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Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第11

Symposium on Calendars Used in Asia and Oceania

A Tribute to the Memory of the Late Yukio Ôhashi
K. RAMASUBRAMANIAN*

Amongst global scholars and outstanding researchers in the field of history of Indian
astronomy and mathematics, Dr. Yukio Ôhashi is an outstanding figure who has displayed
tremendous versatility and scholarship in a wide array of allied fields. Some remarkablefeatures of Ôhashi include his ability to learn multiple languages, approach problems withnew perspectives, and also take on well-established scholars with great confidence backed
up by thorough research. As a doctoral student of the stalwart Prof. K. S. Shukla, he carriedout extensive research on the instruments described in Indian astronomical literature.
Following his untimely and unexpected demise, this article attempts to pay a tribute to him
and spans two main sections covering a bibliographic note and highlights that showcase his
acuity in research.
Keywords
Yukio Ôhashi, Tribute, Biographical Note, Research Overview, Obituary
Contents
I

Biographical Note
1 Educational Background
2 Studies in India: Meeting his mentor Prof. K. S. Shukla
3 An exceptional student-advisor combination
4 A life filled with challenges
II Acuity in Research
1 An overview of Ôhashi’s publications
2 Insights into the calendrical system of the Vedāṅga Jyotiṣa
3 Place of the composition of the Vedāṅga Jyotiṣa
4 Sharp observations about the Classical Siddhānta period
5 Outstanding contributions on astronomical instruments of India(1) Instruments from the Classical Siddhānta period that have been studied by Ôhashi(2) Eye for detail(3) Instruments and observatories in Post Siddhānta period
III Concluding Remarks* Indian Institute of Technology, Bombay

20

I

history of Indian astronomy, though we do not exactly

Biographical Noteknow what particular reading or incident might haveinspired and propelled him in this direction.1 He then1 Educational Backgroundbegan learning Sanskrit and Hindi in the Eastern

Shibuya, Tokyo. His educational background has

Institute (Toho Gakuin) and was awarded a scholarship

spanned different fields, which certainly empoweredby this institute to study in India. Encouraged by this,

him to carry out research in the highly inter-disciplinaryÔhashi, at the age of 28, had set forth upon a new

domain of History of Mathematics and Astronomy.

journey.

Having completed his undergraduate degree in Physics

2 Studies in India: Meeting his mentor Prof.

at Saitama University (Tokyo) in 1979, he went on totake up an M.A. from the Department of Chinese

K. S. Shukla

Studies at Saitama University and completed it in 1983.

He was accepted as a visiting scholar in the Depart-His Master’s thesis was titled ‘Some problems of Hùhàn

ment of Mathematics and Astronomy at the Universitysìfēn lì’ wherein he discussed one of the oldest officialof Lucknow in India, where he met his guide andcalendars in China.

mentor, the illustrious historian of Indian astronomy andHe then got himself enrolled in the doctorate program

mathematics, Prof. K. S. Shukla. Combining a flair for

at Hitotsubashi University to study modern astronomy.

mathematics with a strong grasp of Sanskrit, Prof.

In the meantime, Ôhashi seems to have been suddenly

Shukla is well known for his immense contributions in

swept by a strong wave that made him drift towards theadvancing our understanding of the history and development of mathematics and astronomy in India. Prof.
Shukla’s erudition and contributions are ably captured
in Kolachana et al. (2019).
Ôhashi was indeed fortunate to have had the mentorship of Prof. Shukla, who not only shaped but also
honed Ôhashi’s skills to take up a completely new areaof research into Indian astronomy. Taking up suchresearch work in such domains demands expertise in
Sanskrit as well as science. While this is an arduous taskeven for native scholars who would have an edge overforeign scholars (who may be completely new to the
Sanskrit language in which most texts are available)Ôhashi seems to have had an unwavering mind andabundant enthusiasm to take up this challenge andacquire the skills necessary to carry out intensive
research work.
Ôhashi reminisces about his early days in the following words written by him in the chapter titled

Photo of Dr. Yukio Ôhashi presenting his paper at the
ICOA-5 conference in Chiang Mai in 2004

“Reminiscences of Prof. K. S. Shukla” that was published in Kolachana et al. (2019).

(Source: Orchiston and Nakamura (2020))

1

In the obituary Orchiston and Nakamura (2020), it is shared that when Ôhashi “was an undergraduate student it was an inspiring lecture
by Professor Hideo Hirose (1909 ‒1981), a former Director of Tokyo Astronomical Observatory that whetted his appetite to study thehistory of astronomy.” Nonetheless we do not know what made Ôhashi turn towards India after having completed his masters in Chinesestudies.

21

A Tribute to the Memory of the Late Yukio Ôhashi

On March 13, 1955, Yukio Ôhashi was born inI arrived at Lucknow in 1983. It was my first experi-

cal music several times. Mr. Ratan Shukla, a son ofence to go abroad. At that time, Prof. Kripa Shankar

Prof. Shukla, was kind enough to take me to several

Shukla already had retired from the Department ofhistorical places…

Mathematics and Astronomy of Lucknow University,号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第11

but sometimes came to the department… I studied theFrom the above descriptions, we can discern that

history of Indian mathematics and astronomy fromÔhashi grew to not only enjoy the close mentorship of1983 to 1987 as a research scholar under the guidance

Prof. K. S. Shukla but also went on to enjoy the cultur-of Prof. K. S. Shukla, and was awarded Ph.D. degree

ally rich Indian life.
It may not be out of place here to quote a subhāṣitā

(History of Mathematics) in 1992.

that highlights with beautiful similies what values anastute learner should possess.

The new environment would have posed challenges
on both the cultural and the academic front. Nonetheless,
we can infer that Ôhashi remained exuberant with a    positive attitude and a mindset dedicated to learning,  !"#$ %notwithstanding the obstacles and hardship one may
have to face to accomplish the undertaking. He shareskākaceṣṭā, bakadhyānaṃ, śvānanidrā tathaiva ca 

his experience in these words:

alpāhārī gṛhatyāgī vidyārthīpañcalakṣaṇam %At that time, I was young, and travelled several places

Perseverance of a crow, concentration of a crane,

in India to collect source materials. Photocopy was[light] sleep of a dog, moderate indulgence in food,not so popular in India at that time, and I took several

and renouncement [from attachments] of homephotographs of manuscripts by my camera… There(comfort-zone!) are the five signs of one who is

are some corrections in manuscripts which cannot becommitted to learning.

seen clearly by pictures or photocopies. So, I visited
Tagore Library several times to copy the manuscripts,

These values seem to have been in a fully blossomed

and then visited Prof. Shukla’s house. At that time,state in Ôhashi during his young, aspiring and learning

the primary mode of transport to go to Prof. Shukla’s

days.

house was cycle rickshaw. (By the way, the Indian
word “rickshaw” is originated in a Japanese word

3 An exceptional student-advisor combination“jin-riki-sha”, which means human-powered trans-

Prof. Shukla had retired from the university depart-

port. “Jin” in Japanese means human, “riki” means

ment by the time Ôhashi had come in as a visiting

force or power, “sha” means car. If it is driven byscholar. Even then, Prof. Shukla gave special attention

bicycle, it is called “cycle rickshaw”, and if it isand close guidance to Ôhashi. He was indeed fortunate

driven by motor cycle, it is called “auto rickshaw”.)

to be one among the only five doctoral students who
were guided by Shukla directly. Since Shukla was notÔhashi also fondly recollects his close association

regularly visiting the department after his retirement,with the son of Prof. Shukla and an affinity for the cityÔhashi by and large used to learn at his residence.

and the entertainments it could offer in these words:

Referring to the extraordinary kindness of Shukla,Ôhashi says (Kolachana et al., 2019 p. 3):

Lucknow is a beautiful city with several historicalsites. It was formerly “Awadh” ruled by Nawabs. It

Prof. Shukla taught me how to read Sanskrit andhas a tradition of delicious cuisine. And also,

Hindi texts on mathematics and astronomy, usually in

Bhatkhande Music Institute was situated nearby

his house.

Lucknow University, and I could enjoy Indian classi-

22Unlike today, back in the India of the 1980s, printing

notings of the emendations made by various scholars. In

was done using the letterpress, wherein the typesettersa later section, we present some interesting points fromused to compose the text in a metallic frame of a given

the “Notes and References” sections of Ôhashi , which

dimension, employing a variety of metallic fonts stored

serve as testimony to this.
Ôhashi started to read Yantra-rājādhikāra (Chapter 1

not happen all in one go as we do it today. At most 16 orof the Yantra-kiraṇāvalī) of Padmanābha, as two manu-

32 sheets could be printed at one time, and if there were

scripts were available in Lucknow itself. This was theto be any slip in proofreading, it could not be corrected

beginning of his journey that led to marquee publica-

again since the frame would have been completely dis-

tions about early Indian astronomical instruments. His

mantled once the pages were printed. Hence the author

legacy of research publications first began from a con-

had to be all the more careful in proof-reading the text.

ference held between November 13 and 15, 1985. This

Reminiscing how punctiliously and tirelessly Prof.

paper was titled “A note on some Sanskrit manuscripts

Shukla worked to ensure that the books he edited wereon astronomical instruments.” He shares his experiences

error-free, Ôhashi observes:in these words:

When I was in Lucknow, the Vaṭeśvara Siddhānta and

In

1985,

General AssemblyofInternational

Gola of Vaṭeśvara was being printed at a press in

Astronomical Union was held in New Delhi, and I

Lucknow. Prof. Shukla visited the press almost every

went to New Delhi with Prof. Shukla by train in orderday, supervised its printing work by himself, and readto attend its colloquium on the history of oriental

its proofs very carefully. From this fact, we canastronomy. It was my only one experience of travel

understand why his edition is so reliable. These origi-

with Prof. Shukla. The colloquium was held in INSA

nal sources are the most important foundation for(Indian National Science Academy), and we met

future research.

several specialists of oriental astronomy from many
parts of the world.

Extolling Shukla’s meticulous way of maintaining
After completing his studies in the role of a visiting

notes, and his commitment towards his doctoral stu-scholar for about five years in India, Ôhashi returned todents, Ôhashi notes:

Tokyo in 1987. Then he seems to have enrolled for a
When we read his notes, we feel as if we are being

doctorate in Social History of the East at Hitotsubashi

taught by him directly. It should also be mentioned

University in Tokyo and in 1988 and 1989 completed

that he noted several parallel statements in otherthe coursework component (Orchiston and Nakamura

Sanskrit texts in the footnotes of his English transla-2020). But apparently he withdrew from the doctoral

tions. So, his English translations can also be used asprogram there and with the mentoring of Prof. K. S.

a kind of annotated index of Sanskrit astronomical

Shukla, he worked with the University of Lucknow forand mathematical texts. Only Prof. Shukla could do

his doctoral dissertation and was awarded his Ph.D. inthis…

1992. The title of the dissertation is “A History of
Astronomical Instruments in India”. This dissertation
was published in three issues in the Indian Journal ofThis gives us a pointer to the great reverence Ôhashi

History of Science (IJHS):

had for his mentor and guide. The above statements did
not remain a mere observation. Meticulously following
the path of his mentor, Ôhashi had reflected it all

1. Development of Astronomical Observation inthrough his research taking the torch forward. In the

Vedic and Post-Vedic India, IJHS 28(3), 1993,

works of Ôhashi one can find elaborate notes, close and

185–251.
2. Astronomical Instruments in Classical Siddhāntas,

careful study of the various parallel statements and23

A Tribute to the Memory of the Late Yukio Ôhashi

in a huge type case. Also, the printing of a volume could

IJHS 29(2), 1994, 155–313.

runs of journals, which completely filled his once

3. Early History of the Astrolabe in India, IJHS 32(3),spacious home.

1997, 199–295.
Ôhashi was a long-standing member of the International Astronomical Union, since 1997. He was also a

After his Ph.D., life seems to have not been easy on

member of the Executive Committee of the InternationalÔhashi. Despite his excellent academic achievements,

Conference on Oriental Astronomy (ICOA), and hehe could not find a permanent research position any-

served on the Editorial Board of the Journal ofwhere. He had to work as a part-time lecturer of the

Astronomical History and Heritage (JAHH). In that

Chinese language, history of science, and history ofcapacity, he was indeed refereeing several papers on theastronomy in several different universities. A close

history of astronomy in Indian and South-East Asian

associate of Ôhashi, Prof. Michio Yano (2020) shares

astronomy.

his memory:

Since he was living all alone in his residence inTokyo, the exact date and time of the passing away of11

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Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第4 A life filled with challenges

Whenever I was asked I wrote recommendation

Dr. Yukio Ôhashi are not known. It was learned that heletters for him, but always in vain. He applied to themust have passed away sometime in October of 2019.2

assistantship of the Institute for Research inProf. Michio Yano (2020) writes:

Humanities at Kyoto University, but he was not successful and he became rather pessimistic in finding a

I could not believe when I got this sad news on

permanent job and gradually he turned to be aggres-November 10. It was only on March 12, 2019 that wesive to the established institutes and scholars and heparticipated in the Seventh Symposium on History of

was proud of calling himself ‘amateur historian of

Astronomy held at the National Astronomical

astronomy’. It seems that he wanted to say that ama-

Observatory in Tokyo. After the symposium weteurs represented by him are more learned than pro-joined a dinner party together. We discussed various

fessional scholars who have permanent job.

topics. Ôhashi was very eloquent. He drank two or
three bottles of wine even though he said that he was

While the academic career did not work out as Ôhashi

told by his doctor not to drink too much. I was

may have much deservedly wished for, he was certainly

worried about him.

not holding back in his research pursuits. By 1998 hehad expanded his research areas to include Tibetan

The author of this tribute has had a few occasions toastronomy, astronomical history of China, Vietnam andlisten to the talks given by Ohashi in a few conferences.

Japan. In order to pursue such wide-ranging geographies

This made him develop an appreciation for the novelÔhashi must have possessed extraordinary skills toways of his thinking, and the sharp mind that Ohashi

quickly and keenly learn classical languages including

was blessed with. There were also occasions in which

Sanskrit and Chinese. Orchiston and Nakamura (2020)

the author has witnessed him in his lower moments. In

share the following:

fact, upon finding Ôhashi in an unstable state, not able
to walk properly on one of the days during a symposium

2

Furthermore, in order to facilitate this research, overheld during March 2019 at the National Astronomical

the years Yukio built up an outstanding private

Observatory in Tokyo, it was painful to see a brilliant

research and reference library. By the time he died

mind succumbing to the vagaries of human nature.

this numbered between 7,000 and 10,000 books, plus

Providence, as it was to Ôhashi, may be unfair many aOrchiston and Nakamura (2020) mention the date to be 31 October 2019, in their article’s abstract. Whereas, Ôhashi’s close associate,
Michio Yano (2020) states the exact date is unknown.

24time, but he seemed to have sailed though various chal-David Pingree. Ôhashi has also looked deeply into

lenges with great optimism and enthusiasm. We only

various postulations made in the history of astronomical

wish more help had found its way to him in time, whichtexts and authors in the Classical Siddhāntic period. He

possibly would have enabled him to do more research

has tried to construct a web of all possible theories by

and enrich the field by writing more articles.

daring to enter into fuzzy areas such as the anonymity
The second field where Ôhashi’s achievements are

II Acuity in Researchsignificant is the history of astronomical instruments in

1 An overview of Ôhashi’s publications

India. It may be recalled that it had been a central theme

Prof. Michio Yano (2020) notes that Prof. Takao

of investigation in his doctoral thesis as well. Drawing

Hayashi prepared a list of Ôhashi’s publications andsome important contributions made by Ôhashi, the fol-enumerated about 80 papers, constituting about 30

lowing sections present a few highlights from his work.

papers on Indian astronomy, another 30 papers on

2 Insights into the calendrical system of theChinese astronomy, about 10 papers on Tibetan astronomy and others on the history of astronomy in South-Vedāṅga Jyotiṣa

East Asia and Japan.

The Vedāṅga Jyotiṣa of Lagadha is a small mono-

Orchiston and Nakamura (2020) have discovered thatgraph of astronomy written in Sanskrit. It has two

the digital archives of the Japan National Diet Library

recensions, namely, the Ṛg-vedic and the Yajur-vedic

contain 37 entries in Japanese, which were publishedentitled Ārca-jyotiṣa and Yājuṣa-jyotiṣa respectively.

between 1982 and 2019. Some of these Japanese papers

For its text, English translation and detailed mathemati-seem to even have abstracts in English. Their listing

cal notes see Sastry and Sarma (1984). The calendar

estimates around 40 research papers by Ôhashi in thedescribed there is a luni-solar calendar where two inter-

English language, written over a span of 36 years, fromcalary months are inserted in a 5-year cycle called

1985 to 2020. The authors of the obituary have also

“yuga”. Two intercalary months were inserted at thepresented some interesting analysis that most of his

middle and the end of the 5-year yuga.
David Pingree conjectured that the length of one solar

early papers were elaborate and voluminous ranging

year of the Vedāṅga Jyotiṣa was originally meant to befrom 59 to 159 pages.
The diverse areas that Ôhashi has forayed into are

366 sidereal days, which is 365 civil days and that thiswell beyond the expertise of the author of this tribute.

was borrowed from Egypt or Mesopotamia (Pingree,

Hence this section is restricted to Ôhashi’s contributions

1973). Ôhashi presents a brilliant analysis and refutes

relevant to the history of sciences in India. Ôhashi’s

Pingree’s conjecture and states it is “untenable”. In his

areas of interest in Indian astronomy can be thematicallypaper, Ôhashi (1993) notes:

divided into two areas:
Pingree interpreted that the “day” in the Ṛg-vedic
recension is not the civil day, but the sidereal day. So,(1) the history of mathematical astronomy from thehe conjectured that one solar year was 366 sidereal

Vedic period to the Siddhāntic period.

days, i.e. 365 civil days. The Yajur-vedic recension3(2) the history of astronomical instruments in theclearly states that the number of sidereal days (lit.

Post-Siddhāntic period.

rising of Śraviṣṭha) in a yuga is the number of “days”
Ôhashi made a significant contribution to the study ofplus five, and this statement shows that the “day” is

Jyotiṣa-Vedāṅga, at times even taking a critical view of

the civil (sāvana) day. However, Pingree argued thatcertain conclusions made by the renowned scholar

this is due to the misunderstanding of the compiler of3

Jyotiṣa-Vedāṅga (Y. 29 (a–b))

25

A Tribute to the Memory of the Late Yukio Ôhashi

around the author of the Sūrya-siddhānta.

Jyotiṣa to show that the dates of the new moon and fullmuch later work. Pingree, however, does not show

moon were determined quite accurately based on the

any understandable reason for his argument that therising time of the moon as well as by observing the lunar“day” in the Rg-vedic recension is sidereal, except

phase. An error in the calculation of the lunar phasethat 365-day year is the same as the Egyptian-Persian

would be easily detectable through observation.

4

year …

However, changes in the date of change of seasons are
not easily detectable through observation and hence,

11号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第the Yajur-vedic recension, and this recension is a

We should also keep in mind that sidereal days weresuch an error in the length of the solar year may havenever used for civil purpose in ancient India. Pingree

been present. Ôhashi thus presents mathematical rea-conjectured that the 365-day year was introduced intosoning, textual evidence and logical reasoning to con-

India through Persia, but I shall show that the day include that in the era of Vedāṅga Jyotiṣa a yuga consists

both recensions of the Jyotiṣa-Vedāṅga is definitelyof 1830 civil days and therefore a solar year of 366 civil

the civil day, and there is no similarity between thedays is purely of Indian origin. Though the earlier

calendrical system of the Jyotiṣa-Vedāṅga and that ofstudies of Vedāṅga Jyotiṣa assigned 366 civil days to aancient Egypt or Mesopotamia.

year, Pingree took a deviant view, and sort of maintained
it, even in his article published in 2007, not taking anyÔhashi goes on to consider the value estimated innote of Ohashi’s work, published more than a decademodern times of 62 synodic months and 67 sidereal

before on the same topic.

months of the moon, that are known to be:

3 Place of the composition of the Vedāṅga
62 synodic months = 1830.90 days,

Jyotiṣa

67 sidereal months = 1830.55 days.

Ôhashialso

rejected

Pingree’s

idea

of

the

Mesopotamian origin of the ratio 2:3 of the shortest and
If one solar year is taken to be 366 days, then one

longest daytime found in the Vedāṅga Jyotiṣa. He

yuga constitutes 1830 days, and this number is close to

showed that the ratio was derived not from the interpo-

the above value. However, if one solar year is taken tolation of the data based on the observation of the sol-be 365 days, then one yuga would constitute 1825 days,

stices but from the extrapolation of those based on theand nearly 6 days’ error is produced regarding the syzy-

observation around the equinoxes.

gies, and other observable phenomena. Ôhashi arguesÔhashi has analyzed the possible place of composi-that this “calendrical system was used for the determina-tion of the Vedāṅga Jyotiṣa by precisely looking care-tion of the time of rituals, including the new and full

fully into the verses that pertain to the estimation of themoon offerings, and 6 days’ error is by no means possi-

length of the day. The following are the relevant verses.

ble, because the difference of lunar phase in 6 days is

The first verse (Ṛg-vedic recension v.7 and Yajur-vedic

too much to go unnoticed. Therefore, I conclude that the

recension v.8) reads:

length of 1 year of the Jyotiṣa-vedāṅga was definitely
5/3678 9:2 ";, *&+( 

366 days.”&'"#(Ôhashi also supplied relevant quotes from Vedāṅga

4
5

5

01,2 <=>?30 

> %See Neugebauer and Pingree (ed. and tr.), The Pañcasiddhāntikā of Varāhamihira, Part II, Copenhagen, 1971, p. 81.
In some printed versions of Vedāṅga Jyotiṣa brought out by R Shamasastry (1936) and Kuppana Sastry and KV Sarma (1984) a serious
typographical error has gone unnoticed, thereby replicating into the work of Ôhashi as well. The reading found in those editions is:“&'"# (”. The word cannot be split since it is one compound formed of the two words &'"# + )( = &'"#(. In the compound
form it resembles the word *&+( used in the earlier half of the verse. The vocative case in both these phrases is to be understood as,-,./. If split, then the word 01,2 would not go with the ( and hence the former has to be modified to 034( as found in
one of the manuscripts, which the author could luckily lay his hands on. But this reading is neither warranted nor desirable.

26

gharmavṛddhirapāṃ prasthaḥ kṣapāhrāsa udag-

jectured that this value was borrowed from Mesopotamia

gatau during the Achaemenid occupation of the Indus valleydakṣiṇetau viparyāsaḥ ṣaṇmuhūrtyayanena tu %(Pingree, 1973). Although this latitude, which passes
through Kashmir, was not inaccessible for ancientIndian people, this proposition according to Ôhashi is[the time equivalent of] one prastha of water [in the

not tenable, and he presents the following arguments

clepsydra per day] during the northward course [of(Ôhashi, 1993; 2019):

the sun]. They are in reverse during the southward
course. [The total difference is] 6 muhūrtas during a… that formula (1) was not obtained by the interpola-

half year.

tion of the Jyotiṣa-vedāṅga observations at the solstices, but by the extrapolation from the observationsof the length of daytime around the equinoxes.

The second verse (Ṛg-vedic recension v.22 and Yajur-

Practically, there are two possibilities:

vedic recension v.40) reads:
0@AB0 C  BD E<  &'"#CF0 B 

1. If the formula were obtained from one

&<G HI># JK ,I&E BLM,9/#$ %muhūrta’s difference of the length of daytime
during one solar month after the equinox, theyaduttarasyāyanato

gataṃ

syāt

śeṣaṃ

most suitable latitude for this observation would

tathādakṣiṇato›yanasya tadekaṣaṣṭyā

dviguṇaṃ

be around 27° N.
vibhaktaṃ

2. If it were obtained from two muhūrtas’ differ-sadvādaśaṃ

syāddivasapramāṇam %ence during two solar months, the most suitable
latitude would be around 29° N.

[The number of days] elapsed in the northward courseor remaining in the southward course is doubled,

From the above consideration, I conclude that thedivided by 61, and added to 12. The result is the

Jyotiṣa-vedāṅga was produced at the latitude 27–29°

length of daytime [in terms of muhūrtas].

N or so in north India (most probably the western partof the plain of the Gaṅgā where later Vedic people
resided) without apparent foreign influence.

The above rule can be expressed as follows:2
T = (12 + 61 n)

We find that Ôhashi’s arguments are mathematically(1)spot on, as we plot the linear function (1) and compare it
where T is the length of daytime in terms of muhūrtas

to the actual lengths of the duration of days for various

and n is the number of days elapsed from or remaining

latitudes. Figure 1 graphically represents the variations

until the winter solstice. One muhūrta is 1/30 of a civilin the actual length of the duration of the day from theday or 0.8 hours. Thus from the above equation we see

winter solstice to the summer solstice at specific lati-that according to Vedāṅga Jyotiṣa the duration of thetudes and also charts the linear function of the equation

day is a linear function, where the length of daytime(1).
The length of the day for observers at different lati-changes by roughly one muhūrta during one solar

tudes, at any location on the earth can be computed bymonth.

calculating what is known as the ascensional difference

It may also be noted that according to formula (1), thegiven by the equation:

ratio of daytime and nighttime is exactly in the proportion 2:3 at the time of the winter solstice. This proportion

Ascensional difference = sin-1 (tan φ tan δ)

is akin to the one given by Mesopotamians and seems to
be valid around the latitude 35° N. David Pingree con-

27

(2)

A Tribute to the Memory of the Late Yukio Ôhashi

The increase of daytime and decrease of nighttime is号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第11

Figure 1. Annual variation of the length of day time

where φ is the latitude of the observer and δ is the decli-

was estimated by finding the difference between thenation of the sun. The magnitude of the ascensional

duration of two successive days. If Ti is the computed

difference when added to or subtracted from 6 hours

duration of the `i’th day in hours, during the course of

gives the half-duration of the day.

the sun from winter to summer solstice, then the change

The declination of the sun is conventionally taken toin the magnitude of the duration of the day is given by

be positive when it is in the northern hemisphere andnegative when it is in the southern hemisphere. It is

ΔTi = | Ti − Ti−1 |.

computed using the formula δ = sin-1(sin ε sin λ) where
ε is the obliquity of the ecliptic and λ is the longitude of

The graph depicted in Figure 2 shows that the error

the sun. For different latitudes, the length of a day’s

between the durations of the days computed using theduration in hours has been plotted against the longitude

equation given in Vedāṅga Jyotiṣa and the actual dura-of the sun in Figure 1. It is noted that the plot for latitude

tion is the least for a place having the latitude 28° N.

35° N, though coincides with a straight line at the end-

This makes Ôhashi’s estimates to be highly tenable

points, deviates significantly from the linear function in

thereby compelling us to ignore other arguments pre-most places. However the plots corresponding to lati-sented by scholars like Pingree regarding the place oftudes between 27° and 29° N are in close agreement

origin of Vedāṅga Jyotiṣa. Not limiting himself to cri-with it.

tiquing Pingree’s (1973) postulations regarding Vedāṅga

To determine the latitudes that best correspond to the

Jyotiṣa, Ôhashi (2012) also carried out investigations on

linear equation given by (1) in the Vedāṅga Jyotiṣa, we

various Mesopotamian sources on their zig-zag func-

found the absolute difference between the change in thetions and the data tables in those texts. He argues that,

actual duration of the day computed using (2) and thegiven the option to choose, we should consider thechange given by the linear function, and plotted theprocess of extrapolation to interpret functions of ancientvalues, as it would give an estimate of the latitude forastronomy, as the change in duration around equinoctialwhich the error is minimal. The change of linear func-days is more pronounced than the ones happening

tion obtained by differentiating (1) obviously yields aaround the solstitial days.

constant value of 0.026229 hours (converted frommuhūrtas). The change in the actual duration of the day28

4 Sharp observations about the ClassicalIn short, Ôhashi presents an alternative narrative to

Siddhānta periodthat of Pingree. His argument is based on the formula

Numerous historical theories have been put forward

given for the diurnal variation of the gnomon shadow inby Ôhashi in his discussions about the ClassicalYavana-jātaka (Chapter 79 verse 32) by contrasting it

Siddhānta, possible periods of Greek influence, thewith the Mesopotamian formula. His analysis brings out

possible chronology of the key Siddhānta texts, thethat the Indian formula was developed from observa-

history and historiography of significant astronomers

tional data at the summer solstice in north India (particu-

and mathematicians, their works, their lineage andlarly at the Tropic of Cancer), while the Mesopotamian

associated schools of thought. In this section, with aformula may have originated from the observational

couple of examples, we shall try to demonstrate howdata at the equinox in Mesopotamia.

Ôhashi sheds fresh light through his original thinking,Some of his conclusions and historic comments are

and does not merely subscribe to the views that havedebatable, nonetheless, his study of this period isbeen promoted by various scholars in the past.

exhaustive in covering the different astronomers andScholars have time and again stated that the Greek

mathematicians of the Classical Siddhānta period. His

horoscopy that was at some point introduced into India

appendix on the anonymous author of the Sūrya-is evidenced in the Yavana-jātaka (CE 269/270) of

siddhānta and its commentators is noteworthy.

Sphujidhvaja. [For its text and English translation, see

Although the Sūrya-siddhānta is one of the mostPingree (1978). Also see Shukla (1989).] The Sanskrit

popular works of astronomy written in Sanskrit, itsword “Yavana” is taken to refer to the Greeks. In his

author is not known. Based on his widespread reading

comments on the prominent influence of Vedāṅga

and deep thought, Ôhashi postulates that there are two

Jyotiṣa based thought processes in this text, he sharesdifferent Sūrya-siddhāntas that have come down to us.

the following:

One is a text of the Ārdharātrika school of Hindu
Classical Astronomy, which has been summarized in the

Only its last chapter (Chapter 79) is devoted to math-Pañca-siddhāntikā of Varāhamihira (sixth century CE)

ematical astronomy. The text tells that “the instruction

but is no longer extant. According to Ôhashi, the other isof the Greeks” (Yavana-upadeśa) is explained there,

the “modern Sūrya-siddhānta” (the version commonly

but the developed Greek geometrical astronomy

referred to by simply Sūrya-siddhānta), which is the(epicyclic theory, etc.) is not found there. In contrast,

fundamental text of the Saura school of Hindu Classicalaccording to my study, certain theory which is of the

Astronomy.

stage of Indian Vedāṅga astronomy is found there.

Ôhashi perseveres to date this text by examining

29

A Tribute to the Memory of the Late Yukio Ôhashi

Figure 2. Error when Vedāṅga Jyotiṣa formula is applied to different latitudes

However, in all other earlier versions which I listed

the analysis that the quotations of the Sūrya-siddhānta

above except for that of Mallikārjuna Sūri whose rel-in Bhaṭṭotpala’s commentary (latter half of the tenthevant portion has not been available to me, the word

century CE) on the Bṛhat-saṃhitā of Varāhamihira“veṇu-garbha” (bamboo-receptacle) is used there,(sixth century CE) are not found in the modern Sūrya-and it is only a description of a kind of water clock.

siddhānta. On the other hand, Mallikārjuna Sūri’s com-

Apart from the Sūrya-siddhānta, the earliest Sanskrit

mentary (1178 CE) on the (modern) Sūrya-siddhānta iswork which mentions the sand clock is the Yantra-

extant, and so he says the (modern) Sūrya-siddhānta

prakāśa (1428 CE) of Rāmacandra, and the second ismust have existed at that time. Referring to internal

the Sundara-siddhānta (1503 CE) of Jñānarāja. As

evidence, Ôhashi states that the position of the planetsRaṅganātha is later than both of them, it is not sur-calculated by the (modern) Sūrya-siddhānta is mostprising if he was familiar with the sand clock.

close to the actual planets around the eleventh century
We mention this primarily to indicate the amount ofCE.
More than his efforts to date the Sūrya-siddhānta,meticulous work done by Ôhashi by way of looking into

what stand out are his careful readings of the text fromthe details that are available in various manuscripts —various sources and commentaries. We noted earlier

which are not easy to read, unlike the printed versions of

how appreciative Ôhashi was about the meticulous

the text.

11号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第external and internal evidences. His study leads him toapproach of Prof. Shukla in presenting different read-

5 Outstanding contributions on astronomicalings in all the editions of important works that he hasbrought out. Perhaps it was the training that Ôhashi

instruments of India

received from Prof. Shukla that would have enabled him

The second field where Ôhashi’s achievements areto embark upon his own research journey as well, whichremarkable is in tracing and documenting the history ofis quite evident from his writings.

astronomical instruments in India. The main part of his

There are several commentaries on the Sūrya-dissertation dealing with this topic was published in

siddhānta. Ôhashi provides the authors who are known

IJHS Vols. 29 (1994) and 32 (1997) as mentionedtoincludesearlier. In IJHS Vol. 29 he analyzed Sanskrit texts

Mallikārjuna Sūri (1178 CE), Caṇḍeśvara (1185 CE),dealing with astronomical instruments beginning with

Madanapāla (end of the fourth century CE), Parameśvara

the Āryabhaṭīya of Āryabhaṭa (b. 476 CE) until(1432 CE), Yallaya (1472 CE), Rāmakṛṣna Ārādhya

Bhāskarācārya’s Siddhāntaśiromaṇi (twelfth century).

(1472 CE), Bhūdhara (1572 CE) and Tamma Yajvan

The work done as part of his doctoral thesis is one of the(1599 CE). Among them, the commentary of

most informative resources in the domain of astronomi-

Parameśvara has been published by his own mentor

cal instruments in India.

have

writtencommentaries

which(Shukla, 1957). He also states that the most popular

In the Vedāṅga astronomy period, the gnomon

version of the Sūrya-siddhānta, that is in vogue, is the(śaṅku) and the water clock are the only two astronomi-

text with Raṅganātha’s commentary (1603 CE). Having

cal instruments clearly known to have been used. The

carefully studied different manuscripts of the text withśaṅku was used continually in the later Siddhānta

commentaries, Ôhashi notes the following (Ôhashi,

period. The relationship between the length of the gno-2019):

monic shadow, the latitude of the observer and time
seems to have been developed in this period. A special… a detailed comparative study of the different ver-chapter titled Tripraśnādhyāya in the Siddhāntas was

sions of the text is needed. I shall give one example

devoted exclusively to dealing with this subject. Somehere. In Raṅganātha’s version of the Sūrya-siddhāntaof the key astronomical instruments belonging to this(XIII.21), the sand clock is mentioned, where theperiod, their utility, and the principles behind theirword “reṇu-garbha” (sand-receptacle) is used.

operation have been nicely brought out by Ôhashi.

30

(1) Instruments from the Classical Siddhānta

different from the Greek armillary sphere, which wasperiod that have been studied by Ôhashi

based on ecliptic coordinates, as discerned by Ôhashi.

The staff (yaṣṭi-yantra) is a stick that was used to

He also postulates that it was probably used to determine

sight an object that is far off—celestial or terrestrial.

the celestial coordinates of the junction stars of the lunar

There are some variations of the staff, such as the

mansions.
Ôhashi states that the water clock (ghaṭī-yantra) had

the help of a graduated level circle. The circle-instrument

been widely used until recent times. Unlike the water(cakra-yantra) is a graduated circular hoop or board

clock of the Vedāṅga Jyotiṣa period (which was outflow

suspended vertically. The Sun’s altitude or zenith dis-type), the water clock of this Classical Siddhānta periodtance is determined by this instrument. This is particu-

was a bowl with a hole at its bottom floating on water,

larly useful as the local sidereal time can be calculated

where water flows into the bowl and it sinks after afrom it with reasonable accuracy. Variations include thecertain time interval. The board-instrument (phalaka-

semi-circle instrument (dhanur-yantra) and the quad-yantra) invented by Bhāskarācārya and described inrant (turya-golaka).

Siddhāntaśiromaṇi is a rectangular board with a pin and

A circular board kept horizontally with a central rod

an index arm, used to determine time graphically fromis the chair-instrument (pīṭha-yantra), and a similar

the Sun’s altitude. Ôhashi states: “this is an ingenious

semi-circular board is the bowl-instrument (kapāla-instrument based on the Hindu theory of gnomon.”yantra). The Sun’s azimuth is determined by them andIn addition to discerning these instruments fromtime is roughly calculated from them. A circular board

various source texts, Ôhashi also provides a visual treat

kept in the equatorial plane is the equator-instrument

through his meticulous diagrams that make the reader(nāḍīvalaya-yantra) and it serves like an equatorial

have a feel for the instrument as per the description insundial. The combination of two semi-circular boards,

the texts. These diagrams that are so neatly drawn andone of which is in the equatorial plane, is the scissors-

aesthetically pleasing to see only show how passionately

instrument (kartarī-yantra).

Ôhashi had carried out this study. A sample of thesketches that are hand-drawn by Ôhashi is presented in

The armillary sphere (gola-yantra) in India is foundFigure 3.

to have been based on equatorial coordinates, and is

Figure 3. Astronomical instruments of Classical Siddhānta period sketched by Ôhashi (2019)31

A Tribute to the Memory of the Late Yukio Ôhashi

V-shaped staff for determining an angular distance with

(2) Eye for detail(3) Instruments and observatories in Post
Siddhānta period

The “Notes and References” sections that appear at号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第11

the end of each of his three papers based on his thesis are

In his article published in Vol. 32 of the IJHS, Ôhashi

replete with evidence from which we can infer theoffered detailed explanations of the astrolabe that wascountless hours spent by him in studying Indian astro-

prevalent during the Delhi Sultanate. The astrolabe,

nomical works. In addition to listing references sub-which was called yantra-rāja (king of instruments), wassection-wise, these notes sections are filled with details

one of the most popular astronomical instruments inabout the manuscript folios that he was referring to, andthose days. In this paper Ôhashi thoroughly expounds

how he came to know of some more later, discussions

on the projection method pertaining to the astrolabe in

about emendations, mathematical notes wherever

general and also summarizes the history of astrolabe

needed, and in some cases, his unreserved opinions andbeginning with the Yantrarāja (1370 CE) of Mahendra

critiques as well. A few instances showcase some of the

Sūri.

interesting insights obtained by him while describing

The main part of this paper is on the Yantrarāja-

Sanskrit phrases that could be apparently confusing andadhikāra of Padmanābha (1423 CE). Ôhashi preparedat times even misleading.

the first critical edition of the Sanskrit text using two

For instance, in his paper on the Astronomical

manuscripts belonging to the University of Lucknow

Instruments in Classical Siddhāntas he has provided

and he provided English translation and commentary ofnotes for his critique of the erroneous translation of athe whole text. This is undoubtedly a monumental workphrase “śaṅku-dviguṇa-mānena” by Bruno Dagens

in the history of astrolabe in India. Noting what makes(1970) [p. 186]. This phrase has been translated by

Padmanābha’s work very special, Ôhashi (2019)

Dagens to mean that the diameter of the level circle toobserves:

be drawn is double the length of the gnomon. Ôhashi
argues by supplying internal as well as external evidence

During the reign of Fīrūz Shāh (reign ad 1351–88),

that it refers to the measure of the string that is taken to

the third Sultan of the Tughluq dynasty of India, thedraw the level circle, and hence it is indeed the radiusastrolabe was introduced into India from the Islamicthat is twice the length of the gnomon and not theworld…

diameter.

The significance of Padmanābha’s Yantra-rāja-

Now, what is interesting is that, Ôhashi has picked up

adhikāra is that he explained the principle of thethe rationale provided by Dagens in the footnote that is

astrolabe using Hindu traditional mathematics. Thisoriginally in French and has presented a translation of it

fact shows that the astrolabe was well understood byand says why it is an incorrect rationale. In his final

Hindu astronomers soon after its introduction.

notes section, he supplements the translation of theFrench reading with the original text in French [p. 305].

Even the design of the astrolabe seems to have been

In another instance, in the notes section of his paper on

different from the ones that were designed in the West at

the astrolabe in India, Ôhashi states that he has beenthat time, where the center of the astrolabe is the Northreferring to an English translation of a Russian text on

Pole, whereas the center of Padmanābha’s astrolabe

stereographic projections and that he says that “I haveseems to have the South Pole. Padmanābha is known toborrowed some sentences and some ideas regarding thehave composed the Dhruva-bhramaṇa-yantrādhikāra

drawings from this book” [p. 291]. Securing these(Chapter 2 of his Yantra-ratnāvalī). This is a description

meticulous details when there was no internet and otherof a kind of nocturnal, where time can be obtained fromeasy modes of communication are highly commendable

the direction of α and β Ursae Minoris. These uniqueand clearly demonstrates the passion he had for

facets and details of the various layers of the astrolabe,

research.

the application of stereoscopic projection have all beenbrilliantly discussed by Ôhashi, with the help of intricate

32Figure 5: Ôhashi (2019) presents a picture and explains the principle of the Samrāṭ-yantra

annotated diagram that helps capture the different mea-

diagrams and mathematical notes.
Ôhashi also had a keen interest in studying the tradi-surements that can be made in this observatory. Figure 5

tional astronomical observatories that were built during

captures the diagram given by Ôhashi. Here, φ is the lati-

the first half of the eighteenth century by the thentude of the observer, δ is the Sun’s declination and h is

Mahārāja of Jaipur, Sawai Jai Singh (reign 1699–1743

the Sun’s hour angle. In the afternoon, the shadow of theCE). Jai Singh’s observatory is extant in Jaipur, Delhi,

gnomon (AB) is cast on the quadrant (EFGH), and its

Banaras and Ujjain. His observatory in Mathura has

position (Y) indicates time. In the forenoon, the shadow

already succumbed to the perils of neglect. Of theseof the gnomon (CD) is cast on the quadrant (JKLM).

observatories, the one in Jaipur is the largest. Among the

The position (X) indicates the Sun’s declination.

several instruments in Jai Singh’s observatories, themost famous instrument is probably the Samrāṭ-yantra

III(lit. “emperor instrument”). The nomenclature of thisConcluding Remarks

instrument can be understood in two ways–based on its

In this paper, we have made an honest attempt tosize and its utility. It is the most gigantic instrument,

provide a glimpse of Ôhashi’s remarkable passion andfrom which one could directly read the local sidereal

exceptional artistic skills in trying to bring out various

time of the day, fairly accurate to minutes. It is essen-

facets of Indian astronomy. His pioneering work on

tially an equatorial sundial.

Indian astronomical instruments is outstanding. AÔhashi has explained the astronomical aspects of thiscursory view of his works is a testament to his rigorous

historically significant observatory along with a well-research, enormous patience to draw meticulous

33

A Tribute to the Memory of the Late Yukio Ôhashi

Figure 4: Sketches of the astrolabe of Padmanābha (Ôhashi, 2019)sketches and graphs, ability to learn many languages,

anymore to study them. I hope some young Indian

connect-the-dots across several traditional knowledge

researchers do research on the regional development

systems and mathematical prowess combined with hisof mathematics and astronomy in India!

acumen in history. Unlike other historians, Dr. Yukio号（２０２２）

Research Papers of the Anthropological Institute Vol.11 (2022)『人類学研究所 研究論集』第11Ôhashi could work on the contributions made byThough Dr. Yukio Ôhashi is no longer with us, I truly

various civilizations including but not limited to Indian,believe that his works would continue to inspire young

Chinese and Tibetan astronomy.

scholars and fulfill his dream in the years to come. In

The snippets from his research highlighted in thisÔhashi, Mother India found a son who could shed lighttribute are but a fraction of his lifetime’s works, limited

upon significant aspects of her glorious scientific heri-

to only Indian astronomy. More importantly, Dr. Yukio

tage for the benefit of the world. Needless to say, IndiaÔhashi had courageously challenged the work done bytruly misses this versatile scholar and dedicatedsome of the well-established historians of science suchresearcher. We wish sadgati to this departed ātmā!

as Pingree and Neugabauer. It is quite unfortunate that

Finally, I would like to thank the organizers of theDr. Yukio Ôhashi passed away at just sixty-four years ofconference, particularly Mitsuru Soma for providing anage, while the life expectancy in Japan is usually greater

opportunity to recall the works of Ôhashi. It is important

than eighty years. Though his academic career did not

we reminisce Ôhashi for his brilliance and versatility inturn out the way he/we would have liked, his scholar-

research and pay tribute to his legacy as an exceptional

ship has been top-notch and it is important that the rest

scholar, for it may inspire many more in this interdisci-of the academic community, and especially young

plinary field to take up grand research questions auda-

scholars draw inspiration from the fertile research works

ciously and pursue them rigorously.

of Ôhashi.

References

In his “Reminiscences of Prof. K. S. Shukla”, Ôhashi

Dagens, Bruno (ed. and French tr.)(2019) wrote the following just a couple of years back:1970 Mayamata, Traité Sanskrit d’Architecture, 2 parts,
Pondichéry (1970–76); and Dagens, B. (English tr.):

My life in India was my most exciting period. Now I

Mayamata, New Delhi (1985).

am nearing the age of retirement. I was so lucky that

Ohashi, Yukio
1991

I could study in India as a student of Prof. Shukla.

“Sanskrit Texts on Astronomical Instruments during
the Delhi Sultanate and Mughal Periods”, Studies inThough I am writing this paper as his student, I am

History of Medicine and Science, 10–11, 1986–87, pp.

one of you. We shall study the history of Indian

165–181 (actually published in 1991).

astronomy and mathematics, and exchange informa-

1993“Development of Astronomical Observation in Vedic

tion. I am old, but I would very much wish to corre-

and Post-Vedic India”, Indian Journal of History ofspond with young researchers!

Science, 28(3), 1993, pp. 185–251.
1994“Astronomical Instruments in Classical Siddhāntas”,
Indian Journal of History of Science, 29(2), 1994, pp.

Those words resonate with the jubilant spirit, eager-

155–313.

ness and passion with which he has approached this1997

field of research. To young scholars too, in the very

“Early History of the Astrolabe in India”, Indian
Journal of History of Science, 32(3), 1997, pp.

same article, Ôhashi has left behind an important

199–295.

message:

2002“The Legends of Vasiṣṭha-A Note on the Vedāṅga
Astronomy”, in Ansari, S. M. Razaullah (ed.): Historyof Oriental Astronomy, Kluwer, Dordrecht, pp. 75–82.

… there are several modern manuscripts in Nāgarī
2012

script on foolscap. Still now, there must be several“Mesopotamian zig-zag function of day length from
Indian point of view”, Gaṇita Bhāratī 34 (2012): pp.

unstudied manuscripts in regional scripts or regional

53–64.

languages in local libraries etc. They are worth study-

2019

ing, but I, an old foreigner, cannot engage myself“Reminiscences of Prof. KS Shukla”, in Kolachana,
Aditya, K. Mahesh, and K. Ramasubramanian (ed.):34

Studies in Indian Mathematics and Astronomy.

19(3), Supplement, pp. 1–32, and 19(4), Supplement,

Springer, Singapore, 2019. pp. 3–4.

pp. 33–74.
Shukla, Kripa Shankar

Orchiston, Wayne, and Tsuko Nakamura
2020

1957

“OBITUARY: DR YUKIO ÔHASHI (1955–2019)”,

with

the

commentaryofParameśvara (Hindu Astronomical and Mathematical(2020): pp. 209–217.

Text Series No. 1), Lucknow: Department of Mathe“The Yuga of the Yavanajātaka: David Pingree’s Text

matical Astronomy”, Journal for the History of

and Translation Reviewed”, Indian Journal of History

Astronomy, 4(1), 1973, pp. 1–12.

of Science, 24(4), pp. 211–223.
Yano, Michio
2020Vedāṅga Jyotiṣa of Lagadha with the translation and“Obituary to Dr Yukio Ôhashi”, Indian Journal of
History of Science, 55(1), 2020, pp. 94–98.

notes of Prof. Kuppanna Sastry, critically edited by
K. V. Sarma. Indian Journal of History of Science,

35

A Tribute to the Memory of the Late Yukio Ôhashi

matics and Astronomy, Lucknow University.
1989“The Mesopotamian Origin of Early Indian Mathe-

Sastry, T. S. Kuppanna & K. V. Sarma
1984

Sūrya-siddhānta

Journal of Astronomical History and Heritage 23.1
Pingree, David1973

The