which have been used from time immemorial for that purpose. In meteorological work they are represented in a very interesting manner by the instrument for recording sunshine devised originally by John F. Campbell of Islay in 1853 to show the scorching effect of the sun upon a wooden bowl, and transformed into an effective meteorological instrument by Sir George Stokes in 1879. The instrument makes use of the image of the sun formed by a spherical glass lens. The ordinary sundial uses the shadow thrown by a gnomon or straight edge set parallel to the earth's polar axis, so that, as the earth rotates, the sun, apart from any alteration of its declination during the day, keeps at a fixed angle with the axis of the instrument, and the dial can be graduated in a systematic

manner.

Fig. 5. The tower of Andronikos Kyrrhestes at Athens bearing sculptures of winds on the frieze (see fig. 9) and sun-dials with appropriate graduation on the entablatures beneath the sculptures.

But a graduation-line, such as we are accustomed to, is not really necessary for an effective dial, the shadow of a small object, a knob at the end of a rod, will serve. If we suppose the shadow thrown upon a vertical wall by a knob at the extremity of a rod projecting from the wall, the shadow will pass across the wall during the day as the sun travels between the point of sunrise and that of sunset, and so a line of track can be drawn on the wall. The track will be lower down on the wall next day if the sun is higher in declination and higher if the change is the other way. A series of lines drawn down the wall across the tracks can mark equal stages from sunrise to sunset.

Each of the eight sides of the Tower of the Winds at Athens, which dates back to the first or second century before Christ, is used for a sun-dial of this character; the lines on the walls divide the period between sunrise and sunset into twelve hours. The tower is represented in fig. 5; a shadow of one of the gnomons can be seen under the frieze on the front face. The sides are quite well oriented according to the true points of the compass; no single one of the faces can show all the hours, all the year round, but each face takes its part, and even the North side is duly graduated, though the shadow of its gnomon can only fall on it in the earliest and latest stages of the day in the summer half year.

The division of the day and night each into twelve hours of length dependent upon the season has now been replaced by the division of the mean solar day into twenty-four equal hours carefully guarded by watches and by clocks.

HELIACAL RISING

For the purpose of studying the relation of the stars to the sun in the face of the sky, as a guide to the seasons, we may consider the sun as a star which changes its declination backwards and forwards through 47° in a year. Consequently the length of day is different from day to day, whereas the declination of a fixed star swings backwards and forwards through the 47° only in about 26,000 years. For a single year or even for a short period of years it may be regarded as constant and the star will be above or below the horizon for the same period throughout the year, though the solar time of rising and setting will vary.

The result of this periodical change in the polar axis is that the sun's position among the stars in the Zodiac as seen from the earth at an equinox or solstice will be altered by a degree in about 70 years on the average or about 30° in 2200 years. It will complete its cycle in about 26,000 years.

As the most notable example let us consider the Dog-star, "Sirius," the Egyptian "Sothis," which now has a declination of 16° 36′ 44′′ S, and a consequent period above the horizon of 10 hours in latitude 30°. The sun's declination will vary from 231° N to 231° S; it passes through the position 16° 36' S on November 8 on the way down, and on February 3 on the way. up. In ancient times Sirius would be actually rising simultaneously with the sun in May and consequently invisible, after coincidence it would rise before the sun by a gradually increasing interval until its rising would take place just after sunset when it would be visible the whole night through. The separation would go on until the star would rise in the daytime and be visible setting, just after the sun. All the time since its heliacal rising it has been visible some time of the night but, later on, its setting is earlier than sunset, it will be 10 hours before it will rise again and, if the sun is up before the hours have elapsed, the star will not be seen at all. There is therefore a certain period in the year when the star is not visible day or night. Hence rising and setting have a new kind of significance for a brilliant celestial

in 1900.

object like Sirius; after it rises with the sun it is going to be visible at some time in the night, until it sets with the sun, when it will be invisible until the next heliacal rising.

The calculation of the period when the star will not be visible is a complicated astronomical problem. A star that is within 66° of the North Pole, and has always therefore higher declination than the sun, can have no period of disappearance from the Northern Hemisphere; part of its journey must be in the dark because it is always above the horizon longer than the sun. For stars below that declination a period of invisibility depends upon latitude and seasons; and the fact that the ancients were so familiar with the face of the sky as to be able to recognise these features and their relation to the seasons is very striking evidence of the thoroughness of their scrutiny, which may be recognised also in the amazing ingenuity of the Zodiac.

The stars most frequently used to indicate the seasons were Sirius, Arcturus, the Pleiades, Procyon and Castor and Pollux, and the period of the first appearance of the star for the year when it was a morning star was the most important sign of its influence.

In the early historic times the heliacal rising of Sirius ushered in the rising of the Nile in Egypt, the etesian winds of Athens, the hot summer, the resting period for crops of the Mediterranean countries, "the weary