सिद्धान्तदर्पण (महामहोपाध्याय सामन्त चन्द्रशेखर सिंह - नग्न-नेत्र खगोल वेध एवं गणित महाकोश)

xxvi सिद्धान्त दर्पण
with his work for the full period of six years, and
the first copy was not ready before he was thirty.
This constant strain upon his body which had
never been strong began to undermine his system.
He contracted a disease which has been his constant
companion. Besides, the privations he had to bear,
consequent upon his scrupulous adherence to the
Sastric injunctions of strict vegetarianism, proved
too much for his naturally weak system. Dyspepsia
with its attendant colic has impaired his health. At
times it becomes so painful that he is compelled to
break off conversation and roll down on the ground
till the attack is over. Full meals, frugal as they are,
he has not enjoyed for the last thirty years, and has
seldom permitted himself the indulgence of even
half meals twice a day. The study of astronomy has
been a passion with him, and any medicine you
may prescribe for him, must neither contain any
forbidden ingredient, nor, what is more important,
interfere with his daily work. Even in his present
invalid stale he would willingly sit up a whole night
if it were for anything connected with his favourite
subject. When he came here to receive the title of
honour conferred upon him, he could not be
persuaded to stay a single day after the Durbar, as
an eclipse of the Sun was to occur a few days later.
And how could he stay away from his observatory,
and allow such a momentous event to pass by
unnoticed ?
His naive simplicity and unassuming manners
have rather been a drawback than an advantage to
him. The common people, who do not understand
the difference between astrology and astronomy,
pester him so much with questions on their destiny,
that it is only his amiable disposition that makes

Introduction xxvii
him endure the constant infliction. Even those who
might be expected to know better will not scruple
to ply him with absurd questions and waste the few
moments left to him between the beginning of one
series of daily devotions and the end of another.
If he is a practical mathematician, no one is so
unpractical in worldly matters as he is. Simple as a
child, he depends upon his servants for his
guidance. Neither is he well off, in the sense of
possessing a competency in life; and, related as he
is to a Raja, he is unable to make both ends meet.
A retinue of attendant hereditarily maintained in
his family has to be supported in the usual manner.
The small income of Rs.500 a year from a few small
villages, and a quantity of food grains from his
tenants, are hardly sufficient in these days of high
prices. Poverty has pinched him in his old age and
has compelled him to incur a large debt.
The general public does not care to know his
incomings and outgoings, his privations and
star-gazings. “What has he done after all ?” - asks
the impatient critic. To him, I would say, is it not
enough to find in this man a true lover of science
who regardless of other peoples unfavourable
opinion of his work their taunts and dissusions, has
devoted his whole life to the one pursuit of
knowledge; who has shown the way to original
research amidst difficulties serious enough to
dishearten men in better circumstances who has
employed his time usefully, instead of frittering it
away like the usual run of men of his rank, on a
work which guides the daily routine of millions of
his countrymen ?
I do not pretend to express any opinion on the
literary merits of his work but it appears to me that

xxviii सिद्धान्त दर्पण
the metrical composition alone, apart from its value
as a contribution to Hindu astronomy is such as to
entitle him to a high place among the writers of
Sanskrit verse of the present day. It contains, as he
tells us at the end of the work, 2,500 slokas of
various poetical metres. Of these 2,284 verses have
been composed by him and the remaining 216
quoted from the old Siddhantas. Of the latter, the
Surya-Siddhanta and the Siddhanta-Siromani have
been very largely drawn upon. Indeed, as Bhaskara
has Brahmagupta for his guide, when writing his
Siromani, Chandrasekhara has, in the main,
followed in the footsteps of Bhaskara.
But Chandrasekhara has not been a blind
follower of his master. The elements of the planets,
given by Bhaskara, have not been accepted by his
disciple, and for the simple reason, that they are
not correct for the present day. Bhaskara's elements
are not accurate, though there is no reason for
doubting the accuracy of his observations. This fact
is, he had to depend upon his predecessors -
probably Brahmagupta was his main guide - for the
positions of the planets and was thus led to
erroneous results.
Chandrasekhara had the advantage of
Bhaskara's observations. The latter has, of course,
nowhere recorded his observations. But given his
date and his elements, it is easy to find the positions
of the planets as he must have observed them. For
the elements if employed to calculate the positions
of the planets after a long interval, may lead us to
wrong results; but, it employed for places nearer
his time, will be in accordance with his observations.
Thus, furnished with one set of position at a given
date, Chandrasekhara himself supplied the other

Introduction xxix
set required, and the result obtained is what
Chandrasekhara has given us in the present work.
For easy reference, the sidereal periods as he
ascertained them, are given below side by side with
those of European astronomy, the Surya-Siddhanta
and the Siddhanta-Siromani. It is not my object to
criticise how far the constant employed in these two
Siddhantas were true when they were observed,
though it will be clear from the comparison that
they are certainly erroneous for the present time. It
is easy to follow when someone has led the way;
but it needed the art of a rural Pandit, guiltless of
western "fire" to prove their incorrectness and to
pave the way for further progress in this
department. (See table 1)
It will be seen from the above that Chandra-
sekhara has practically assumed the sidereal periods
of the Sun and the Moon, as given in the
Surya-Siddhanta, but has materially advanced upon
it as regards the periods of the other planets.
Having regard to the comparatively slow motion of
Jupiter and of Saturn, and the nature of the
instruments used, it would have been a surprise if
closer approximation to their true periods were
made.
Let us now compare the mean inclinations of
the orbits of the planets to the ecliptic.(See Table 2)
On account of the difference in the planetary
theories and in the method of calculation between
modern astronomy and our Siddhantas, the
eccentricities of the planetary orbits cannot be
compared with advantage. But as they made no
difference in the case of the Sun and the Moon,
their greatest equations are given here for
comparison. (See Table 3)

सिद्धान्त दर्पण
(TABLE I)
SIDERAL PERIODS IN MEAN SOLAR DAYS

Introduction xxxi
TABLE 2

| | Eng.Ast. | Surya S. | Siromani | Darpana |

| Mercury* ... | 7° 0' 8'' | 5° 55' | 6° 55' | 7° 2' |
| Venus* ... | 3 53 35 | 2 46 | 3 6 | 3 23 |
| Mars ... | 1 51 2 | 1 30 | 1 50 | 1 51 |
| Jupiter ... | 1 18 41 | 1 0 | 1 16 | 1 18 |
| Saturn ... | 2 29 40 | 2 0 | 2 40 | 2 29 |
| Moon ... | 5 8 48 | 4 30 | 4 30 | 5 9 |
| Obliquity of ... | 23 27 | 24 0 | 24 0 | 23 30 |
| the Ecliptic | | | | |

The inclination given in the Siddhantas is reduced to the geocentric system. The general reader may be reminded that the inclinations
are all subject to variation and that the old Siddhanta values were not so far wide of the truth as they appear from the table.
TABLE 3

| | English Astronomy | Surya-Siddhanta** | Siddhanta Darpana** |

| Sun ... | 1° 55' 19'' | 2° 10' 31'' | 1 55' 33'' |
| Moon ... | 6 3 41 | 5 2 46 | 5 1 10 |

** According to Siromoni, the Sun's equation is the same as is shown under Surya-Siddhanta and the Moon's equation is slightly less.

xxxii . सिद्धान्त दर्पण
It will be needless to compare the rates of
motion of the nodes and apsides. It is possible for
modern European astronomy, with instruments
enabling it with ease to measure the three thousand
and six hundredth part of a degree and with its
engines of higher methematics to handle intricate
problems, unheard of before, to deduce the
elements of orbits from a very few observations
made at no distant dates. But it requires the lapse
of years - nay centuries - to do the same with
primitive instruments and equally primitive
mathematics. The motions of the nodes and apsides
are so slow that Bhaskara despaired of ever
measuring them. Chandrashekhara was equally in
despair in these cases. But as the positions of the
Moon's nodes and perigee are often required, and
their motions comparatively rapid, I quote their
side-real period in mean solar days.
              Eng. Ast.   Surya S.   Siromani   Darpana
Node      6798.279   6794.395   6792.254   6792.644
Perigee   3232.575   3232.094   3232.734   3232.657
The reader will notice that Chandrasekhara has
devised a correction to be applied to the
Mandochcha of the planets, Mercury, Mars and
Saturn. He has called it Parochcha and the greatest
amounts are 11' 20', 7° 30' and 5° for the three
planets respectively (Siddhanta Darpan V.76).
It is, however, in computing the Moon's place
that Chandrasekhara has discovered some original
correction, - original in the sense of their having
been unknown to the ancient astronomers of our
country. It is curious to note that they failed to
discover the perturbation, known as Evection which
is said to have been detected by Hipparchus about

Introduction xxxiii
150 years B.C. It is an irregularity which may put
the Moon forward or backward over a degree.
Pandit Sudhakar Dwivedi informs us in his excellent
manual, called Ganaka-Tarangini, that Munjala
(A.D.933) had something like "’evecation’ in his
karana named Laghumanasa. He appears to have
been the oldest Hindu astronomer who detected the
irregularity, through curiously enough, his
successors including Bhaskara left it unnoticed.
The next large irregularity of the Moon, called
"variation," has a period of one month, and a
maximum of 39'31". This inequality does not affect
the time of an eclipse, and the fact sufficiently
explains its absence in Sanskrit Siddhantas.¹ It is
said to have been detected by an Arbian astronomer,
Aboul Wefa about the year 975 A.D., and re-
discovered by Tycho Brahe in the 16th century. The
last large inequality of the Moon's place is called
"annual equation," and has the maximum amount of
11'9". This was also discovered by Tycho Brahe.
It is singular that Chandrasekhara is the only
Indian astronomer who has detected all the three
important irregularities of the Moon. As has been
said before, he did not know English and had not
means of knowing of the existence of the
irregularities from any foreign source; and the
methods of applying the corrections together with
discrepancies between his values and those of
Europe leave no doubt in our mind that he must
be credited with their discovery. He has named the

1. From Dwivedi’s Ganaka-tarangini, it appears that
   Nityananda in 1639 A.D. used a correction called
   Pakshika. But it is not clear from the name alone, if it
   had any connection with "variation".

xxxiv सिद्धान्त दर्पण
inequalities, Tungantara, Pakshika and Digamsa, with
the maximum amounts of 2°40′, 38′12″, and 12′
respectively (S.D.VI.7).
For those who may be inclined to compare his
corrections, his method of applying them is briefly
described here. After the equation of centre
(maximum amount 5° 1′ 10″) has been applied to
the mean Moon, call the result Ist Moon M₁ Then
add to, or subtract from it, according as the anomaly
happens to be within the first six or the second six
signs.
160′ x Sin[A - (0+3)] Sin(M₁-0)
--------------------- x ---------
R R
Ist Moon motion
x ---------------
mean motion
where A stands for the Moon’s apogee, and 0
for the true Sun. The two signs (±) are to be taken
in the case of the light and dark halves of each lunar
month respectively. The result obtained is called the
2nd Moon, M₂.
To apply the Pakshika correction, take
M₂ - 0
------ = a+ b (say). Subtract b from 3 (Signs)
3 3 -
3
and take the less of two quantities, a and
(3 - b ) and say, it is y. Then sin2y is the

3 90
corection required. It should be noted that the
denominator (90) is not constant, but can be
obtained. The correction is to be added to, or
substracted from the 2nd Moon, as the latter lies
within the first or the second quadrature. Call the
Moon thus corrected, the third Moon, M₃-

Introduction xxxv
Now, take 1/10 of the Sun's equation and
mutiply by the first Moon's motion, dividing by its
mean motion. Add the result to the 3rd Moon, when
the Sun's equation is subtractive, and subtract from
it when the Sun's equation is additive. After this,
the other corrections (such as Bhujantara), common
to all the planets, are to be applied before the
Moon's place becomes apparent.¹
On a cursory view, the amount of Tungantara
inequality appears double of that of evection. But
if we take the Moon's greatest equation of centre
into account, the apparent discrepancy vanishes.
For, the amount of the greatest equation of the
Moon is 6° 18′, and the maximum evection 1° 20′
making the total of 7° 38′. Chandrasekhara has 5° 1′
as the greatest equation and 2° 40′ as the greatest
Tungantara, making the total of 7° 41′. The other
inequalities discovered by Chandrasekhara are
about the same as those in use in English
astronomy.
The astronomical constants adopted by our
India astronomers open up a large field for enquiry.
It is not my purpose to discuss their bearings upon
the antiquity of Indian astronomy. But I cannot but
remark that it is often reiterated in season and out
of season than substantiated, that the Indian
astronomers borrowed largely from Greek
astronomy. As far as I am aware, this assertion is
based upon (1) the identity of certain Sanskrit and
Greek astronomical terms, (2) the fact of Garga
praising the Yavanas for their proficiency in

1. It should be noted here that the last-named inequality
   (Digamsa) is also applied to the Moon's node in the
   above-mentioned manner (S.D. VIII, 33).

xxxvi सिद्धान्त दर्पण
astronomy, and (3) the presence in Sanskrit of
certain astronomical treatises words admittedly of
foreign origin. This is not the place to discuss the
subject throughly. But as far as my knowledge goes,
these arguments, when weighed against others, are
not at all convincing.
The presence of Greek terms in Sanskrit is
certainly a strong presumption in favour of the
theory. But when the uses of the terms are taken
into consideration, it is found that with the possible
exception to the word "Kendra'¹ meaning
"anomaly", all the rest properly belong to astrology.
Of course, when once the terms had been
introduced into Sanskrit, our astronomers did not
hesitate to use them freely in astronomy, side by
side with pure Sanskrit terms. The passage where
Garga extolled the Yavanas does not occur in an
astronomical work, but in a Samhita which was
rather a work on astrology than astronomy. Nor
can we logically infer from the passage that the
Yavanas were proficient in astronomy rather than
in astrology, or that the Hindus borrowed the
knowledge from them. The name Yavanacharya
occurs only in connection with Samhita. Next the
presence of Romaka² and Paulisa Siddhantas among
others of purely Indian origin proves nothing
beyond the bare fact of their presence and I do not
see how it can be taken to imply that the Hindus
had not obtained the constants of their Siddhantas

1. See, however Bhaskara's derivation of the word in his
   Siromani.
2. The Romaka-Siddhanta of Varaha-mihita is in no way
   superior to his Saura-Siddhanta, as was remarked by
   himself.

Introduction xxxvii
by independent observation. On the contrary, the
fact of their retaining the foreign name (at least the
name Romaka), shows that the foreign Siddhantas
were distinct from what were Indian, and there is
no proof that the Romaka or any other foreign
Siddhanta was ever in use in this country,
superseding the purely Indian productions. To give
an analogy, a Sanskrit translation of the British
Pharmacopoeia will no more prove the absence of
Charaka than an English translation of the later will
prove the absence of the former. All that we can
logically infer is that there was intimate intercourse
between the Hindus and the Yavanas, a fact
otherwise known from political history. The Hindus
may have been indirectly influenced by the
teachings of the Yavanas. But it must be admitted
that the Yavanas may have been also influenced by
their presence among the Hindus.
We can safely go so far, omitting all sorts of
possibilities and vague conjectures. Having regard
to our ignorance of the state of astronomy and its
gradual development in India anterior to
Aryabhatta, and our equal ignorance of the source
of the knowledge credited to Hiparchus, it is
hazardous to speak of the indebtedness of the one
nation to the other. If the Hindus learnt the science
of astronomy from the Yavanas, how is it that the
constants of sanskrit astronomy are so different
from those of Ptolemy ? How is it that the early
Hindu writers were unacquainted with such useful
as well as remarkable facts as the precesion of the
equinoxes, or the evection inequality of the Moon ?
On the contrary, the constants ought to have been
identical, not only becaus they are believed to have
a common origin, but also because they represent

xxxviii सिद्धान्त दर्पण
facts, as true for India as for Egypt or Greece. When
one learns a science from another, it is natural to
expect to find him copying not only the theory but
also the practice, write or wrong. Dr. Thibaut
repeats the suggestion made by Biot, that the early
Hindus learnt their astronomical theories probably
from Greek astrologers, and, the Doctor adds, also
from almanac-makers, whose knowledge was as
limited as that of there proto-types in the present
day.¹ This is certainly an ingenious hypothesis; but
as has been already remarked having regard to our
ignorance respecting the growth and development
of the science in India as well as in Egypt, we cannot
but regard the hypothesis as not proven. I am
inclined to believe that our knowledge of the source
of Hindu astronomy has not advanced beyond the
point where Colebrooke found it. All that can be
safely asserted is what the illustrious oriental scholar
said, that "the Hindus have certainly received and
welcomed communications from other rations on
topics of astrology and we add, that their
indebtedness to Greece for the knowledge of
scientific astronomy is still an open question.²
But this a digression. We have said that
Chandrasekhara had made a real advance upon
existing Hindu astronomy. But the best test of a
theory lies in facts. For the reason given below, it
is not easy, however, to satisfy oneself whether his

1. See, Introduction to Pancha-Siddhantika by Dr. Thibaut
   and Mm. Suddhakara Dwivedi.
2. It is much to be desired that some competent scholar
   would collect the arguments for and against the theory
   of indebtedness, and let us know how far, and in
   what-direction, Greek influence on Hindu astronomy
   extended.

Introduction xxxix
ephemeris is correct, and how much confidence may
be placed in it. For rough comparison, the places
of the planets computed by him are shown below,
toegther with their places, first according to the
British Nautical almanac, and next according to a
widely circulated Bengali almanac said to have been
computed after the Surya-Sidhanta. The correction
for precession in the places given in the Bengali
almanac has been made by adding 20°54′ to them
in accordance with the almanac. Besides these, I
append ephemeris for two other days from the
Nautical almanac and the Siddhanta-Darpana.
For various reasons, neither Chandrasekhara's,
nor for that matter - any other Hindu almanac can
coincide with the Nautical almanac. Neglecting
minor corrections unknown in our almanacs, there
is the determination of the exact amount of
precession, without which no comparison is
possible with European almanacs. To avoid it, the
relative distance of the planets may be taken. It will
be seen that while the Bengali almanac may be in
error by as much as 4°, the error in the ephemeris
by the Siddhanta-Darpana is limited to
half-a-degree. The reader will, however, remember
that a Hindu astronomer depends upon unaided
vision, and is satisfied if the longitudes are correct
to a half degree. Accepting this as our standard,
the ephemerides by the Siddhanta-Darpana
compare favourably with those of the N.A., while
the greater discrepancies in the Bengali almanac
conclusively prove how urgent has been the
question of the revision of our existing almanacs in
the light of observations now made. (See Table )

xl सिद्धान्त दर्पण
LONGITUDES OF PLANETS OF THE 31ST JANUARY 1893 (KATAK, 6 p.m.)

| Siddhanta-Darpana | Bengali Almanac | Dec. by | Dec. by |
| Nautical Almanac | From Fixed Aries | From Vernal Equinox | From Fixed Aries | From Vernal Equinox | N.A. | S.D. |
| (1) | (2) | (3) | (4) | (5) | (6) | (7) |
| Sun ... 10° 11° 54' | 9° 19° 31' | 10° 11° 56' | 9° 19° 40' | 10° 10° 34' | 17° 14' S | 17° 15' S |
| Moon ... 4 4 24 | 3 12 16 | 4 4 41 | 3 12 1 | 4 2 55 | 24 1 N | 24 15 N |
| Mars ... 0 22 48 | 0 0 7 | 0 22 22 | 11 29 43 | 0 20 37 | 9 14 S | 2 7 S |
| Mercury ... 10 0 33 | 9 8 23 | 10 0 58 | 9 12 16 | 10 3 10 | 21 45 S | 21 15 S |
| Jupiter ... 0 19 27 | 11 26 43 | 0 19 8 | 11 27 6 | 0 18 0 | 6 32 N | 6 50 N |
| Venus ... 9 19 19 | 8 26 48 | 9 19 12 | 8 27 46 | 9 18 40 | 22 7 S | 22 1 S |
| Saturn ... 6 12 43 | 5 20 38 | 6 13 3 | 5 22 14 | 6 13 8 | 2 41 S | 3 0 S |
20th February 1894 (Katak, 6 p.m.) Ist March 1894 (Katak, 6 p.m.)
N.A. S.D. N.A. S.D.
Sun ... 11 2° 8' 11° 2° 9' 11° 11° 10' 11° 11° 11'
Moon ... 0 21 40 0 21 46 4 27 7 4 27 4
Mars ... 1 6 5 1 5 30 1 12 3 1 11 27
Mercury ... 11 5 14 11 4 57 11 22 14 11 22 39
Jupiter ... 0 22 58 0 22 34 0 24 46 0 24 21
Venus ... 10 14 16 10 12 42 10 25 28 10 25 25
Saturn ... 6 12 1 6 12 23 6 11 13 6 11 56

• It may be mentioned here that Ayanamsa on that day according to Chandrasekhara's Siddhanta Darpana was 22° 25', while Lahiri's
  Ayanamsa as accepted by Govt. of India now, was 22° 21' 41" - EDITOR.

Introduction xli
But before any reformation is attempted, an
exact determination of the amount of precession
becomes a question of paramount importance. The
reader is a awre that in the Hindu system, the
longitudes of celestial bodies are measured from a
fixed point - say a star - in the ecliptic, instead of
from the movable vernal equinox as is the practice
in Europe. The question has therefore the same
bearing upon our calculations, as the position of the
so called First Point of Aries upon those of the
Nautical almanac.
Unfortunately, all attempts to solve the*
question have been practically fruitless. The reader
will hence understand the chaos into which our
almanacs have sunk. The gravity of the situation,
and the difficulty of escaping from it, demand a
fuller discussion than our space would permit. But
then this alone can give us an opportunity of
ascertaining Chandrasekhara's success in this
direction.
Promising, then, that we measure longitudes of
planets from a fixed point in the ecliptic, the
question resolves itself into a determination of the
point. In other words, what is that point, or what
is its longitude from the vernal equinoctical point ?
Whatever and wherever that point may be, it is the
starting point of our zodiac, and its longitude is
known as ayanamsa, which literally means amount
of solstices. For, we do not speak of the precession
of the equinoxes as often as we do of the precession
of the solstices. Hence, the ayana-chalanam of
Sanskrit astronomy is equivalent to the precession
of the equinoxes. To avoid ambiguity we shall use
the term ayanamsa rather than the amount of
precession.

xlii सिद्धान्त दर्पण
The exact amount of the ayanamsa may be
apparently determined in different ways. 1. The
Siddhantas furnish a rule for computing it, which
is in principle the same as the method of finding
the longitude of a star at any given date by applying
the amount of precession to its longitude at some
other date. 2. Defining the initial with the help of
other data, such as the recorded longitudes of stars,
its present longitude from the equinoctial point may
be ascertained. 3. Knowing the exact year when the
initial point was fixed, its present longitude
(ayanamsa) may be calculated from the known rate
of precession. But it so happens that the results
obtained by these three methods do not agree.
To begin with the first method, it will be seen
that the different Siddhantas do not agree, either
in the nature of precessional movement, or in its
annual rate. According to some, the equinoxes have
an oscillatory motion, turning to the right and to
the left of the initial point within certain limits, and
extending over a large interval of time; while others
maintain their continuous motion backwards.
Colebrooke compared the views of the libration and
revolution theorists, and gave the rate of precession
accordign to each. They are as follows:-
Liberation Theory | Annual Rate
Surya-Siddhanta | 54″
Soma¹ Siddhanta | 54″
Sakalya Siddhanta | 54″
Laghu-Vasishtha Siddhanta | 54″
Parasara-Siddhanta | 52″.35

1. Ranganatha, in his commentary to the Surya-Siddhanta,
   quotes Soma-Siddhanta in support of the reading.

Introduction xliii
Liberation Theory Annual Rate
Aryashta Satika
(quoted by Munisvara) 46″.25
Manjula (quoted by Bhaskara)¹ 59″.9
Bhasvati 60″
Grahalaghava 60″
The derangement of the equinox from the intial
point is 27° on either side according to the
Surya-Siddhanta, and this limit was probably
accepted by other libration theorists.
Aryashta-Satika, however, gives the limit of 24°
instead of 27' (Colebrooke).
We are not concerned here with the theories or
the limits of libration. Surya-Siddhanta and the
works based upon it, are now almost universally
adopted throughout India for computing an
almanac, though in some places Grahalaghava
occupies the field. Now from the first, we find the
ayanamsa for the first day of Saka 1816² (13th April
1894) was 20° 55′, and from the second, 22°50′ for
the same day. These amounts represent. the
minimum and maximum ayanamsa obtained from
Siddhanta rules.
Both the Surya-Siddhanta and Siddhanta-

1. Bhaskara did not believe in the liberation theory. For, as
   has been shown by Chandrasekhara (VI.100), he has
   directed us always to add the ayanamsa and never to
   subtract it.
2. In common parlanac, we speak of the year being Saka
   1816, though in reality we ought to say the first day of
   Saka 1817. The facts herein discussed were collected
   sometime ago, and as it immaterial which year is taken
   for illustration, they are not altered to suit the current
   year.

xliv सिद्धान्त दर्पण
Siromani, the standard Siddhantas at present in use,
give a rule to test the amount of ayanamsa by
observation. It consists in subtracting from 12 signs
the longitude of the Sun computed after the
Siddhantas for the moment when the Sun crosses
the vernal equinoctial point. Thus, on the 13th April
1894, the Sun’s longitude for Greenwich mean noon
was 23°32′7″, while an almanac gives us 1°21′25″
as the Sun’s longitude for the same instant, making
the ayanamsa 22°10′37″. It will be seen therefore
that not withstanding the higher precessional rate
of the Surya-Siddhanta, the calculated amount
becomes less than the actual by nearly 1°16′, while
the Grahalaghava makes it greater by about 39″.
To come to the second method, viz. to find the
true longitude of the initial point as defined by stars.
All the modern Siddhantas agree in the statement
that the longitudes of all heavenly bodies are to be
measured from the Star Revati situated on the
ecliptic. The star has been identified with Picicum.
Now, this is a star of the fifth magnitude and is
barely visible to the naked eye. The question is,
why was this particular star out of the many situated
on the ecliptic, - some of which are larger, - chosen
for marking the beginning of the zodiac? The answer
has been - and there is no doubt about the accuracy
of the answer - that the vernal equinox happened
near the star when the present system of
astronomical measurement came into vogue.
So far it is plant sailing. For, we can easily find
the longitude of the star from the vernal equinoctial
point and at once get the required ayanamsa. From
the Right Ascension and Declination of the star,
ζ Piscium, on the 13th April, 1894, we get 18°23′49″

Introduction xlv
as its longitude.¹ This is however, less than the
amount obtained above. It is clear therefore that
either the star Revati is not ζ Piscium, or it did not
mark the initial point. No doubt exists about the
identity of the star, neither can we suppose all the
Siddhantas false in their assertion.
The latitudes and longitudes of thirty-four
others stars are given in the Surya-Siddhanta. They
were not measured in the usual way. But from the
express instructions as to the method of
measurement adopted, we understand that the
so-called longitudes, Dhurvas, are the longitude of
the Right Ascensions of the stars supposing them
to be on the ecliptic, and that the latitudes
(Vikshepas) are the distances, north or south, of the
stars from the ecliptic, measured along the
declination circles passing through the stars. Now,
taking only the 27 stars of the zodiac, and
comparing their reduced Dhruvas with their present
longitude, we find ourselves confronted with a
curious result.² The difference between the recorded
and the present longitudes is not the same for every
star. Indeed, it varies from about 18° to 24°.
Omitting Visakha, of which I am not certain,
the mean difference of the longitudes of the stars
of the first half of the zodiac, i.e. from Asvini to
Chitra is 21°, while that of the stars of the second
half amounts to 19° only. So, while the mean
―――――

1. The modern Surya-Siddhanta gives 359°50′ as the
   longitude of the star Revati. This would make the present
   ayanamsa greater by 10′ only.
2. I understand that Prof. Whitney has discussed the point,
   and regret that I have no access to his edition of the
   Surya-Siddhanta at present.