\documentclass[narrow,11pt]{stm}
\usepackage{xetex-generic}
\usepackage{stm-biblatex}

\usepackage{tfrupee}

\usepackage{hyperref}
\hypersetup{pdftex, colorlinks=true, linkcolor=blue, citecolor=blue, filecolor=blue, 
	urlcolor=blue, pdftitle=Toke L. Knudsen; , pdfauthor=Dominik Wujastyk, pdfsubject=, 
	pdfkeywords=}

\usepackage[cover]{stm-hssa}
\emergencystretch .1\textwidth
\begin{document}
	
	\firstpage{7}
	\lastpage{9}
	
	\title{Review of: S. Balachandra Rao,\emph{ Indian Astronomy: Concepts and Procedures} 
	(Bengaluru: M. P. Birla Institute of Management, 2014)}
	\author{Toke Lindegaard Knudsen}
	
	\covercitation{Toke Lindegaard Knudsen (2016), ``Review of: S. Balachandra Rao,\emph{ 
	Indian Astronomy: Concepts and Procedures} (Bengaluru: M. P. Birla Institute of 
	Management, 2014),'' 
		\emph{History  of
			Science in South Asia} 4 (2016): 
		\textsc{r}\thefirstpage--\textsc{r}\thelastpage.}
	
	\coverpage
	
	\copyrightspage
	
	
	%\maketitle
	
	\ifcover\setcounter{page}{\thefirstpage}\else\setcounter{page}{\thelastpage}\fi
	
	\myfooter[C]{history of science in south asia 4 (2016): 
		\textsc{r}\thefirstpage--\textsc{r}\thelastpage}
	
	\addtocounter{page}{-1}
	\makeatletter
	\def\@oddhead{\hfil \textsc{r}\thepage}
	\def\@evenhead{\hfil \textsc{r}\thepage}
	\makeatother
	
	
	
	\noindent
	
	
	
	
	%\title{Dhruv Raina, Needham's Indian Network: The Search for a Home for the 
	%History of Science in India (1950-1970) (New Delhi: Yoda Press, 2015) 135 pp}
	%\author{Dominik Wujastyk}
	%\date{2016-09-04T14:53:03.769755497}
	
	
	
	\noindent S. Balachandra Rao, \emph{Indian Astronomy: Concepts and Procedures}
(Bengaluru: M. P. Birla Institute of Management, 2014) (New Delhi: Yoda Press,
2015), pp.\,xiv, 328. \rupee\,450.
	
	\bigskip
	
\noindent \lettrine[lines=2,loversize=.1]{I}{n} addition to being the year in
which Dr.~S.\ Balachandra Rao's book \emph{Indian Astronomy:\ Concepts and
	Procedures} was published, the year 2014 was marked by the 900th birth-anniversary
of one of the most renowned astronomers of Indian history, namely, Bh\={a}skara~II
(born 1114 \CE). It is appropriate that Dr.\ Balachandra Rao's book, a wonderful
contribution to the study of astronomy in India, should appear in a year in which
there was a heightened focus on Indian astronomy.

As indicated by its title, the present book deals with the concepts and procedures
of Indian astronomy. More specifically, it deals with the concepts and procedures
of the classical schools of Indian astronomy, which arose around the middle of the
first millennia \CE. A brief introduction to the earlier history of astronomy in
India, namely, astronomy in the Vedic texts and the
\emph{Ved\={a}\.{n}gajyoti\d{s}a} (an ancient Sanskrit text dealing with the
determining the correct time for performing various sacrifices), is given
(pp.\,1--5), but the remainder of the book deals with classical Indian astronomy.

The topics covered in the book are by and large those found in a
\emph{siddh\={a}nta}; that is, the topics found in a comprehensive treatise of one
of the classical schools of Indian astronomy, covering not only the formulae
needed for making astronomical calculations but also expounding the theory and the
underlying model of the scientific system. The topics include the celestial sphere
and its great circles, coordinate systems, time, mean and true positions of the
luminaries and planets, lunar and solar eclipses, and conjunctions of heavenly
bodies. The book also covers, significantly, the Indian calendar
(\emph{pa\~{n}c\={a}\.{n}ga}) and astronomical tables in the Indian astronomical
tradition.

It is important to note that the book is not an academic study of Indian
astronomy. While Dr.~Balachandra Rao's erudition is evident to readers of his
book, the book is intended for students and general readers.  Its purpose is to
generate an awareness of Indian astronomy and proficiency in the computational
procedures developed by the tradition over many centuries (p.\,iv).  By this I do
not mean to imply that the book is not useful for scholars studying the history of
astronomy in India. On the contrary, such scholars will benefit from one of the
significant contributions of the book, namely, the carefully worked-out examples
found throughout it.

While academic studies present and comment on the formulae given in a source text,
the emphasis is rarely on their practical use. Rather, emphasis is put on the
exact phrasing of the formula, a theoretical discussion of the formula's
correctness, or a comparison of the formula with similar formulae found elsewhere
in the Indian astronomical tradition (or in other traditions, such as Islamic
astronomy).

Dr.~Balachandra Rao's book, on the other hand, does not proceed chronologically in
terms of the historical development of the system, nor does he discuss variations
of the formulae in the works of different astronomers. Rather, he presents the
formulae clearly and illustrates them with useful examples. Considering the
complexity of many of the formulae and methods, simply having access to a correct
formulation of particular formula is not sufficient for understanding how it is to
be used practically. It takes some practice and experience to become familiar with
the system and how the formulae work within it.

The book uses two texts as representatives of Indian astronomy as found in
\emph{siddh\={a}nta} treatises, namely, the modern
\emph{S\={u}rya\-siddh\={a}nta}, generally dated to the 9th or 10th century \CE,
and the \emph{Grahal\={a}ghava} of Ga\d{n}e\'{s}a Daivaj\~{n}a, composed in the
early 16th century (p.\,14). There are, of course, numerous other excellent texts
that could have been used, but the two chosen are good choices. While there are
differences between the various texts, if one is able to master the computational
system of one text, working with the system of another will not prove too
difficult.

To give an example, formulae from Indian astronomy often rely on the so-called
“day-group” (Skt.\ \emph{aharga\d{n}a}), the number of civil days elapsed since a
given epoch is used, where the epoch is a specified time used for astronomical
computations. However, given a date in our current calendar, it is not
straightforward to compute the number of days elapsed since a given epoch from
Indian astronomy (the epoch could be the beginning of the \emph{kaliyuga}, a time
period from Indian mythology which began more than 5,000 years ago, or a given
historical date used by an astronomer in a text).

Chapter 8 in the book, which covers the \emph{aharga\d{n}a}, contains many
practical examples. Two such examples (p.\,62--63) provide practical examples of
how to compute the \emph{aharga\d{n}a} of a given date (April~12, 1991 and
December~24, 2010, respectively) when the epoch is the beginning of the
\emph{kaliyuga}. Other examples demonstrate how to find the modern date
corresponding to a date in the Indian calendar via the \emph{aharga\d{n}a}
(pp.\,67--68).

Other examples of useful worked-out procedures include how to practically compute
true positions for the luminaries and planets, described in chapters 10--11. The
Indian model for planetary motion is complex, involving two epicycles to describe
the motion of the five planets known to the Indian astronomers (the model
describes the motion of the sun and moon through one epicycle for each). The two
epicycles are presented as if independent though in reality they are not. As such,
their combination is not obvious and is computationally complicated. The inclusion of
the worked-out examples in this case are extremely useful as they enable the
reader to understand how the model works on a deeper level.

Furthermore, the examples of the computations involved with lunar and solar
eclipses in chapter 13--14 are equally valuable. These computations involved with a
solar eclipse are especially complicated.

Overall, the worked-out examples constitute a significant contribution to the
field. It enables the interested reader to get to know the Indian astronomical
model at a deeper computational level. At the same time, it does the same for the
specialist scholar of Indian astronomy, who can use the book as a reference work
to be consulted on computational aspects.

Beyond computational examples, Dr.~Balachandra Rao's book makes another important
contribution to the study of Indian astronomy in chapter~20, which focuses on
astronomical tables in Indian astronomy.
%
The important topic of astronomical tables in Indian astronomy has only recently received 
significant attention. As such, the discussion in the book is important. Moreover, in addition 
to merely discussing known tables, Dr.~Balachandra Rao reports on new material in the 
book. More specifically, he managed to procure a manuscript of a text entitled the 
\emph{Grahaga\d{n}ita-padak\={a}ni} from a private collection (p.\,288). The manuscript 
belongs to a place named Ty\={a}garti in Karnataka and the tables are based on the modern 
\emph{S\={u}rya\-siddh\={a}nta}.

The book thereby provides a glimpse into how astronomical computations were done in 
practice at a local level. This glimpse provides a wonderful companion to the material 
covered previously in the book.

It is also important to note that the book has an extremely useful glossary of
technical terms. The glossary has both an ``English to Sanskrit'' and a ``Sanskrit
to English'' part. The glossary is especially useful for a student working on an
Indian astronomical text in the original Sanskrit.

Overall, Dr.~Balachandra Rao's book is a real contribution to the field of Indian
astronomy. It is recommended for both interested readers and scholars working more
seriously with the history of Indian astronomy.

\begin{flushright}
	Toke Lindegaard Knudsen, Ph.D.\\
	Department of Mathematics, Computer Science, and Statistics,\\
	State University of New York at Oneonta,\\
	Oneonta, U.S.A.
\end{flushright}    


\coverlastpage
\end{document}





