Sorry again. Found the solution.
#+begin_threeparttable must come after name and caption.
The following works:
Org syntax:
#+NAME: gharsondi-yield
#+CAPTION: Average yields of selected crops in Gharsondi, Gwalior, Madhya Pradesh and India, 2007-08 (kilograms per acre)
#+begin_threeparttable
#+RESULTS: gharsondi-yield-in
| Crop | Gharsondi | Gwalior | Madhya Pradesh | India |
|-----------+-----------+---------+----------------+-------|
| Soybean | nil | 689 | 442 | 500 |
| Paddy | 1553 | 866 | 569 | 1337 |
| Urad | 53 | 142 | 142 | 192 |
| Sesame | 101 | 127 | 153 | 170 |
| Wheat | 824 | 664 | 652 | 1134 |
| Chick pea | 462 | 445 | 288 | 308 |
| Rapeseed | 501 | 280 | 375 | 405 |
#+begin_tablenotes
\item [] \footnotesize{Note: Yield of rice Gwalior, Madhya Pradesh and
India were converted to paddy equivalents.}
\item [] \footnotesize{Source: Data for Gwalior, Madhya Pradesh and
India taken from the website Directorate of Economics and Statistics,
Ministry of Agriculture, Government of India}
#+end_tablenotes
#+end_threeparttable
Gives this:
\begin{threeparttable}
\caption{\label{gharsondi-yield}Average yields of selected crops in Gharsondi, Gwalior, Madhya Pradesh and India, 2007-08 (kilograms per acre)}
\begin{center}
\begin{tabular}{lrrrr}
Crop & Gharsondi & Gwalior & Madhya Pradesh & India\\
\hline
Soybean & nil & 689 & 442 & 500\\
Paddy & 1553 & 866 & 569 & 1337\\
Urad & 53 & 142 & 142 & 192\\
Sesame & 101 & 127 & 153 & 170\\
Wheat & 824 & 664 & 652 & 1134\\
Chick pea & 462 & 445 & 288 & 308\\
Rapeseed & 501 & 280 & 375 & 405\\
\end{tabular}
\end{center}
\begin{tablenotes}
\item [] \footnotesize\{Note: Yield of rice Gwalior, Madhya Pradesh and
India were converted to paddy equivalents.\}
\item [] \footnotesize\{Source: Data for Gwalior, Madhya Pradesh and
India taken from the website Directorate of Economics and Statistics,
Ministry of Agriculture, Government of India\}
\end{tablenotes}
\end{threeparttable}