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

xiv सिद्धान्त दर्पण
circumstances something, however poor, is laid
before us, something, however crude, is evolved
from within, we should rejoice over it.
Whatever may be thought of the merits of the
work, I regard it as a misfortune that the author
has not found a man to introduce his work, better
qualified than myself, whose daily avocations run
in a different groove. For my part, I shall deem my
efforts amply rewarded, if my countrymen, to
whom original researches are as yet a thing of the
future, find in the life and doings of my author a
living example of what patient inquiry after truth
and diligent struggle after knowledge can achieve.
But I caution them again against high hopes. To
apperciate the man, one must compare his work
with others produced under similar conditions. It
will be unfair to expect anything new in the work
which will be useful to those who have studied
European Science. Let me therefore briefly recount
a few bright names from the annals of our ancient
astronomy that the present work may be taken and
its true worth.
Not to dive into the antiquity of Hindu
astronomy, which is as old as the Vedas and
regarding which abler men have measured swords,
let me begin the story from the point where we
tread on the firm ground of history. It begins with
Aryabhatta of Kusumapura (Pataliputtra), the
Andubarius of the Greeks, the Arjabhara of the
Arabs, and the Indian founder of the theory of the
earth's daily rotation. He was born in the Saka year
398 (A.D.476) and wrote his famous work at the age
of twenty-three. It was he in whose work we find,
as far as our present knowledge goes the first
successful attempt to solve indeterminate equations

Introduction xv
of the first degree. He enjoyed a wide reputation
which can only be explained by supposing that he
was an original observe and made improvements
upon older astronomy.
Hindu astronomy was then passing through the
state of childhood, and a few years later, we find
Varaha-mihira of Avanti (Ujjayini), adoring the court
of Vikramaditya the Great, about whom many a tale
of adventure and narrow escape from death has
been recounted. Varaha's encyclopaedic knowledge
made him famous. But he is remembered more as
a compiler than as an original worker. His
astronomical compilation, named Panchasiddha-
ntika was written about the Saka year 427 (505 A.D.)
Next, the name of Brahmagupta, son of Jishnu,
introduces an important chapter in the history of
Sanskrit astronomy. He wrote his work,
Brahmasphuta-siddhanta in Saka 550 (628 A.D.) at
the age of thirty, somewhere near Rewa. He was a
practical astronomer, and made several corrections
in the older astronomy. Indeed, the form in which
we find Hindu astronomy at the present day, dates
from him. He was a consummate algebraist, from
whom the Arabs got their knowledge of the science.
An indeterminate equation of the second degree, of
which he gives solution, was a prize problem in
Europe as late as the 17th century.
But the fame of Bhaskar born in the Saka year
1036 (1114 A.D.), near the Sahyadri (Western
Ghats), threw all his predecessors into the shade.
He is a glory to us, a wonder among Europeans.
His great work Siddhanta-Siromani, is one of the
standard treaties of the present day. He appears to
have made use of the Differential Calculus.

xvi सिद्धान्त दर्पण
With the death of Bhaskara, the living breath
of mathematical science parted from India. Repeated
invasions by a barbarous nation poured forth an
abundance of calamities and in the troubled times
the sacred muse of learning fled and hid herself
among a herd of commentators in the Deccan. In
the dark ages that followed, amidst the petty
dissensions of a host of semi-indepndent States, we
find intellectual effort at a stand-still; men were
content to chew the cud of what their predecessors
had thought and done. At last, one name of this
period is worth mentioning. This is Ganesa of
Nandigrama who wrote his Graha-laghava in Saka
1442 (1520 A.D.), a work which has been employed
as an easy hand-book of astronomy in some parts
of the country. Arab influence and, latterly, the
contact with Europeans did not benefit the science
much. It was during the reign of Jayasimha of
Jayapura so late as the 17th century, that the Arabic
Almagest and Euclid were translated into Sanskrit,
and it was he at whose instance five observatories
were built at various places in Northern India.
The long chain of astronomers was snapped
asunder for a period of at least four hundred years.
No doubt, there were astronomers, as there are
now, and some of them may have for a time enjoyed
a reputation, however local in character. But they
have hardly left any permanent mark on the
progress of the science.
Will it be estimating this work too highly if we
regard Chandrasekhara as forming a link in the long
chain ? Be that as it may, it is a most gratifying
thing that Chandrasekhara has not laboured in vain.
His work has already exercised an influence upon
Hindu astronomy, and hence upon Hindu society.

Introduction XVII
I say upon Hindu society, to which a correct
knowledge of the ever-changing positions of the
heavenly bodies is neither a matter for the
inquisitive, nor one which may be safely let alone.
For, Hindu life is nothing if not a routine of religious
practices, due observance of which necessitates a
knowledge of the positions of the planets and the
stars. Indeed, a correct almanac is an indispensable
equipment of every Hindu household. All religious
observances and rites are regulated by the almanac,
and some of these require very accurate
determinations. For instance, a Hindu must know
the exact moment when a particular position ends
and another begins.
It has, however, been observed that no two
current almanacs agree in their computations. A .
fierce controversy is going on between the
conservatives and the liberals in Hindu India about
the correction of almanacs, and therefore about the
data of the Siddhantas. The orthodox of the Hindu
community refuse to believe in the existence of
errors that have crept into the figures of the old
Siddhantas in course of time. To use the foreign
Nautical Almanac to regulate the religious
observances is out of the question. Any correction,
if necessary, must come from within, from a Hindu
uninfluenced by foreign education. It is not for
Europe, with all her brilliant scientific discoveries
and wonderful inventions of labour-saving
machinery, to take the place of the old Rishis, whose
hallowed names are associated with every
department of useful knowledge. Europe may be
our guide in matters temporal, but must not dictate
a work in matters spiritual. Materially, a Hindu is

xviii सिद्धान्त दर्पण
hardly of old days, though spiritually, I believe, he
is still the same.
The value of the Siddhanta-darpana, the work
of an orthodox Hindu, showing errors in our
current almanacs, cannot thus be over-rated. Here
is a man who has practically tested the elements
hitherto followed, and found reasons for correction.
And he has authority for doing so from the
honoured Rishis, who have given their sanction to
the adoption of such corrections as may be
necessary for the purpose of making calculation
agree with observation.
The influence which Chandrasekhar’s work has
already exerted upon society is not inconsiderable.
Some twenty-three years ago a meeting of learned
Panditas and Hindu astronomers was called at Puri
to select an almanac according to which the
numerous daily rites of worship were to be
conducted in the temple. The meeting decided in
favour of the almanac computed after this work.
One of the Chandrasekhar’s pupils has been
computing an almanac every year, which is used
not only at Puri but throughout the greater part of
Orissa. Another pupil of his publishes a Bengali
almanac which has a by no means insignificant sale.
Thus Chandrasekhara has already gained a
foot-hold in Hindu society and has inaugurated
silently but effecually an advance upon the current
almanacs. At any rate, he has silenced all
opponents, and has made the question of correction
possible in the near future.
To fully apperciate him, it is necessary to say
a few words on his early life and education. Some
four years ago, I first made his acquaintance, and
from conversation with him on astronomical

Introduction xix
subjects, I was surprised to find in him a man of
genius and extraordinary merit. Since then I have
looked into his work, Siddhanta-darpana, written
on palm leaves in Oriya character, the result of his
life-long labour in the field of astronomical research.
Two years ago¹ he was honoured by Government
with the title of Mahamahopadhyaya, a title hitherto
enjoyed only by Brahman versed in Sanskrit lore.
Chandrasekhara however, is not a Brahman but a
Kshattriya by caste.
He was born in the Saka-year 1757 (1835 A.D.)²
in the small village of Khandapara, some 50 or 60
miles West of Katak, amidst the hills and jungles
for which Western Orissa is famous. It is the chief
town of the Raja of Khandapara - one of the
tributary chiefs of Orissa. Chandrasekhara belongs
to the Raj family, the present Raja, Natabara
Mardaraj, Bhramaravara Ray being a son of
Chandrasekhara's eldest cousin. The full name of
the author is Chandrasekhara Simha Samanta
Harichandana Mahapatra. Harichandana and
Mahapatara are mere titles bestowed by the Raja of
Puri, whose influence upon the destinies of the
Rajas of Orissa is still as unbounded as was that of
the Pope of Rome on the vassals of medieval
Europe. He is styled Samanta as befits a member
of the Raj family. In Orissa, however he is best

1. The sanad conferring the Mahamahopadhyaya to Samanta
   Chandrasekhar bears the date 3rd June, 1893. Hence this
   portion was written by late Prof. Jogesh Ch. Ray in the
   year 1895 and the article was complete and printed finally
   in the year 1899.
2. Prof. Jogesh Ch. Roy has simply added 78 to the Saka
   era 1757 to get the A.D. But actually the date of birth
   when calculated comes to be 11th January, 1836 A.D.

xx सिद्धान्त दर्पण
known by the familar name of Pathani Saanta
(corrupted from Pathan and Samanta), a nickname
given him by his parents on account of their first
two children having died in infancy.
At an early age Chandrasekhara received
instruction in Sanskrit. For sometime he studied
Sanskrit Grammar, Smritis and Puranas, logic and
medicine, and read all the important Kavyas in the
original. His education has thus been varied and
many sided. But it has stood him in much better
stead than the modern elaborately arranged
curriculum of the English schools, through which
he would have been thrust, had he lived nearer a
town.
At the age of ten, one of his uncles¹ taught him
a little of astrology. He shewed the young
Chandrasekhar some of the stars to satisfy his
curiosity so natural in young children and thus
gradually initiated him into the mysteries of
astrology. At this age, his extraordinary desire to
test for himself the position of the stars as they
changed night after night was predominant. The
determination of lagnas is a very frequent necessity
in horoscopy; and the varying position of the
planets among the stars, without a knowledge of
which astrological predictions could not be made,
led him to watch their movements. This idle
curiosity exhibited in star-gazing developed into the
habit, of a really fruitful study of astronomy. There
was, however, no teacher who could instruct him
in the science, and he was quite ignorant of any
language save Sanskrit and his mother-tongue

1. It was his father but not uncle according to the biographer
   Pt. Chandrasekhar Mishra of Khandapara:

Introduction xxi
Oriya. He found, however, a few Sanskrit
Siddhantas in the family library, and applied
himself diligently to master them with the help of
commentaries.
At the age of fifteen, when he came to learn
the meaning of lagna and the rules for calculating
ephemerides of planets, he was surprised to find
that neither did the stars apear on the horizon at
the right moment, nor could the planets be seen in
their right places. Again and again, he measured
with a graduated rod the relative distances of the
heavenly bodies in the vain hope of finding an
agreement between calculation and observation,
and, again and agian his hopes were dashed to the
ground. Was it possible that the rules and the
figures of the famous Siddhantas were not accurate
enough, or was it possible that he had made errors
in his daily observations? Correct observation was
the only test to settle the question. There were no
mathematical instrument-makers to supply him with
the requisite instruments. The old Siddhantas give
brief instructions for constructing them, and he had
no other alternative than to make for himself, a few
primitive instruments for measuring time and
angular distance.
Some of my readers may be desirous of
knowing something of his observatory. It was the
clear, blue vault of the heavens that was his
observatory; and its equipment consisted of an
armillary sphere and a vertical wheel as substitutes
for modern transit and alta-azimuth, and the
time-honoured clepsydra took the place of the
sidereal clock. Of course, the all-useful gnomon
found a place in the observatory, and I am
informed, he had also a self-revolving instrument

xxii सिद्धान्त दर्पण
made of the pericarps of the Bottle-Gourd
(Lagenaria Vulgaris) with water and mercury. But
it was more of the nature of a curiosity than of
much practical use. The instrument, of which he
made constant use, was one devised by himself.
This, which he is fond of calling his Manayantra
(measuring instrument), may be properly called a
tangent-staff, it consists of a thin rod of wood,
twenty-four digits long, at one end of which is fixed
another rod at right angles in the form of a T. The
cross-piece is notched and also pierced with holes
at distance equal to the tangents of the angles
formed at the free extremity of the other rod. Of
course, such a rude instrument did not admit of
being so divided as to enable him to measure a
degree with any accuracy.
But it is a real pleasure to see him handling his
Manayantra with a precision marvellous to behold.
Constant practice has given him such facility with
it, that he would not care to have recourse to his
other instruments although better suited for
measurement of vertical angles. Indeed, in most
cases, mere inspection is often sufficient to enable
him to hit the angle to the nearest degree.
One instance of the perfection he has attained
by practice came before us when I saw him for the
first time. Some of my friends doubted his
pretensions to practical astronomy, and were
desirous of testing his knowledge. One evening
when Mars and Venus were about 6° apart in the
western sky, he was requested to show, if he could,
with the help of any improvised instrument the
actual distance between the planets. After a
moment’s pause, he made his manyantra out of a
stick 42 digits long, attaching a crosspiece of 4-1/2

Introduction xxiii
digits to one end. The trigonometrical functions of
sines and cosines were all committed to his memory.
The necessary calculations were mentally made, and
his instrument was ready in a few minutes.
On this occasion, he saw a telescope for the
first time. He had heard of its wonderful powers,
but had no idea of its performances. He requested
me to show him the planets through one.
Unfortunately, I had with me then a telescope no
bigger than a refractor of 3-1/2″ diameter. This was
adjusted for him with a power of 80. The keen
delight with which he looked at the varied and
picturesque appearance of the moon, absorbing him
for sometime can better be imagined than described.
When the novelty of the aspect had abated a-little,
he wanted to know the magnifying power. He was
told to find it out for himself, if he could. The
question is itself puzzling, and I did not expect any
answer. But he startled me by saying that the
instrument magnified about one hundred
diameters. He had measured the enlarged image of
the moon as seen through the telescope and had
compared it with the appearant to diameter
well-known to him.
The planet jupiter was next shown through the
telescope. I should rather say that he directed the
instrument to the planet and saw it himself. The
apparent motion of the planet quickened by about
a hundred times through the instrument, was
followed by him for sometime till he could see the
belts and the satellites to his heart’s content. It was
at this moment that he gave vent to his bitter regret
that he had not the advantage of such instruments
in his younger days.
Next morning we had a talk about tithis. I said

xxiv सिद्धान्त दर्पण
that the almanac-makers of Bengal would not be
believe in any variation in accepted duration of the
tithis. Hearing this, he was silent for a minute or
two, as if he doubted the fact. Being pressed for
his opinion, he quoted a line from his work,
meaning that arguments can never defeat the results
of direct observation.
He had read in a vernacular text book that the
sun sometimes exhibited dark spots on his radiant
orb, and was anxious to see if it was really so. I
asked him to accept the fact as true; but he said he
would not believe it unless he saw spots with his
own eyes. To this I retorted by asking if he had
ever believed in the existence of the seven
atmospehrs of the Siddhantas. His reply was that
the statement was to be taken at what it was worth,
and he had no opinion of his own to give. The
minimum sun-spot period had been passing; but a
few that he saw made him reflect upon them a long
while.
None can read his life without gaining a fresh
insight into the marvellous thoroughness with
which our ancestors devoted themselves to their
studies, our universitymen being only surface-deep
in subjects more than one. The living breath of
science has departed from India with the departure
of men whom Chandrasekhara had made his ideal.
He is an adherent of truth obtained by direct
observation, and with all his respect for the
ancients, would not hesitate to denounce a Sastric
authority, if a proof to the contrary were obtained.
Were he placed in a well-equipped observatory of
modern days, I doubt not he would enrich science
with his assiduous labour and valuable obser-
vations.

Introduction xxv
Unaided and surrounded, as he was by practical
difficulties, what patient labour he must have
undergone in his early days to observe and workout
practically the astronimical elements of the planets.
What numberless observations must he have made
to test every figure used in the Siddhantas, in order
to see if it remained true or not. Night after night
passed away in the all-absorbing business of
star-measurement. An eclipse of the sun or of the
moon was an event in his life never to be forgotten.
Thus it was that his early days passed. To the
uninitiated, his was frivolous work fit for children
in want of better employment. Those who cared to
understand his business failed to appreciate it. What
if the planets moved out of their path ? Besides,
was it not the work of professional astrologers ?
And was it not unbecoming one in his position ?
He began to be called by the people Raj-Jyotishi as
a sort of nickname. The Raja of the State considered
himself degrated by the profession of his uncle, and
could never countenance his pursuits. Thus his
relations with the Raja have become far from cordial,
and the later has been unable to appreciate the
utility of his work.
At the age of twenty-three, Chandrasekhar
began to note down systematically the results of his
observations and three years later the idea of
embodying them in a work flashed into his mind.
By this time, his mastery over Sanskrit had become
so complete that he could compose elegant verses
in it impromptu. Indeed, the composition of his
work had begun in his mind long before it was
written on palm-leaf. In this way, between
observation and measurement and composition his
days were divided. He was increasantly engaged

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".