## Sunday, 28 July 2013

### 1 Kaala alavu or Measurement of Time

Our ancestors had observed the periodic occurrences of various seasons. Their agricultural society forced them to try predicting the season cycle. This need forced them to prepare, what is now called, calendar. However, this task was not very easy.

They began the process by recording the periodic movements in the celestial sky. The sun rises from the east and sets in the west. A day or pagal is the period between sunrise and sunset and a night or iravu is the period between sunset and next sunrise. A day and night together makes a naal (usually, in English we refer this as day). Today we know this is due to the rotation of earth on its axis. Indian mathamatician Arybhatta has knowledge of this phenomenon of spinning on its axis. Thus, one complete rotation of earth on its axis makes a naal. Our ancestors measured the rotation of earth on its axis as the duration between successive sunrises. Seen from the north-pole of the earth, the earth spins on its axis from west to east. This is the reason behind sun rising in the east and setting in the west.

One naal (complete day) was subdivided in to 60 division, called nazhigai. There was a reason to choose the 60 subdivision. Recall that we are talking of times when counting was manual. Thus, any subdivision of a day should facilitate usage of fractions of a day in day-to-day life. This is equivalent to ﬁnding the smallest number which has most of the early natural numbers as factors. For instance, $12$ is the ﬁrst number which has factors $1,2,3,4,6$ but not $5$. Thus, if $12$ was chosen as a subdivision of a day one can talk of $1∕6$, $1∕4$, $1∕3$ or $1∕2$ but not $1∕5$ fraction of a day. With this idea, $60$ is the ﬁrst number which has $1,2,3,4,5,6$ has its factors. If, in addition, one demanded the fraction $1∕7$ then we would have to go as big as $420$. So, for all practical reasons, $60$ was good enough and manageable.

Two nazhigai makes one muhurtam. Each nazhigai was, further, subdivided in to 60 parts, called thuli. Each thuli was, further, subdivided in to 60 parts, called nodi. Each nodi was subdivided in to 60 parts, called kuzhi or kuRRuzhi. One kuRRuzhi or kuzhi is the time taken by the krithigai natchatiram (Pleiades stars) to glitter once.

In modern terminology, one day is of $24$ hours, thus one nazhigai is of $24$ minutes and one muhurtam is of $48$ minutes. Similarly, one thuli is of $24$ seconds, one nodi is $0.4$ seconds and one kuRRuzhi is $0.04∕6=0.00666$ seconds. One kannimai, the time taken for normal wink of an eye, is equal to 10 kuRRuzhi. One aNu is $4$ seconds and one kaNam is $4$ minutes. One saamam referred to the modern day one hour which was deﬁned as $2.5$ nazhigai. $4$ saamam (or 4 hours) constituted one siRupozhuthu and $6$ siRupozhuthu made one complete day. They had names for the siRupozhuthu as follows: Assuming $6:00$ am sunrise,

 S.No. Time Slot Name 1 06:00 - 10:00 kaalai 2 10:00 - 14:00 nanpagal 3 14:00 - 18:00 yerpaadu 4 18:00 - 22:00 maalai 5 22:00 - 02:00 yaamam 6 02:00 - 06:00 vaikarai

#### 1.1 Raasi (Zodaic)

The concept of raasi might be a contribution of Sanskrit culture. I feel so because the names of raasi have Sanskrit origin and do not have a tamil equivalent. Our ancestors seem to have known that the earth is spherical in shape. The proof of this is the illustration of earth as a spherical object in Varaha avatar (third) of lord Vishnu. Our ancestors (who believed in geo-centric theory) divided the celestial sphere containing stars and planets in to 12 segments, each division is called raasi or zodiac. They observed the motion of planets against the backdrop of raasis. Today, we know this is the division of the elliptical path of earth around sun. Each raasi identiﬁes a 30 degrees segment of the celestial sphere. Half-a-siRupozhuthu or $2.5$ muhurtam (deﬁned in previous section) is the time taken by earth to spin from one raasi to other. The twelve raasi are:

 No. Raasi Symbol 1 Mesham Ram (Goat) 2 Rishabam Bull 3 Mithunam Woman-Man pair 4 Katakam Crab 5 Simmam Lion 6 Kanni Virgin (in a boat) 7 Thulaam Man holding balance 8 Vrichigam Scorpion 9 Dhanus Man holding Bow 10 Makaram Deer faced Crocodile 11 Kumbham Water Bearer 12 Meenam Two ﬁshes

Note that the raasis have no order (as given above). It is cyclic with no beginning and end. However, later we shall see that the raasi gets an order once we introduce the concept of new year and ﬁrst month of a year. The raasis are spread on the elliptical path within a span of 8-9 degrees (north-south) from the equator of earth.

#### 1.2 Muhurtam, Nazhigai and Laganam (Spin of Earth)

As mentioned above, in Tamil calendar a complete day starts with sunrise and ends with next day sunrise. Imagine this as the earth’s 360 degree spin on its axis, which makes a complete day. Imagine dividing the earth’s surface into 60 parts along longitude direction (north-south), with $6$ degrees between successive lines. The time taken by earth to spin 6 degrees is called a nazhigai, a duration of 24 minutes. 2 nazhigais makes a muhurtam, a spin of 12 degrees by earth on its axis. Thus, a complete day contains 30 muhurtams and each muhurtam is of 48 minutes duration. The names of the 30 muhurtams, in order in which they occur after sunrise till next sunrise, are as follows (assuming sunrise is at 0600 am):

 S.No. Time Slot Name Eﬀect 1 06:00 - 06:48 Rudra bad 2 06:48 - 07:36 Ahi bad 3 07:36 - 08:24 Mitra good 4 08:24 - 09:12 Pitru bad 5 09:12 - 10:00 Vasu good 6 10:00 - 10:48 Vara good 7 10:48 - 11:36 Visvadeva good 8 11:36 - 12:24 Vidhi good (except monday + friday) 9 12:24 - 13:12 Satamukhi good 10 13:12 - 14:00 Puruhuta bad 11 14:00 - 14:48 Vahini bad 12 14:48 - 15:36 Naktancara bad 13 15:36 - 16:24 Varuna good 14 16:24 - 17:12 Aryama good (except sunday) 15 17:12 - 18:00 Bhaga bad 16 18:00 - 18:48 Girisha bad 17 18:48 - 19:36 Ajapad bad 18 19:36 - 20:24 Ahirbudhnya good 19 20:24 - 21:12 Pusa good 20 21:12 - 22:00 Aswini good 21 22:00 - 22:48 Yama bad 22 22:48 - 23:36 Agni bad 23 23:36 - 24:24 Vidhatr good 24 24:24 - 01:12 Canda good 25 01:12 - 02:00 Aditi good 26 02:00 - 02:48 Jiva good 27 02:48 - 03:36 Visnu good 28 03:36 - 04:24 Yumigadyuti good 29 04:24 - 05:12 Brahma very good 30 05:12 - 06:00 Samudram good

Of the above muhurtams, Brahma muhurtam (29) is the most auspicious and considered good for all spiritual purposes, especially meditation. It is considered good to have bath in the Brahma muhurtam. Superstitious? No idea! In fact, all the three sandhi kaalam viz. day meeting night, night meeting day and mid-day are all considered good for spiritual purposes.

Let us explain the concept of lagnam. The division of lagnam is same as raasi. It is the same twelve division of a complete day each of duration two hours. However, the deﬁnition of lagnam is related to an individual time and place of birth. This is to diﬀerentiate between two persons born on the same day but at diﬀerent places (or diﬀerent longitudinal divisions) or two persons born on same day, same place but at diﬀerent time of the day. In modern terms this is to diﬀerentiate people born on the same day but at diﬀerent time zones. Thus, a person born on same day but in diﬀerent longitudinal division is born while Earth is facing diﬀerent raasi. Thus, lagnam of a person is the raasi faced by the part of the Earth surface on which he is born. Fix a point on the surface of earth. Note that the point will face all the 12 segments (raasis) of celestial sky, while the earth spins on its axis. Since the raasis are 30 degree segment, the point will take 2 hours (or 5 nazhigais or 2.5 muhurtam) to move from one raasi to other. A day is divided in to 12 lagnams or ascendant with each lagnam of two hour duration. A person’s lagnam is the lagnam on which he is born on a given day of the given place.

#### 1.3 Nakshathiram (Revolution of Moon)

Our ancestors also divided the celestial sphere in to 27 divisions, called nakshathiram, as a means to describe the motion of moon across the sky. The moon rose in one segment each day taking 27 days to rise again in the same segment, hence the 27 parts of celestial sphere. A raasi, introduced in previous section, approximately covered the region of $2.5$ nakshathiram. Today, we know that moon takes approximately 27 days to revolve around earth, called the sidereal month. The 27 nakshathiram are as follows:

 No. Nakshathiram Constellation 1 Asvini 3 stars (horse face) 2 Barani or Apa Barani 3 stars (pot) 3 Krithigai or Krittika 6 stars (razor) 4 Rohini 5 stars (chariot) 5 Mrigaseersham or Mrigasira 3 stars (deer head) 6 Thiruvaadhirai or Aarudra 1 star (bead) 7 Punarpoosam or Punarvasu 5 stars (bow) 8 Poosam or Pushya 3 stars (ﬂower) 9 Aayilyam or Aslesha 6 stars (serpent) 10 Magam or Magha 5 stars (palanquin) 11 Pooram or Poorva Palguni 4 stars (leg of cot) 12 Uttaram or Uttara Palguni same as above 13 Hastham or Hastha 5 stars (palm) 14 Chithirai or Chitra 1 star (pearl) 15 Svaathi 1 star (sapphire) 16 Visaakam or Visaka 3 stars (potter wheel) 17 Anusham or Anuradha 3 stars (umbrella) 18 Kettai or Jyesta same as above 19 Moolam or Moola 6 stars (crouching lion) 20 Pooraadam or Poorvashada 4 stars (square) 21 Uttaraadam or Uttarashada same as above 22 Thiruvonam or Sravana 3 stars (arrow) 23 Avittam or Sravishta or Dhanista 4 stars (drum) 24 Sadhayam or Sathabishak 100 stars (ﬂower) 25 Poorataadhi or Poorva Broshtapadha 4 stars (leg of cot) 25 Uttarataadhi or Uttara Broshtapadha same as above 27 Revathi 3 stars (ﬁsh)
 No. Raasi Nakshathiram 1 Mesham Asvini Barani Krithigai (1/4) 2 Rishabam Krithigai (3/4) Rohini Mrigaseersham (1/2) 3 Mithunam Mrigaseersham (1/2) Thiruvaadhirai Punarpoosam (3/4) 4 Katakam Punarpoosam (1/4) Poosam Aayilyam 5 Simmam Magam Pooram Uttaram (1/4) 6 Kanni Uttaram Hastham Chithirai (1/2) 7 Thulaam Chithirai (1/2) Svaathi Visaakam (3/4) 8 Vrichigam Visaakam (1/4) Anusham Kettai 9 Dhanus Moolam Pooraadam Uttaraadam (1/4) 10 Makaram Uttaraadam (3/4) Thiruvonam Avittam (1/2) 11 Kumbham Avittam (1/2) Sadhayam Poorataadhi (3/4) 12 Meenam Poorataadhi (1/4) Uttarataadhi Revathi

A person’s janma nakshathiram or birth star is the nakshathiram on which moon rose (resided) on the day of his/her birthday. However, a careful note here is that the janma raasi of a person is not deﬁned as the raasi on which sun rose on his birthday. The janma raasi of a person is the raasi corresponding to the person’s janma nakshathiram. Thus, note that our birth-raasi is not same as the sun-sign (zodiac).

#### 1.4 Lunar and Solar Month (Revolution of Earth)

A thingal or lunar month (also called synodic month) is the period between two amavaasai(new moon) or pournami (full moon). The duration of a lunar month is approximately 29.5 days. The Tamil name for month is thingal and a synonym of Moon is thingal.

A solar month is the duration in which Sun rises with the same raasi as its backdrop. Today, we know that ignoring the spin of earth on its axis, the earth takes 30 days to shift from one raasi to the other. Thus, we have twelve months, each month symbolising the shift of earth on its orbit by 30 degrees. The tamil months are as follows, corresponding to the raasi in which earth (or sun) resides:

 S.No. Month number of days Modern duration 1 Cittirai (Mesham) 31 mid-April–mid-May 2 Vaikaci (Rishabam) 31 mid-May–mid-June 3 Aani (Mithunam) 32 mid-June–mid-July 4 Aadi (Katakam) 31 mid-July–mid-Aug 5 Aavani (Simmam) 31 mid-Aug–mid-Sept 6 Purattaci (Kanni) 31 mid-Sept–mid-Oct 7 Aippaci (Thulaam) 30 mid-Oct–mid-Nov 8 Karttikai (Vrichigam) 29 mid-Nov–mid-Dec 9 Markazhi (Dhanus) 30 mid-Dec–mid-Jan 10 Tai (Makaram) 29 mid-Jan–mid-Feb 11 Maci (Kumbham) 30 mid-Feb–mid-Mar 12 Pankuni (Meenam) 30 mid-Mar–mid-April

The name of tamil month is motivated from the nakshathiram on which moon rises on the pournami (full-moon) day of the tamil month.

The duration for the Sun to return to its rising raasi is one aaNdu or year. The number of days in a aaNdu is, approximately, 365 and 15 nazhigai, 31 vinaadi and 15 Tharparai where 1440 vinaadi makes one nazhigai and 60 Tharparai makes one vinaadi. Today, we know this is precisely the duration in which the Earth goes around Sun once, in its elliptical orbit. This duration is $11$ minutes short of $365\frac{1}{4}$ days. On some years, we have an excess day in Aadi or Aavani month to make 366 days in year to compensate the small error in each year.

The ﬁrst Tamil month starts in mid-April, the new year day. Why mid-April? The reason is to choose the month that has the same length of day and night. With modern precision and metric this may seem wrong! We know today that equal length of day and night happens when the Sun rises exactly in east and sets in west. Today, we know this happens exactly twice a year, one on March 21 and the other on September 23. Both these days have equal length of day and night. We also know the reason behind this phenomenon to be the inclination of the axis of rotation of earth by 23.25 degrees. Thus, in mid-Jul the latitude line 23.25 degrees north of equator, called tropic of Cancer, is where the Sun rises and sets. One ayanam is six months. As seen from Earth, Mid-July to mid-Jan is called dakshinaayanam, when sunrise is towards south-east. In mid-Jan the latitude line 23.25 degrees south of equator, called tropic of Capricon, is where the sun rises and sets. Mid-Jan to mid-July is called uttarayanam, when sunrise direction is towards north-east.

But recall that our ancestors calculated length of day (or night) based on the number of nazhigai. With a total of 60 nazhigai in one full day, if both day and night had 30 nazhigai’s each then they have the same length. This happens in the month of Cittirai and Aippaci. Then, why choose Cittirai as the ﬁrst month? Because the ﬁve months after Cittirai have days longer than night. Day gets the priority! Similarly, the ﬁve months after Aippaci have nights longer than day. There is a tamil poem which describes these aspects. It also gives the formula (vee-doo-poo-mu-di) to compute the number of nazhigai’s by which a day or night is longer in a particular month. Thus, it says: the day is longer in the months of Vaikaci, Aani, Aadi, Aavani and Purattaci by 18, 30, 36, 30 and 18 minutes, respectively; and the night is longer in the months of Karttikai, Markazhi, Tai, Maci and Pankuni by 18,30,36,30 and 18 minutes, respectively.

#### 1.5 Perum-pozhuthu, aaNdu, Yugam etc.

Recall that our ancestors had divided a complete day into six siRupozhuthu. Similarly, they had divided a year (aaNdu) into six perum-pozhuthu or seasons. Two thingal (or months) constituted one perum-pozhuthu or season. The six perum-pozhuthu in a aaNdu are:

 No. Season Description Period 1 ila-venil Light warmth (Vasantam) Mid Apr - Mid Jun 2 mudhu-venil Harsh warmth (Grishmam) Mid Jun - Mid Aug 3 kaar Dark clouds (Rain) Mid Aug - Mid Oct 4 kulir Chill, Cold (Sharadam) Mid Oct - Mid Dec 5 mun-pani Early dew (Hemantam) Mid Dec - Mid Feb 6 pin-pani Late dew (Sishiram) Mid Feb - Mid Apr

One vattam or century is made of 60 years. After every sixty years, the years are repeated, as we do in months and weeks. The 60 years are as follows:

 S.No. Year (Sanskrit) Name Tamil Name Period 1 Prabhava Nantrontral 1987–1988 2 Vibhava Uyarthontral 1988-1989 3 Sukla Velouli 1989-1990 4 Pramodoota Peruvagai 1990-1991 5 Prachorpaththi Makkatchelvam 1991-1992 6 Aangirasa Ayalmuni 1992-1993 7 Srimukha Thirumugam 1993-1994 8 Bhava Thotrram 1994-1995 9 Yuva Ilamai 1995-1996 10 Dhaatu Maazhai 1996-1997 11 Eesvara Eechchuram 1997-1998 12 Bahudhanya Kulavalam 1998-1999 13 Pramathi Munmai 1999-2000 14 Vikrama Nerniral 2000-2001 15 Vishu Vilaipayan 2001-2002 16 Chitrabaanu Oviyakathir 2002-2003 17 Subhaanu Narkathir 2003-2004 18 Dhaarana Thaangkezhil 2004-2005 19 Paarthiba Nilvaraiyan 2005-2006 20 Viya Virimaanbu 2006-2007 21 Sarvajith Mutrarivu 2007-2008 22 Sarvadhari Muzhuniraivu 2008-2009 23 Virodhi Theerpagai 2009-2010 24 Vikruthi Valmattram 2010-2011 25 Kara Seinerththi 2011-2012 26 Nandhana Narkuzhavi 2012-2013 27 Vijaya Uyarvaagai 2013-2014 28 Jaya Vaagai 2014-2015 29 Manmatha Kathanmai 2015-2016 30 Dhunmuki Vemmugam 2016-2017 31 Hevilambi Potradai 2017-2018 32 Vilambi Atti 2018-2019 33 Vikari Ezhilmaral 2019-2020 34 Sarvari Veeriyezhal 2020-2021 35 Plava Keezharai 2021-2022 36 Subakrith Narseikai 2022-2023 37 Sobakrith Mangalam 2023-2024 38 Krodhi Pagaikedu 2024-2025 39 Visuvaasuva Ulaganiraivu 2025-2026 40 Parabhaava Aruttotram 2026-2027 41 Plavanga Nachchupuzhai 2027-2028 42 Keelaka Pinaiviragu 2028-2029 43 Saumya Azhagu 2029-2030 44 Sadharana Pothunilai 2030-2031 45 Virodhikrithu Eegalveeru 2031-2032 46 Paridhaabi Kazhivirakkam 2032-2033 47 Pramaadhisa Natralaimai 2033-2034 48 Aanandha Perumagazhchi 2034-2035 49 Rakshasa Perumaram 2035-2036 50 Nala Thaamarai 2036-2037 51 Pingala Ponmai 2037-2038 52 Kalayukthi Karumaiveechchu 2038-2039 53 Siddharthi Munniyamudithal 2039-2040 54 Raudhri Azhali 2040-2041 55 Dunmathi Kodumathi 2041-2042 56 Dhundubhi Perikai 2042-2043 57 Rudhrodhgaari Odingi 2043-2044 58 Raktakshi Semmai 2044-2045 59 Krodhana Ethiretram 2045-2046 60 Akshaya Valangkalan 2046-2047

This is the reason for celebrating the $60$-th birthday of a person because he is supposed to have lived a century and moves in to the same year he was born. This is very similar to celebrating centenary birthdays.

The time is divided in to four yugams, viz.

1.
Krita/Sathya yugam ($17,28,000=4×4,32,000$ years)
2.
Tretha yugam ($12,96,000=3×4,32,000$ years)
3.
Dvaapara yugam ($8,64,000=2×4,32,000$ years)
4.
Kali yugam ($4,32,000$ years)

The four yugas together comprise one chaturyuga or maha-yuga, which comprises of 4.32 million years (4,320,000 years). Thousand maha-yugas constitute one “kalpam”, i.e., 4,320,000,000 (4.32 billion years). One kalpam is one day of Brahma and equal number of years for night, making a complete day of Brahma, a time period of 8.64 billion years. Manvantaram is one-fourteenth of a kalpam. According to Aryabhata (of 6th century), the kali-yuga started in 23 January, 3102 BCE of Gregorian calendar. This division of yugas is disputed by Swami Sri Yukteswar Giri in his book The Holy Science.

### 2 Panchangam

A day was ascribed 5 attributes called panchangam. The word is a combination of words “pancha” meaning ﬁve and “angam” meaning limbs. Thus, a day is determined by ﬁve factors, viz.,

1.
Tithi (Phase of moon)
2.
Nakshathiram (Home of moon)
3.
Kizhamai (day of week)
4.
Yogam
5.
Karnam (2 Karnam is one tithi)

#### 2.1 Tithi

We have already seen that the period between two amavasai (new moon) is 29.5 days (thingal or synodic month). This period has 15 days of waxing (sukhla paksham) and equal number of waning period (krishna paksham). These paksham is a Sanskrit name. A $15$ day period, in Tamil, is called azhuvam. Thus, the period is divided in to 14 tithis for both waxing and waning period. The zeroth starts at amavasai, followed by 14 thithis (waxing) and ﬁfteenth being pournami (full moon), followed by the same 14 tithis (waning), followed by amavaasai again. The names of the tithi are:

 S. No. Tithi 0 Amavasya, the new moon day 1 Prathamai 2 Dvithiyai 3 Thrithiyai 4 Chathurthi 5 Panchami 6 Sashti 7 Sapthami 8 Ashtami 9 Navami 10 Dasami 11 Ekaadasi 12 Dvaadasi 13 Thrayodasi 14 Chathurdasi 15 Pournami, the full moon day

After Pournami, the tithis once again go on from 1 to 14 to complete one cycle.

#### 2.2 Nakshathiram

We have already elaborated on what nakshathiram is and have already listed them. The Moon rises each day on a diﬀerent nakshtram. Thus, a day is distinguished based on the nakshathiram in which Moon rises that day.

#### 2.3 Kizhamai

Our ancestors were able to distinguish planets, from stars, by their motion in the celestial sphere. They identiﬁed what they called “nava graha” or nine planets. The ﬁrst seven of these planets are: Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn. In addition, our ancestors imagined two diametrically opposite points on the celestial sphere as Raahu and Kethu, respectively. This was to accommodate the occurrence of eclipses. These imaginary points were the intersection of the orbits of Sun and Moon in the celestial sphere.

They ordered the planets according to their speed in the celestial sphere. We have already seen that the sun takes approximately 30 days to shift from one raasi to other. We shall see the duration taken by every other planet to cover one raasi (and all 12 raasis):

1.
Moon 2.5 days (30 days)
2.
Mercury 30 days (one year)
3.
Venus 30 days (one year)
4.
Sun 30 days (one year)
5.
Mars 45 days (540 days or approx. 1.5 years)
6.
Jupiter one year (12 years)
7.
Rahu 1.5 years (18 years)
8.
Kethu 1.5 years (18 years)
9.
Saturn 2.5 years (30 years)

Thus ordering from slowest to fastest, we have: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. The time between sunrise and sunset is divided by 12 and sunset and next sunrise by 12 to get what is called planetary hours or horai. Each horai is ruled by the planets in the above order. The concept of a planet dominating (or ruling) an horai is not comprehensible to me. Suppose the ﬁrst horai after sunrise of a day is ruled by Saturn, we call it Saturday. The next horai is then ruled by Jupiter and so on, so that the 12th horai, at sunset, is ruled by Venus. Continuing this way, we see that the ﬁrst horai (or 25th horai) on the next day is ruled by Sun, called Sunday. In this procedure, the next day is Monday. Proceeding this way, we can identify a day as:

1.
Saturday (Saturn) Sani
2.
Sunday (Sun) Gnayayiru
3.
Monday (Moon) Thingal
4.
Tuesday (Mars) Sevvai
5.
Wednesday (Mercury) Pudhan
6.
Thursday (Jupiter) Viyazhan
7.
Friday (Venus) Velli

This attribute of a day is called kizhamai or week. The above explanation also justiﬁes the reason behind the speciﬁc order of the days of a week. This, probably, also explains why Friday was holiday being the last day of the week which, may be, changed after british politically took over the country.

#### 2.6 Raahu Kaalam and Yama Gandam

The Raahu kaalam and Yama gandam is calculated by dividing the duration between sunrise and sunset by 8, each division called the “octant”. Thus, each octant is approximately of 90 minutes duration (assuming 12 hours between sunrise and sunset). The raahu kaalm is assigned in following order:

 II octant Monday III octant Saturday IV octant Friday V octant Wednesday VI octant Thursday VII octant Tuesday VIII octant Sunday