The Hindus have had from very ancient times the system of lunisolar
cycles, made by the combination of solar years, regulated by the course
of the sun, and lunar years, regulated by the course of the moon, but
treated in such a manner as to keep the beginning of the lunar year near
the beginning of the solar year. The exact manner in which they arranged
the details of their earliest calendar is still a subject of research.
We deal here with their calendar as it now stands, in a form which was
developed from about A.D. 400 under the influence of the Greek astronomy
which had been introduced into India at no very long time previously.
The Hindu calendar, then, is determined by years of two kinds, solar and
lunar. For civil purposes, solar years are used in Bengal, including
Orissa, and in the Tamil and Malayalam districts of Madras, and lunar
years throughout the rest of India. But the lunar year regulates
everywhere the general religious rites and festivals, and the details of
private and domestic life, such as the selection of auspicious occasions
for marriages and for starting on journeys, the choice of lucky moments
for shaving, and so on. Consequently, the details of the lunar year are
shown even in the almanacs which follow the solar year. On the other
hand, certain details of the solar year, such as the course of the sun
through the signs and other divisions of the zodiac, are shown in the
almanacs which follow the lunar year. We will treat the solar year
first, because it governs the lunisolar system, and the explanation of
it will greatly simplify the process of explaining the lunar calendar.
The astronomical solar year.
The civil solar year is determined by the astronomical solar year. The
latter professes to begin at the vernal equinox, but the actual position
is as follows. In our Western astronomy the signs of the zodiac have, in
consequence of the precession of the equinoxes, drawn away to a large
extent from the constellations from which they derived their names; with
the result that the sun now comes to the vernal equinox, at the first
point of the sign Aries, not in the constellation Aries, but at a point
in Pisces, about 28 degrees before the beginning of Aries. The Hindus,
however, have disregarded precession in connexion with their calendar
from the time (A.D. 499, 522, or 527, according to different schools)
when, by their system, the signs coincided with the constellations; and
their sign Aries, called Mesha by them, is still their constellation
Aries, beginning, according to them, at or near the star [zeta] Piscium.
Their astronomical solar year is, in fact, not the tropical year, in the
course of which the sun really passes from one vernal equinox to the
next, but a sidereal year, the period during which the earth makes one
revolution in its orbit round the sun with reference to the first point
of Mesha; its beginning is the moment of the Mesha-samkranti, the
entrance of the sun into the sidereal sign Mesha, instead of the
tropical sign Aries; and it begins, not with the true equinox, but with
an artificial or nominal equinox.
The length of this sidereal solar year was determined in the following
manner. The astronomer selected what the Greeks termed an _exeligmos_,
the Romans an _annus magnus_ or _mundanus_, a period in the course of
which a given order of things is completed by the sun, moon, and planets
returning to a state of conjunction from which they have started. The
usual Hindu _exeligmos_ has been the Great Age of 4,320,000 sidereal
solar years, the aggregate of the Krita or golden age, the Treta or
silver age, the Dvapara or brazen age, and the Kali or iron age, in
which we now are; but it has sometimes been the Kalpa or aeon,
consisting according to one view of 1000, according to another view of
1008, Great Ages. He then laid down the number of revolutions, in the
period of his _exeligmos_, of the _nakshatras_, certain stars and groups
of stars which will be noticed more definitely in our account of the
lunar year; that is, the number of rotations of the earth on its axis,
or, in other words, the number of sidereal days. A deduction of the
number of the years from the number of the sidereal days gave, as
remainder, the number of civil days in the _exeligmos_. And, this
remainder being divided by the number of the years, the quotient gave
the length of the sidereal solar year: refinements, suggested by
experience, inference, or extraneous information, were made by
increasing or decreasing the number of sidereal days assigned to the
_exeligmos_. The Hindus now recognize three standard sidereal solar
years determined in that manner. (1) A year of 365 days 6 hrs. 12 min.
30 sec. according to the _Aryabhatiya_, otherwise called the _First
Arya-Siddhanta_, which was written by the astronomer Aryabhata (b. A.D.
476): this year is used in the Tamil and Malayalam districts, and, we
may add, in Ceylon. (2) A year of 365 days 6 hrs. 12 min. 30.915 sec.
according to the _Rajamriga ka_, a treatise based on the
_Brahma-Siddhanta_ of Brahmagupta (b. A.D. 598) and attributed to king
Bhoja, of which the epoch, the point of time used in it for
calculations, falls in A.D. 1042: this year is used in parts of Gujarat
(Bombay) and in Rajputana and other western parts of Northern India. (3)
A year of 365 days 6 hrs. 12 min. 36.56 sec. according to the present
_Surya-Siddhanta_, a work of unknown authorship which dates from
probably about A.D. 1000: this year is used in almost all the other
parts of India. It may be remarked that, according to modern science,
the true mean sidereal solar year measures 365 days 6 hrs. 9 min. 9.6
sec., and the mean tropical year measures 365 days 5 hrs. 48 min.
46.054440 sec.
The result of the use of this sidereal solar year is that the beginning
of the Hindu astronomical solar year, and with it the civil solar year
and the lunar year and the nominal incidence of the seasons, has always
been, and still is, travelling slowly forward in our calendar year by an
amount which varies according to the particular authority.[1] For
instance, Aryabhata's year exceeds the Julian year by 12 min. 30 sec.
This amounts to exactly one day in 115(1/5) years, and five days in 576
years. Thus, if we take the longer period and confine ourselves to a
time when the Julian calendar (old style) was in use, according to
Aryabhata the Mesha-samkranti began to occur in A.D. 603 on 20th March,
and in A.D. 1179 on 25th March. The intermediate advances arrange
themselves into four steps of one day each in 116 years, followed by one
step of one day in 112 years: thus, the Mesha-samkranti began to occur
on 21st March in A.D. 719, on 22nd March in A.D. 835, on 23rd March in
A.D. 951, and on 24th March in A.D. 1067 (whence 112 years take us to
25th March in A.D. 1179). It is now occurring sometimes on 11th April,
sometimes on the 12th; having first come to the 12th in A.D. 1871.
The civil solar year.
The civil solar year exists in more varieties than one. The principal
variety, conveniently called the Meshadi year, i.e. "the year beginning
at the Mesha-samkranti," is the only one that we need notice at this
point. The beginning of it is determined directly by the astronomical
solar year; and for religious purposes it begins, with that year, at the
moment of the Mesha-samkranti. Its first civil day, however, may be
either the day on which the _samkranti_ occurs, or the next day, or even
the day after that: this is determined partly by the time of day or
night at which the _samkranti_ occurs, which, moreover, of course varies
in accordance with the locality as well as the particular authority that
is followed; partly by differing details of practice in different parts
of the country. In these circumstances an exact equivalent of the
Meshadi civil solar year cannot be stated; but it may be taken as now
beginning on or closely about the 12th of April.
The solar month.
The solar year is divided into twelve months, in accordance with the
successive _samkrantis_ or entrances of the sun into the (sidereal)
signs of the zodiac, which, as with us, are twelve in number. The
names of the signs in Sanskrit are as follows: Mesha, the ram (Aries);
Vrishabha, the bull (Taurus); Mithuna, the pair, the twins (Gemini);
Karka, Karkata, Karkataka, the crab (Cancer); Simha, the lion (Leo);
Kanya, the maiden (Virgo); Tula, the scales (Libra); Vrischika, the
scorpion (Scorpio); Dhanus, the bow (Sagittarius); Makara, the
sea-monster (Capricornus); Kumbha, the water-pot (Aquarius); and Mina,
the fishes (Pisces). The solar months are known in some parts by the
names of the signs or by corrupted forms of them; and these are the
best names for them for general use, because they lead to no
confusion. But they have elsewhere another set of names, preserving
the connexion of them with the lunar months: the Sanskrit forms of
these names are Chaitra, Vaisakha, Jyaishtha, Ashadha, Sravana,
Bhadrapada, Asvina or Asvayuja, Karttika, Margasira or Margasirsha
(also known as Agrahayana), Pausha, Magha, and Phalguna: in some
localities these names are used in corrupted forms, and in others
vernacular names are substituted for some of them; and, while in some
parts the name Chaitra is attached to the month Mesha, in other parts
it is attached to the month Mina, and so on throughout the series in
each case. The astronomical solar month runs from the moment of one
_samkranti_ of the sun to the moment of the next _samkranti_; and, as
the signs of the Hindu zodiac are all of equal length, 30 degrees, as
with us, while the speed of the sun (the motion of the earth in its
orbit round the sun) varies according to the time of the year, the
length of the month is variable: the shortest month is Dhanus; the
longest is Mithuna. The civil solar month begins with its first civil
day, which is determined, in different localities, in the same manner
with the first civil day of the Meshadi year, as indicated above. The
civil month is of variable length; partly for that reason, partly
because of the variation in the length of the astronomical month. No
exact equivalents of the civil months, therefore, can be stated; but,
speaking approximately, we may say that, while the month Mesha now
begins on or closely about 12th April, the beginning of a subsequent
month may come as late as the 16th day of the English month in which
it falls.
The seasons.
The solar year is also divided into six seasons, the Sanskrit names of
which are Vasanta, spring; Grishma, the hot weather; Varsha, the rainy
season; Sarad, autumn; Hemanta, the cold weather; and Sisira, the dewy
season. Vasanta begins at the Mina-samkranti; the other seasons begin
at each successive second _samkranti_ from that. Originally, this
scheme was laid out with reference to the true course of the sun, and
the starting-point of it was the real winter solstice, with Sisira, as
the first season, beginning then; now, owing partly to the disregard
of precession, partly to our introduction of New Style, each season
comes about three weeks too late; Vasanta begins on or about 12th
March, instead of 19th or 20th February, and so on with the rest. It
may be added that in early times the year was also divided into three
or four, and even into five or seven, seasons; and there appears to
have been also a practice of reckoning the seasons according to the
lunar months, which, however, would only give a very varying
arrangement, in addition to neglecting the point that the seasons are
naturally determined by the course of the sun, not of the moon. But
there is now recognized only the division into six seasons, determined
as stated above.
The solstitial divisions of the year.
The solar year is also divided into two parts called Uttarayana, the
period during which the sun is moving to the north, and Dakshinayana,
the period during which it is moving to the south. The Uttarayana
begins at the nominal winter solstice, as marked by the
Makara-samkranti; and the day on which this solstice occurs, usually
12th January at present, is still a special occasion of festivity and
rejoicing; the Dakshinayana begins at the nominal summer solstice, as
marked by the Karka-samkranti. It may be added here that, while the
Hindus disregard precession in the actual computation of their years
and the regulation of their calendar, they pay attention to it in
certain other respects, and notably as regards the solstices: the
precessional solstices are looked upon as auspicious occasions, as
well as the non-precessional solstices, and are customarily shown in
the almanacs; and some of the almanacs show also the other
precessional _samkrantis_ of the sun.
The civil day.
The civil days of the solar month begin at sunrise. They are numbered
1, 2, 3, &c., in unbroken succession to the end of the month. And, the
length of the month being variable for the reasons stated above, the
number of the civil days may range from twenty-nine to thirty-two.
The weekday.
The civil days are named after the weekdays, of which the usual
appellations (there are various synonyms in each case, and some of the
names are used in corrupted forms) are in Sanskrit Adityavara or
Ravivara, the day of the sun, sometimes called Adivara, the
beginning-day (Sunday); Somavara, the day of the moon (Monday);
Mangalavara, the day of Mars (Tuesday); Budhavara, the day of Mercury
(Wednesday); Brihas-pativara or Guruvara, the day of Jupiter
(Thursday); Sukravara, the day of Venus (Friday); and Sanivara, the
day of Saturn (Saturday). It may be mentioned, as a matter of
archaeological interest, that, while some of the astronomical books
perhaps postulate an earlier knowledge of the "lords of the days," and
other writings indicate a still earlier use of the period of seven
days, the first proved instance of the use of the name of a weekday is
of the year A.D. 484, and is furnished by an inscription in the Saugor
district, Central India.
Divisions of the day.
The divisions of the civil day, as far as we need note them, are 60
_vipalas_ = 1 _pala_ = 24 seconds; 60 _palas_ = 1 _ghatika_ = 24
minutes; 60 _ghatikas_ = 24 hours = 1 day. There is also the _muhurta_
= 2 _ghatikas_ = 48 minutes: this is the nearest approach to the
"hour." The comparative value of these measures of time may perhaps be
best illustrated thus: 2(1/2) _muhurtas_ = 2 hours; 2(1/2) _ghatikas_
= 1 hour; 2(1/2) _palas_ = 1 minute; 2(1/2) _vipalas_ = 1 second.
Civil time.
As their civil day begins at sunrise, the Hindus naturally count all
their times, in _ghatikas_ and _palas_, from that moment. But the
moment is a varying one, though not in India to anything like the
extent to which it is so in European latitudes; and under the British
Government the Hindus have recognized the advantage, and in fact the
necessity, especially in connexion with their lunar calendar, of
having a convenient means of referring their own times to the time
which prevails officially. Consequently, some of the almanacs have
adopted the European practice of showing the time of sunrise, in hours
and minutes, from midnight; and some of them add the time of sunset
from noon.
The lunar year.
The lunar year consists primarily of twelve lunations or lunar months,
of which the present Sanskrit names, generally used in more or less
corrupted forms, are Chaitra, Vaisakha, &c., to Phalguna, as given above
in connexion with the solar months. It is of two principal varieties,
according as it begins with a certain day in the month Chaitra, or with
the corresponding day in Karttika: the former variety is conveniently
known as the Chaitradi year; the latter as the Karttikadi year. For
religious purposes the lunar year begins with its first lunar day: for
civil purposes it begins with its first civil day, the relation of which
to the lunar day will be explained below. Owing to the manner in which,
as we shall explain, the beginning of the lunar year is always shifting
backwards and forwards, it is not practicable to lay down any close
equivalents for comparison: but an indication may be given as follows.
The first civil day of the Chaitradi year is the day after the new-moon
conjunction which occurs next after the entrance of the sun into Mina,
and it now falls from about 13th March to about 11th April: the first
civil day of the Karttikadi year is the first day after the new-moon
conjunction which occurs next after the entrance of the sun into Tula,
and it now falls from about 17th October to about 15th November.
The lunar month.
The present names of the lunar months, indicated above, were derived
from the _nakshatras_, which are certain conspicuous stars and groups
of stars lying more or less along the neighbourhood of the ecliptic.
The _nakshatras_ are regarded sometimes as twenty-seven in number,
sometimes as twenty-eight, and are grouped in twelve sets of two or
three each, beginning, according to the earlier arrangement of the
list, with the pair Krittika and Rohini, and including in the sixth
place Chitra and Svati, and ending with the triplet Revati, Asvini and
Bharani. They are sometimes styled lunar mansions, and are sometimes
spoken of as the signs of the lunar zodiac; and it is, no doubt,
chiefly in connexion with the moon that they are now taken into
consideration. But they mark divisions of the ecliptic: according to
one system, twenty-seven divisions, each of 13 degrees 20 minutes;
according to two other systems, twenty-seven or twenty-eight unequal
divisions, which we need not explain here. The almanacs show the
course of the sun through them, as well as the course of the moon; and
the course of the sun was marked by them only, before the time when
the Hindus began to use the twelve signs of the solar zodiac. So there
is nothing exclusively lunar about them. The present names of the
lunar months were derived from the _nakshatras_ in the following
manner: the full-moon which occurred when the moon was in conjunction
with Chitra (the star [alpha] Virginis) was named Chaitri, and the
lunar month, which contained the Chaitri full-moon, was named Chaitra;
and so on with the others. The present names have superseded another
set of names which were at one time in use concurrently with them;
these other names are Madhu (= Chaitra), Madhava, Sukra, Suchi,
Nabhas, Nabhasya, Isha, Urja (= Karttika), Sahas, Sahasya, Tapas, and
Tapasya (= Phalguna): they seem to have marked originally solar
season-months of the solar year, rather than lunar months of the lunar
year.
A lunar month may be regarded as ending either with the new-moon,
which is called _amavasya_, or with the full-moon, which is called
_purnamasi_, _purnima_: a month of the former kind is termed _amanta_,
"ending with the new-moon," or _sukladi_, "beginning with the bright
fortnight;" a month of the latter kind is termed purnimanta, "ending
with the full-moon," or _krishnadi_, "beginning with the dark
fortnight." For all purposes of the calendar, the _amanta_ month is
used in Southern India, and the _purnimanta_ month in Northern India.
But only the _amanta_ month, the period of the synodic revolution of
the moon, is recognized in Hindu astronomy, and for the purpose of
naming the lunations and adjusting the lunar to the solar year by the
intercalation and suppression of lunar months; and the rule is that
the lunar Chaitra is the _amanta_ or synodic month at the first moment
of which the sun is in the sign Mina, and in the course of which the
sun enters Mesha: the other months follow in the same way; and the
lunar Karttika is the _amanta_ month at the first moment of which the
sun is in Tula, and in the course of which the sun enters Vrischika.
The connexion between the lunar and the solar months is maintained by
the point that the name Chaitra is applied according to one practice
to the solar Mina, in which the lunar Chaitra begins, and according to
another practice to the solar Mesha, in which the lunar Chaitra ends.
Like the lunar year, the lunar month begins for religious purposes
with its first lunar day, and for civil purposes with its first civil
day.
Intercalation and suppression of lunar months.
One mean lunar year of twelve lunations measures very nearly 354 days
8 hrs. 48 min. 34 sec.; and one Hindu solar year measures 365 days 6
hrs. 12 min. 30 sec. according to Aryabhata, or slightly more
according to the other two authorities. Consequently, the beginning of
a lunar year pure and simple would be always travelling backwards
through the solar year, by about eleven days on each occasion, and
would in course of time recede entirely through the solar year, as it
does in the Mahommedan calendar. The Hindus prevent that in the
following manner. The length of the Hindu astronomical solar month,
measured by the _samkrantis_ of the sun, its successive entrances into
the signs of the zodiac, ranges, in accordance with periodical
variations in the speed of the sun, from about 29 days 7 hrs. 38 min.
up to about 31 days 15 hrs. 28 min. The length of the _amanta_ or
synodic lunar month ranges, in accordance with periodical variations
in the speed of the moon and the sun, from about 29 days 19 hrs. 30
min. down to about 29 days 7 hrs. 20 min. Consequently, it happens
from time to time that there are two new-moon conjunctions, so that
two lunations begin, in one astronomical solar month, between two
_samkrantis_ of the sun, while the sun is in one and the same sign of
the zodiac, and there is no _samkranti_ in the lunation ending with
the second new-moon: when this is the case, there are two lunations to
which the same name is applicable, and so there is an additional or
intercalated month, in the sense that a name is repeated: thus, when
two new-moons occur while the sun is in Mesha, the lunation ending
with the first of them, during which the sun has entered Mesha, is
Chaitra; the next lunation, in which there is no _samkranti_, is
Vaisakha, because it begins when the sun is in Mesha; and the next
lunation after that is again Vaisakha, for the same reason, and also
because the sun enters Vrishabha in the course of it: in these
circumstances, the first of the two Vaisakhas is called
Adhika-Vaisakha, "the additional or intercalated Vaisakha," and the
second is called simply Vaisakha, or sometimes Nija-Vaisakha, "the
natural Vaisakha." On the other hand, it occasionally happens, in an
autumn or winter month, that there are two _samkrantis_ of the sun in
one and the same _amanta_ or synodic lunar month, between two new-moon
conjunctions, so that no lunation begins between the two _samkrantis_:
when this is the case, there is one lunation to which two names are
applicable, and there is a suppressed month, in the sense that a name
is omitted: thus, if the sun enters both Dhanus and Makara during one
synodic lunation, that lunation is Margasira, because the sun was in
Vrischika at the first moment of it and enters Dhanus in the course of
it;[2] the next lunation is Magha, because the sun is in Makara by the
time when it begins and will enter Kumbha in the course of it; and the
name Pausha, between Margasira and Magha, is omitted. When a month is
thus suppressed, there is always one intercalated month, and sometimes
two, in the same Chaitradi lunar year, so that the lunar year never
contains less than twelve months, and from time to time consists of
thirteen months. There are normally seven intercalated months, rising
to eight when a month is suppressed, in 19 solar years, which equal
very nearly 235 lunations;[3] and there is never less than one year
without an intercalated month between two years with intercalated
months, except when there is only one such month in a year in which a
month is suppressed; then there is always an intercalated month in the
next year also. The suppression of a month takes place at intervals of
19 years and upwards, regarding which no definite statement can
conveniently be made here. It may be added that an intercalated
Chaitra or Karttika takes the place of the ordinary month as the first
month of the year; an intercalated month is not rejected for that
purpose, though it is tabooed from the religious and auspicious points
of view.
The manner in which this arrangement of intercalated and suppressed
months works out, so as to prevent the beginning of the Chaitradi
lunar year departing far from the beginning of the Meshadi solar
year, may be illustrated as follows. In A.D. 1815 the Mesha-samkranti
occurred on 11th April; and the first civil day of the Chaitradi year
was 10th April. In A.D. 1816 and 1817 the first civil day of the
Chaitradi year fell back to 29th March and 18th March. In A.D. 1817,
however, there was an intercalated month, Sravana; with the result
that in A.D. 1818 the first civil day of the Chaitradi year advanced
to 6th April. And, after various shiftings of the same kind--including
in A.D. 1822 an intercalation of Asvina and a suppression of Pausha,
followed in A.D. 1823, when the first civil day of the Chaitradi year
had fallen back to 13th March, by an intercalation of Chaitra
itself--in A.D. 1834, when the Mesha-samkranti occurred again on 11th
April, the first civil day of the Chaitradi year was again 10th April.
The lunar fortnight.
The lunar month is divided into two fortnights (_paksha_), called
bright and dark, or, in Indian terms, _sukla_ or _suddha_, _sudi_,
_sudi_, and _krishna_ or _bahula_, _badi_, _vadi_: the bright
fortnight, _sukla-paksha_, is the period of the waxing moon, ending at
the full-moon; the dark fortnight, _krishna-paksha_, is the period of
the waning moon, ending at the new-moon. In the _amanta_ or _sukladi_
month, the bright fortnight precedes the dark; in the _purnimanta_ or
_krishnadi_ month, the dark fortnight comes first; and the result is
that, whereas, for instance, the bright fortnight of Chaitra is the
same period of time throughout India, the preceding dark fortnight is
known in Northern India as the dark fortnight of Chaitra, but in
Southern India as the dark fortnight of Phalguna. This, however, does
not affect the period covered by the lunar year; the Chaitradi and
Karttikadi years begin everywhere with the bright fortnight of Chaitra
and Karttika respectively; simply, by the _amanta_ system the dark
fortnights of Chaitra and Karttika are the second fortnights, and by
the _purnimanta_ system they are the last fortnights, of the years.
Like the month, the fortnight begins for religious purposes with its
first lunar day, and for civil purposes with its first civil day.
The lunar day.
The lunar fortnights are divided each into fifteen tithis or lunar
days.[4] The _tithi_ is the time in which the moon increases her
distance from the sun round the circle by twelve degrees; and the
almanacs show each _tithi_ by its ending-time; that is, by the moment,
expressed in _ghatikas_ and _palas_, after sunrise, at which the moon
completes that distance. In accordance with that, the _tithi_ is
usually used and cited with the weekday on which it ends; but there
are special rules regarding certain rites, festivals, &c., which
sometimes require the _tithi_ to be used and cited with the weekday on
which it begins or is current at a particular time. The first _tithi_
of each fortnight begins immediately after the moment of new-moon and
full-moon respectively; the last _tithi_ ends at the moment of
full-moon and new-moon. The _tithis_ are primarily denoted by the
numbers 1, 2, 3, &c., for each fortnight; but, while the full-moon
_tithi_ is always numbered 15, the new-moon _tithi_ is generally
numbered 30, even where the _purnimanta_ month is used. The _tithis_
may be cited either by their figures or by the Sanskrit ordinal words
_prathama_, "first," _dvitiya_, "second," &c., or corruptions of them.
But usually the first _tithi_ of either fortnight is cited by the term
_pratipad_, _pratipada_, and the new-moon and full-moon _tithis_ are
cited by the terms _amavasya_ and _purnima_; or here, again,
corruptions of the Sanskrit terms are used. And special names are
sometimes prefixed to the numbers of the _tithis_, according to the
rites, festivals, &c., prescribed for them, or events or merits
assigned to them: for instance, Vaisakha sukla 3 is Akshaya or
Akshayya-tritiya, the third _tithi_ which ensures permanence to acts
performed on it; Bhadrapada sukla 4 is Ganesa-chaturthi, the fourth
_tithi_ dedicated to the worship of the god Ganesa, Ganapati, and the
_amanta_ Bhadrapada or _purnimanta_ Asvina krishna 13 is
Kaliyugadi-trayodasi, as being regarded (for some reason which is not
apparent) as the anniversary of the beginning of the Kaliyuga, the
present Age. The first _tithi_ of the year is styled
Samvatsara-pratipada, which term answers closely to our "New Year's
Day."
The civil day.
The civil days of the lunar month begin, like those of the solar
month, at sunrise, and bear in the same way the names of the weekdays.
But they are numbered in a different manner; fortnight by fortnight
and according to the _tithis_. The general rule is that the civil day
takes the number of the _tithi_ which is current at its sunrise. And
the results are as follows. As the motions of the sun and the moon
vary periodically, a tithi is of variable length, ranging, according
to the Hindu calculations, from 21 hrs. 34 min. 24 sec. to 26 hrs. 6
min. 24 sec.: it may, therefore, be either shorter or longer than a
civil day, the duration of which is practically 24 hours (one minute,
roughly, more or less, according to the time of the year). A _tithi_
may end at any moment during the civil day; and ordinarily it ends on
the civil day after that on which it begins, and covers only one
sunrise and gives its number to the day on which it ends. It may,
however, begin on one civil day and end on the next but one, and so
cover two sunrises; and it is then treated as a repeated _tithi_, in
the sense that its number is repeated: for instance, if the seventh
_tithi_ so begins and ends, the civil day on which it begins is
numbered 6, from the _tithi_ which is current at the sunrise of that
day and ends on it; the day covered entirely by the seventh _tithi_ is
numbered 7, because that _tithi_ is current at its sunrise; the next
day, at the sunrise of which the seventh _tithi_ is still current and
during which it ends, is again numbered 7; and the number 8 falls to
the next day after that, when the eighth tithi is current at
sunrise.[5] On the other hand, a _tithi_ may begin and end during one
and the same civil day, so as not to touch a sunrise at all: in this
case, it exists for any practical purposes for which it may be wanted
(it is, however, to be avoided if possible, as being an unlucky
occasion), but it is suppressed or expunged for the numbering of the
civil day, in the sense that its number is omitted; for instance, if
the seventh _tithi_ begins and ends during one civil day, that day is
numbered 6 from, as before, the _tithi_ which is current at its
sunrise and ends when the seventh _tithi_ begins; the next day is
numbered 8, because the eighth _tithi_ is current at its sunrise; and
there is, in this case, no civil day bearing the number seven. In
consequence of this method of numbering, it sometimes happens, as the
result of the suppression of a _tithi_, that the day of a full-moon is
numbered 14 instead of 15; that the day of a new-moon is numbered 14
instead of 30; and that the first day of a fortnight, and even the
first day of a lunar year, is numbered 2 instead of 1.
There are, on an average, thirteen suppressed _tithis_ and seven
repeated _tithis_ in twelve lunar months; and so the lunar year
averages 354 days, rising to about 384 when a month is intercalated.
It occasionally happens that there are two suppressions of _tithis_ in
one and the same fortnight; and the almanacs show such a case in the
bright fortnight of Jyaishtha, A.D. 1878: but this occurs only after
very long intervals.
The Karana.
The _tithi_ is divided into two _karanas_; each _karana_ being the
time in which the moon increases her distance from the sun by six
degrees. But this is a detail of astrological rather than
chronological interest. So, also, are two other details to which a
prominent place is given in the lunar calendars; to yoga, or time in
which the joint motion in longitude, the sum of the motions of the sun
and the moon, is increased by 13 degrees 20 minutes; and the
_nakshatra_, the position of the moon as referred to the ecliptic by
means of the stars and groups of stars which have been mentioned above
under the lunar month.
In the Indian calendar everything depends upon exact times, which
differ, of course, on every different meridian; and (to cite what is
perhaps the most frequent and generally important occurrence)
suppression and repetition may affect one _tithi_ and civil day in one
locality, and another _tithi_ and civil day in another locality not
very far distant. Consequently, neither for the lunar nor for the
solar calendar is there any almanac which is applicable to even the
whole area in which any particular length of the astronomical solar
year prevails; much less, for the whole of India. Different almanacs
are prepared and published for places of leading importance; details
for minor places, when wanted, have to be worked out by the local
astrologer, the modern representative of an ancient official known as
Sammvatsara, the "clerk of the year."