for Research in the History of

Ancient and Medieval Astronomy

By Benno van Dalen, former research associate at the Institut für Geschichte der Naturwissenschaften, Frankfurt am Main (Germany).

PARAMS, a database
of astronomical parameters occurring in Islamic
sources,
developed with Delphi and CodeBase during my stay in Frankfurt am Main
in 1997/1998, will in the end be available in versions for Windows 3.1
(16 bits) and Windows 95 and later (32 bits). Because of lack of time,
the
addition
of a number of functions (such as more sophisticated queries) and the
input
of the remaining parameter data contained in Prof. Kennedy's
handwritten
file has not yet been carried out. The presently available
PARAMS16
(see below) has to be considered as a
test version. I hope that some future project will allow me to make the
full database available, but it is still unclear when this will happen.

The sexagesimal calculator SCTR and the calendar conversion program CALH display on the screen at any time a complete overview of all available operations and include brief manuals. I hope that Windows users will appreciate them as auxiliary programs in a (relatively small) DOS window.

TA is a powerful command-line program for the input, analysis, and output of astronomical tables of Ptolemaic type. It has context-sensitive help (invoked by pressing F1) and a brief manual explaining its general principles. MM shares the manual and most of the available functions with TA, but operates especially on (pseudo-linear) mean motion tables. Since MM does not contain a context-sensitive help system, it might be recommendable to get acquainted with TA first.

All programs are available as zipped files, which you can download onto your computer by clicking the appropriate links below. No special installation is required; simply copy all files in the ZIP archives into a single directory and run the file with extension .EXE.

occurring in Islamic astronomical sources)

The version of PARAMS that can be downloaded through the link below is a preliminary one which still requires a lot of work. In particular, only around 400 values from Kennedy's original cardbox have been entered until now (these include all obliquity values, the solar mean motion parameters, the year lengths and the excesses of revolution). Furthermore, more complicated queries (for example, to select all values of a certain parameter found in a particular primary source) still have to be implemented. I would be very grateful for any suggestions that can make PARAMS a really useful tool for scholars working on Islamic astronomy.

- View the Manual for SCTR (19 KByte in ASCII format)
- Load SCTR.ZIP (Version 2.2, 39 KByte)

A very similar program CALM includes a number of calendars used in more recent times. Besides the Gregorian and Julian calendars, these are the Muslim, Jewish, Coptic, French revolutionary, and Iranian Hijri-i Shamsî calendars. CALM does not come with a separate manual and does not have all the advanced possibilities that CALH offers.

- View the Manual for CALH (10 KByte in ASCII format)
- Load CALH.ZIP (34 KByte)
- Load CALM.ZIP (26 KByte)

Tables of many of these types can be entered by giving certain tabular values and then correcting the predicted remaining values with presses of the + or - or numerical keys. Two versions of each tabular value can be kept, called "manuscript" and "corrected". The tables can be saved in files with extension .ZIJ and can be shown on the screen and written to text files in various formats, including LaTeX.

Among the available commands for analysing astronomical tables are: calculation of tabular differences; checking of symmetry; estimation of parameters with least squares, least number of errors criterion, Fourier estimation, or direct calculation from 1, 2 or 3 tabular values. Various functions have been implemented that can be used to check the statistical conditions for the application of the various estimators. Arbitrary types of tables can be calculated with the command TC (Table-Calculator) and various types of first- and second order interpolation in given tables can be simulated.

A new version 1.2 of TA was released in February 1999. It includes not only corrections of mistakes, but also various improvements in the way in which data are entered and new commands, such as SE for displaying the scribal errors in a table, LB for displaying the external zijes in a whole directory branch, and CV for copying a range of values from one table into another. Seven new types of functions (all related to planetary equations) were added and the context-sensitive help system was updated completely. A new manual is not yet available, but the file TACHANGE.TXT lists all changes in versions 1.1 and 1.2 of TA.

- View the Manual for TA and MM (35 KByte in ASCII format)
- View the list of changes in version 1.2 of TA (9 KByte in ASCII format)
- Load TA.ZIP (version 1.2, 193 Kbyte)

The entered mean motion tables may be saved in files with extension .MMT and can be recomputed, compared, and printed on the screen. The underlying mean motion parameters can be estimated in one of several ways, of which the Least Number of Errors criterion, which finds the parameter values for which a recomputation contains the least number of differences with the entered table, is usually the most accurate.

MM differs from TA in particular in the internal representation of the sexagesimal tabular values. Whereas TA uses a 10-byte decimal representation, MM actually saves all numbers sexagesimally and carries out all necessary calculations with an accuracy of up to 12 sexagesimal digits. The peculiar structure of mean motion tables, whose subtables may or may not be based on the same parameter value and whose tabular values are almost always given modulo 360 (i.e., complete rotations are left out) was the other mean reason to make TA and MM two separate programs.

A new version 1.2 of MM was released in February 1999. Besides some corrections of mistakes, it contains many improvements in the way in which data are entered and new commands, such as CA (Calculate Almanac) for calculating mean motion positions from a given table for a set of dates to be specified, SE for displaying the scribal errors in a table, and LB for displaying the external zijes in a whole directory branch. The Maliki (or Jalali) calendar, a true solar calendar based on the vernal equinox, was added to the set of calendars handled by MM and more general forms of the Julian and Byzantine calendars were implemented. A new manual is not available, but the file MMCHANGE.TXT lists all changes in versions 1.1 and 1.2 of MM.

- View the Manual for MM and TA (35 KByte in ASCII format)
- View the list of changes in version 1.2 of MM (13 KByte in ASCII format)
- Load MM.ZIP (version 1.2, 148 Kbyte)

Last modification: January 3, 2011.