The science of astronomy flourishes only amongst a civilized people.
Hence, considerable advancement in it is itself proof of the high
civilization of a nation. Hindu astronomy has received the homage of
numerous European scholars.
Sir William Hunter (1840-1900) says "The Astronomy of the Hindus has
formed the subject of excessive admiration."
"Proof of very extraordinary proficiency," says Lord Elphinstone, "in
their astronomical writings are found."
(source: Hindu Superiority - By Har Bilas Sarda p. 332 - 348).
William Robertson wrote: "It is highly probable that the knowledge of
the twelve signs of zodiacs was derived from India."
(source: An Historical Disquisition Concerning the Knowledge which the
Ancients had of India - By William Robertson p. 280).
India has left a universal legacy determining for instance the dates of
solstices, as noted by 18th century French astronomer Jean-Claude Bailly
(1736–93) 18th century French astronomer and politician. His works on
astronomy and on the history of science (notably the Essai sur la
théorie des satellites de Jupiter and History of Astronomy) were
distinguished both for scientific interest and literary elegance and
earned him membership in the French Academy, the Academy of Sciences,
and the Academy of Inscriptions. Bailly, who was guillotined during the
French Revolution, maintained that the Brahmins of India had been tutors
of the Greeks and, through them, of Europe.
Jean-Claude Bailly said:
" The motion of the stars calculated by the Hindus before some 4500
years vary not even a single minute from the tables of Cassine and Meyer
(used in the 19-th century). The Indian tables give the same annual
variation of the moon as the discovered by Tycho Brahe - a variation
unknown to the school of Alexandria and also to the Arabs who followed
the calculations of the school... "The Hindu systems of astronomy are by
far the oldest and that from which the Egyptians, Greek, Romans and -
even the Jews derived from the Hindus their knowledge."
(source: The Politics of History - By N. S. Rajaram Voice of India ISBN
81-85990-28-X. 1995 p. 47).
The paper of John Playfair (1748-1819) (FRS and Professor of Mathematics
at the University of Edinburgh) is a detailed review (published in 1790)
of the book 'Traite de ';astronomie Indienne et Orientale,' by J. S.
Bailly (Paris 1787), the famous French historian of astronomy. Taken as
if by surprise by Bailly's rather positive evaluation of the origin,
antiquity and achievements of Indian astronomy, Playfair states that: "I
entered on the study of that work, not without a portion of skepticism....The
result was, an entire conviction of the accuracy of the one, and of the
solidity of the other.' Both Bailly's book and Playfair's article
examine in detail some of the astronomical tables (based on Indian
astronomy) that the French had procured from Siam (Thailand), Playfair's
main conclusions are the following:
1. The observations on which the astronomy of India is founded, were
made more than three thousand years before the Christian era; and in
particular, the places of the sun and the moon, at the beginning of the
Kali-yoga/Calyougham (i.e., 17/18 February 3102 B.C.), were determined
by actual observation.
2. Though the astronomy which is now in the hands of the Brahmins, is so
ancient in its origin, yet it contains many rules and tables that are of
3. The basis of the four systems of astronomical tables which we have
examined, is evidently the same.
4. The construction of these tables implies a great knowledge of
geometry, arithmetic, and even of the theoretical part of astronomy.
Playfair argues that 'communication is more likely to have gone from
India to Greece, than in the opposite direction."
(source: India Through The Ages: History, Art Culture and Religion - By
G. Kuppuram p.671-672).
Hindu astronomy received considerable homage from European scholars. Sir
William Hunter (1840-1900) says: "The astronomy of the Hindus has formed
the subject of excessive admiration." "In some points the Brahmins made
advances beyond Greek astronomy. Their fame spread throughout the West,
and found entrance into the Chronicon Paschale (commenced about 330 A.D.
and revised under Heraclius 610-641). "The Sanskrit term for the apex of
a planet's orbit seems to have passed into the Latin translations of the
Arabic astronomers. The Sanskrit uccha became the aux (genaugis) of the
later translators." "The Arabs became their (Hindus) discipline in the
8th century, and translated Sanskrit treatises, Siddhanats, under the
Albrecht Weber (1825-1901) says:
"The fame of Hindu astronomers spread to the West, and the Andubarius
(or probably, Ardubarius), whom the Chronicon Paschale places in
primeval times as the earliest Indian astronomer, is doubtless none
other than Aryabhatta, the rival of Pulisa, and who is likewise extolled
by the Arabs under the name of Arjabahar."
(source: Indian Literature - By Albrecht Weber ISBN: 1410203344 p. 255).
Research scholars like Sylvain Bailley (1736-1793) and Charles Francois
Dupuis (1742-1809) aver that the Hindu Zodiac is the earliest known to
man and that the first calendar was made in India in about B.C. 12,000.
(Refer to Bailley's Histoire de Astonomie Ancienne p. 483 as well as the
Proceedings of the Society of Biblical Archaeology - December 1901 part
The Hon. Emmeline M. Plunket (1835- ) in the great work Ancient
Calendars and Constellations p. 192 - says that there were very advanced
Hindu Astronomers in B.C. 6,000.
(source: Hinduism: That Is Sanatana Dharma - By R. S. Nathan p. 38
published by Central Chinmaya Mission Trust. Bombay).
Horace Hyman Wilson (1786-1860) wrote: "The science of astronomy at
present exhibits many proofs of accurate observation and deduction,
highly creditable to the science of the Hindu astronomers. The division
of the ecleptic into lunar mansions, the solar zodiac, the mean motions
of the planets, the procession of the equinox, the earth's self-support
in space, the diurnal revolution of the earth on its axis, the
revolution of the moon on her axis, her distance from the earth, the
dimensions of the orbits of the planet, the calculations of eclipses are
parts of a system which could not have been found amongst an
But the originality of the Hindus is not less striking than their
proficiency. Wilson says: "The originality of Hindu astronomy is at once
established, but it is also proved by intrinsic evidence, and although
there are some remarkable coincidences between the Hindu and other
systems, their methods are their own."
(source: History of British India - by James Mill Volume II p, 106-107).
Mountstuart Elphinstone wrote: "Proofs of very extraordinary proficiency
in their astronomical writings are found."
The Hindu astronomy not only establishes the high proficiency of our
ancestors in this department of knowledge and exacts admiration and
applause: it does something more. It proves the great antiquity of the
Sanskrit literature and the high literary culture of the Hindus.
"Monsieur Bailly, the celebrated author of the History of Astronomy,
inferred from certain astronomical tables of the Hindus, not only
advanced progress of the science, but a date so ancient as to be
entirely inconsistent with the chronology of the Hebrew scriptures. His
argument was labored with the utmost diligence and was received with
unbounded applause. All concurred at the time with the wonderful
learning, wonderful civilization and wonderful institutions of the
(source: History of British India - By James Mill Volume II. p. 97-98).
Albrecht Weber (1825-1901) says: "Astronomy was practiced in India as
early as 2780 B.C." "The fame of Hindu astronomers spread to the West,
and the Andubarius (or probably, Ardubarius), whom the Chronicon
Paschale places in primeval times as the earliest Indian astronomer, is
doubtless none other than Aryabhatta, the rival of Pulisa, and who is
likewise extolled, by the Arabs under the name of Arjabahar."
(source: Indian Literature - By Albrecht Weber p. 30-255).
But some of the greatest modern astronomers have decided in favor of a
much greater antiquity. Cassini, Bailly, Gentil and Playfair maintain
"that there are Hindu observations extant which must have been made more
than three thousand years before Christ, and which evince even then a
very high degree of astronomical science."
Count Magnus Fredrik Ferdinand Bjornstjerna (1779-1847) proves
conclusively that Hindu astronomy was very far advanced even at the
beginning of the Kaliyug, or the iron age of the Hindus (about 5,000
years ago). He says: "According to the astronomical calculations of the
Hindus, the present period of the world, Kaliyug, commenced 3,102 years
before the birth of Christ, on the 20th of February, at 2 hours 27
minutes and 30 seconds, the time being thus calculated of the planets
that took place, and their tables show this conjunction. Bailly states
that Jupiter and Mercury were then in the same degree of the ecliptic,
Mars at a distance of only eight, and Saturn of seven degrees; whence it
follows, that at the point of time given by the Brahmins as the
commencement of Kaliyug, the four planets above-mentioned must have been
successively concealed by the rays of the sun (first Saturn, then Mars,
afterwards Jupiter and lastly Mercury)....The calculation of the
Brahmins is so exactly confirmed by or own astronomical tables, that
nothing but an actual observation could have given so correspondent a
The learned Count continues: "He (Bailly) further informs us that
Laubere, who was sent by Louis XIV as ambassador to the King of Siam,
brought home, in the year 1687, astronomical tables of solar eclipses
and that other similar tables were sent to Euorpe by Patouillet (a
missionary in the Carnatic - India), and by Gentil, which later were
obtained from the Brahmins in Tirvalore, and that they all perfectly
agree in their calcuations although received from different persons, at
different times, and from places in India remote from each other. On
these tables Bailly, makes the following observation. The motion
calculated by the Brahmins during the long space of 4,385 years (the
period eclipsed between these calculations and Bailly's), varies not a
single minute from the tables of Cassini and Meyer; and as the tables
brought to Europe by Laubere in 1687, under Louis XIV, are older than
those of Cassini and Meyer, the accordance between them must be the
result of mutual and exact astronomical observations." Then again,
"Indian tables give the same annual variation of the moon as that
discovered by Tycho Brahe, a variation unknown to the school of
Alexandria, and also to the Arabs, who followed the calculation of this
"These facts," says the erudite Count, "sufficiently show the great
antiquity and distinguished station of astronomical science among the
Hindus of past ages." The Count then asks "if it be true that the Hindus
more than 3,000 BC., according to Bailly's calculation, had attained so
high a degree of astronomical and geometrical learning, how many
centuries earlier must the commencement of their culture have been,
since the human mind advances only step by step on the path of science."
The length of the Hindu tropical year as deduced from the Hindu tables
is 365 days, 5 hours, 50 minutes, 35 seconds, while La Callie's
observation given 365-5-48-49. This makes the year at the time of the
Hindu observation longer than at present by 1'46". It is however, an
established fact that the year has been decreasing in duration from time
immemorial and shall continue to decrease.
(source: The Theogony of the Hindoos with their systems of Philosophy
and Cosmogony - By Count Bjornstjerna p. 32).
W Brennand had said in his book Hindu Astronomy:
"It is certain that the ancient Hindu astronomers, many centuries before
the Christian Era, were in possession of knowledge, derived from
observations made by them of the motions of the heavenly bodies, which
they were able to use, and did actually use, in very accurate
computations of time. "
"Upon the first point (the antiquity of that system), it may be
remarked, that no one can carefully study the information collected by
various investigators and translators of Hindu works relating to
Astronomy, without coming to the conclusion that, long before the period
when Grecian learning founded the basis of knowledge and civilization in
the West, India had its own store of erudition. Master minds, in those
primitive ages, thought out the problems presented by the ever recurring
phenomena of the heavens, and gave birth to the ideas which were
afterwards formed into a settled system for the use and benefit of
succeeding. Astronomers, Mathematicians, and Scholiasts, as well as for
the guidance of votaries of religion."
It is in the light of such consideration as these, that the investigator
of the facts relating to Hindu Astronomy, is compelled to admit the
extreme antiquity of the science. An impartial investigation of the
circumstances relating to the question whether the Grecian Astronomy was
original in its nature, and was copied by the Hindus, places it beyond
doubt that the Hindu system was essentially different from and
independent of the Greek.
“No nation in existence can afford to compare to latter [India] in many
tenets of science, with its earliest theories and cosmography, without a
smile at the expense of ancestors, but the Hindus, in this view, may,
with not a little justifiable pride, point to their science of
astronomy, arithmetic, algebra, geometry and even of trignometry, as
containing within them evidence of a traditional civilisation compared
formally with that of any other nation in the world.”
(source: Hindu Astronomy - By W Brennand p. 34 and 320 - 323).
Paul G Johnson has observed in his book, God and World Religions:
"In 600 B.C.E. the writer of Genesis perceived Earth to be the
motionless centerpiece of creation, and above its flat surface were two
great lights – the Sun and the Moon. Fourteen centuries before, the
Hindu scripture – The Rig Veda – had a more accurate picture. Not only
did the Sun, Moon, and Earth revolve in orbits, but “the Earth in its
orbit revolves around the Sun.” (8:2).
(source: God and World Religions - By Paul G Johnson p. 3).
"In India, we see the beginning of theoretical speculation of the size
and nature of the earth. Some one thousand years before Aristotle, the
Vedic Aryans asserted that the earth was round and circled the sun. A
translation of the Rig Veda goes: " In the prescribed daily prayers to
the Sun we find..the Sun is at the center of the solar system. ..The
student ask, "What is the nature of the entity that holds the Earth? The
teacher answers, "Rishi Vatsa holds the view that the Earth is held in
space by the Sun."
"Two thousand years before Pythagoras, philosophers in northern India
had understood that gravitation held the solar system together, and that
therefore the sun, the most massive object, had to be at its center."
"Twenty-four centuries before Isaac Newton, the Hindu Rig-Veda asserted
that gravitation held the universe together. The Sanskrit speaking
Aryans subscribed to the idea of a spherical earth in an era when the
Greeks believed in a flat one. The Indians of the fifth century A.D.
calculated the age of the earth as 4.3 billion years; scientists in 19th
century England were convinced it was 100 million years."
(source: Lost Discoveries: The Ancient Roots of Modern Science - By Dick
Teresi p. 1 - 8 and 159 and 174 -239). For more on Dick Teresi refer to
chapters Quotes301_320, GlimpsesVI and GlimpsesVII ).
Historian A. L. (Arthur Llewellyn) Basham wrote:
"The procession of the equinoxes was known, and calculated with some
accuracy by medieval astronomers, as were the lengths of the year, the
lunar month, and other astronomical constants. These calculations were
reliable for most practical purposes, and in many cases more accurate
than those of the Greco-Roman world. Eclipses were forecast with
accuracy and their true cause understood."
These were achieved without the help of a telescope. Accurate
measurement was made possible by the decimal system of numerals,
invented by the Indians.
It is certain that the Vedic Indians knew something of astronomy and
that it had a high utilitarian value for them as it did for all peoples
of antiquity. The Vedic priests had to make careful calculations of
times for their rituals and sacrifices, and also had to determine the
time of sowing and harvest. Moreover, astronomical periods played an
important role in Vedic thought for they were considered to be
successive parts of the ever returning cosmic cycle.
The Rig Veda lists a number of stars and mentions twelve divisions of
the sun's yearly path (rashis) and also 360 divisions of the circle.
Thus, the year of 360 days is divided into twelve months. The sun's
annual course was described as a wheel with twelve spokes, which
correspond to the twelve signs of the zodiac.
The theory of the great cycles of the universe and the ages of the world
is of older origin than either Greek or Babylonian speculations about
the "great year," the period within which all the stars make a round
number of complete revolutions. But there is remarkably close numerical
concordance in these theories. The Indian concept of the great year (mahayuga)
developed from the idea of a lunisolar period of five years, combined
with the four ages of the world (yugas) which were thought to be of
unequal perfection and duration, succeeding one another and lasting in
the ration of 4:3:2:1.
The last, the Kaliyuga, was one-tenth of the mahayga or 432,000 years.
This figure was calculated not only from rough estimates of planetary
and stellar cycles, but also from the 10,800 stanzas of the Rig Veda,
consisting of 432,000 syllables. The classical astronomers calculated
the great period as one of 4,320,000 years, the basic element of which
was a number of sidereal solar years, 1,080,000 a multiple of 10,800.
According to Berossus, the Babylonian great year was a period of 432,000
years, comprising 120 "saroi" of 3,600 years apiece.
The Rig Veda talks about the annual motion of the earth. The diurnal
motion is described in the Yajur Veda. The Aiteriya Brahmana explains
that "the sun neither sets nor rises, that when the earth, owing to the
rotation on its axis is lighted up, it is called day" and so on.
(source: Haug's Aitreya Brahmana Volume II. p. 242).
The Indian astronomer, Aryabhata lived in during the period in which the
Surya Siddhanta was composed. He was born in 476 and reputedly completed
his famous work, Aryabhatiya, at the age of twenty-three. A concise and
brilliant work of astronomy and mathematics.
The Aryabhatiya introduced certain new concepts, like Aryabhata's new
epicyclic theory, the sphericity of the earth, its rotation on its axis
and revolution around the sun, the true explanation of eclipses and
methods of forecasting them with accuracy, and the correct length of the
year were his outstanding contributions. The Arabs preserved the theory
of sphericity of earth, and Pierre d'Ailly employed it in 1410 in his
map, which was used by Columbus.
As regards the stars being stationary, Aryabhatta says:
"The starry vault is fixed. It is the earth which, moving round its
axis, again and again causes the rising and setting of planets and
stars." He starts the question: "Why do the stars seem to move? and
himself replies: "As a person in a vessel, while moving forwards sses an
immovable object moving backwards, in the same manner do the stars,
however immovable, seem to move daily."
The Polar days and nights of six months are also described by him. T. E.
Colebrooke says: "Aryabhatta affirmed the diurnal revolutions of the
earth on its axis. He possessed the true theory of the causes of solar
and lunar eclipses and disregarded the imaginary dark planets of
mythologists, affirming the moon and primary planets to be essentially
dark and only illuminated by the sun."
(source: T. E. Colebrooke's Essays, Appendix G. p. 467). For more refer
to Surya Siddhanta.
Centuries ago Aryabhatta told Pluto is not a planet
"Indian astrology did not include Pluto as a planet and the latest
announcement by leading global astronomers after a marathon week-long
meeting at Prague on Thursday only endorsed the Indian mathematical
astrology of Aryabhatta and Varahamihira in the sixth century," eminent
mathematical astrologer Mangal Prasad told PTI. "Western astrology uses
Pluto as a planet while Pluto was always out of Indian astrology and we
do not use it in our calculations. This is the practice from the days of
Aryabhatta and Varahamihira," Prasad said.
"Indian astrology is mathematically concerned with the nine planets, two
of which are Rahu and Ketu that are nothing but derivatives from the
diameter of the Earth, which is a circle having a value Pi (22/7)
imbedded in the equator of earth," he said.
"This was discovered and mathematically shown by Aryabhatta and
Varahamihira in the sixth century during the golden period of the Guptas,"
said Prasad, the author of books based on the work of the two great
sixth century scientists.Indian astrology is concerned more with
astronomy and the derivations are from the equator of the Earth,
diameter of the moon, the solar year and how the planets are viewed in
the northern lattitudinal region during January and February, soon after
the sun has crossed the Tropic of Capricon and moved towards the
northern part of the hemisphere.
(source: Pluto demotion vindicates Aryabhatta - ibnlive.com).
As regards to the size of the earth, it is said: "The circumference of
the earth is 4,967 yojanas and its diameter is 1,581 1/24 yojanas. A
yojanas is equal to five English miles, the circumference of the earth
would therefore be 24, 835 miles, and its diameter 7, 905 5/24 miles.
The Yajur Veda says that the earth is kept in space owing to the
superior attraction of the sun. The theory of gravity is thus described
in the Siddhanta Shiromani centuries before Newton was born:
"The earth, owing to its force of gravity, draws all things towards
itself, and so they seem to fall towards the earth." etc..
As regards to the solar and lunar eclipses it is said: "When the earth
in its rotation come between the sun and the moon, and the shadow of the
earth falls on the moon, the phenomenon is called lunar eclipse, and
when the moon comes between the sun and earth the sun seems as if it was
being cut off - this is solar eclipse.
The following is taken from Varahamihira's observations on the moon:
"One half of the moon, whose orbit lies between the sun and the earth,
is always bright by the sun's rays; the other half is dark by its own
shadows, like the two sides of a pot standing in the sunshine."
About the eclipses, he says: "The true explanation of the phenomenon is
this: in an eclipse of the moon, he enters into the earth's shadow; in a
solar eclipse the same thing happens to the sun. Hence the commencement
of a lunar eclipse does not take place from the west side, nor that of
the solar eclipse from the east."
(source: Brihat Samhita Chapter V v. 8).
Brahmagupta who was born in 598 and worked in Ujjain, foreshadowed
Newton by declaring that " all things fall to the earth by a law of
nature, for it is the nature of the earth to attract and keep things".
But the law of gravitational itself was not anticipated.
Recognition of the superiority of the Vedic mathematics was also
recorded as long as 662 A.D. by Severus Sebokht, the Bishop of Qinnesrin
in North Syria. As reported in Indian Studies in Honor of Charles
Rockwell (Harvard University Press. Cambridge, MA. Edited by W. E.
Clark, 1929), Sebokht wrote that the Indian discoveries in astronomy
were more ingenious than those of the Greeks or Babylonians, and their
numerical (decimal) system surpasses description.
"I will omit all discussion of the science of the Hindus [Indians], a
people not the same as Syrians, their subtle discoveries in the science
of astronomy, discoveries more ingenious than those of the Greeks and
the Babylonians; their valuable method of calculation [the decimal
system]; their computing that surpasses description. I wish only to say
that this computation is done by means of nine signs. If those who
believe because they speak Greek, that they have reached the limits of
science should know these things, they would be convinced that there are
also others who know something."
(source: Proof of Vedic Culture's Global Existence - By Stephen Knapp.
World Relief Network ISBN: 0961741066 p 22)
The celebrated European astronomer, John Playfair (1748-1819) says: "The
Brahmin obtains his result with wonderful certainty and expedition in
(source: Playfair on the astronomy of the Hindus. Transactions of the
Royal Asiatic Society of Great Britain and Ireland. Volume II. p.
Professor Sir M. Williams wrote: "It is their science of astronomy by
which the (Hindus) heap billions upon millions, trillions upon billions
of years, and reckoning up ages upon ages, eons upon eons, with even
more audacity than modern geologists and astronomers. In short, an
astronomical Hindu ventures on arithmetical conceptions quite beyond the
mental dimensions of anyone who feels himself incompetent to attempt a
task of measuring infinity."
Mrs. Charlotte Manning exclaimed: "The Hindus had the widest range of
mind of which man is capable."
Bramin's Observatory At Benares - By Sir Robert Barker
Benares in the East Indies, one of the principal seminiaries of the
Bramins or priests of the original Gentoos of Hindostan, continues still
to be the place of resort of that sect of people; and there are many
publick charities, hospitals, and pagodas, where some thousands of them
now reside. Having frequently heard that the ancient Brahmins had a
knowledge of astronomy, and being confirmed in this by their information
of an approaching eclipse both of the Sun and Moon, I made inquiry, when
at that place in the year 1772, among the principal Bramins, to endeavor
to get some information relative to the manner in which they were
acquainted of an approaching eclipse.
(source: Indian Science and Technology in the 18th Century - By
Sun the center of the Solar System
Dick Teresi has observed that:
"The Vedas recognized the sun as the source of light and warmth, the
source of life, and center of creation, and the center of the spheres.
This perception may have planted a seed, leading Indian thinkers to
entertain the idea of heliocentricity long before some Greeks thought of
it. An ancient Sanskrit couplet also contemplates the idea of multiple
"Sarva Dishanaam, Suryaham Suryaha, Surya."
Roughly translated this means, "There are suns in all directions, the
night sky being full of them," suggesting that early sky watchers may
have realized that the visible stars are similar in kind to the sun. A
hymn of the Rig Veda, the Taittriya Brahmana, extols, nakshatravidya
(nakshatra means stars; vidya, knowledge)."
"Two thousand years before Pythagoras, philosophers in northern India
had understood that gravitation held the solar system together, and that
therefore the sun, the most massive object, had to be at its center. "
(source: Lost Discoveries: The Ancient Roots of Modern Science - By Dick
Teresi p. 1 and 130). For more refer to Surya Siddhanta.
Ancient Indians knew Atlantic Ocean
Buddhist Jataka stories wrote about large Indian ships carrying seven
hundred people. In the Artha Sastra, Kautilya wrote about the Board of
Shipping and the Commissioner of Port who supervised sea traffic. The
Harivamsa informs that the first geographical survey of the world was
performed during the period of Vaivasvata. The towns, villages and
demarcation of agricultural land of that time were charted on maps.
Brahmanda Purana provides the best and most detailed description of
world map drawn on a flat surface using an accurate scale. Padma Purana
says that world maps were prepared and maintained in book form and kept
with care and safety in chests.
Surya Siddhanta speaks about construction of wooden globe of earth and
marking of horizontal circles, equatorial circles and further divisions.
Some Puranas say that the map making had great practical value for the
administrative, navigational and military purposes. Hence the method of
making them would not be explained in general texts accessible to the
public and were ever kept secret. Surya Siddhanta says that the art of
cartography is the secret of gods. This being the general thinking at
those times, yet, there was one group of people who realized that the
maps or the secret texts that contained the geographical surveys will
not last a very long time. Only cryptology using words and names would
last longer than any.
(source: Ancient Indians knew Atlantic Ocean - By Dr. V.Siva Prasad
Retired Professor of Engineering. Andhra University, India).