PARAMS (Database of parameter values
occurring in Islamic astronomical sources)
The computer database
PARAMS is based on the hand-written parameter
file of Islamic astronomy kept by Prof. E.S. Kennedy. It was programmed
in Delphi and CodeBase by Benno van Dalen during a stay at the
for History of Science in Frankfurt am Main (Germany) sponsored by the
Alexander von Humboldt Foundation.
Contents of this
background of the parameter database, Files, Commands,
Fields, To do, Links
(general). Recommended escape routes: Benno
van Dalen's homepage, Description of Benno
van Dalen's computer programs.
changes to this page: some minor
changes were made in September 1998.
works on mathematics and astronomy, a particularly
category is that of zîjes, astronomical
text and mathematical tables for the computation of planetary
times of eclipses, rising and setting times, astrological functions,
of the parameter database
Whereas some early zîjes
were based on Indian
theory, most later ones made use of the geometrical planetary models
out by the Greek astronomer Ptolemy (Alexandria, second century) in his
Almagest. Muslim astronomers carried out extensive observational
programs in order to update and improve Ptolemy's astronomical
(parameters), such as the obliquity of the ecliptic, the mean motion,
and epicycle radius of the sun, moon and planets, the inclination of
lunar and planetary orbits, and the apparent diameters of the sun,
and shadow of the earth (for the calculation of eclipses). On the basis
of the results, the Muslim astronomers calculated Ptolemy's tables
At the same time the accuracy of the tabular values increased due to
in the methods of computing the trigonometrical functions which lie at
the basis of most computations occurring in zîjes.
More than 200
different zîjes, of which over 100 are
were written in Arabic, Persian and various other languages. In many
manuscripts of extant zîjes provide little explicit
about the historical and technical background of their contents. Often
we find in a single manuscript tables from completely different sources
without an indication of their origin. In order to establish the
for such tables, a comparison of their mathematical characteristics has
turned out to be very useful. Such a comparison in the first place
the underlying astronomical parameters, which vary significantly among
Muslim astronomers from different periods and regions. In many cases, a
given set of parameters can be considered to be typical for a certain
or group of astronomers. After the underlying parameters have been
the exact method of computation of a table (algorithm used, rounding
at intermediate steps of the computation, use of auxiliary tables,
may be analysed to obtain more detailed information.
Because of the
importance of the determination of astronomical
underlying tables in Islamic astronomical handbooks for the
of the origin of material in such works, E.S. Kennedy started a parameter
file for Islamic astronomy in the 1950s. The idea for such a file
received from O. Neugebauer, who kept a similar file containing, in
Babylonian and Indian astronomical parameters.
file by now consists of approximately 3000 small
hand-written cards, each containing a numerical value that was found in
a zîj or other Islamic primary source concerned with
or in the secondary literature about zîjes. Along with
numerical values, the cards contain information about the sources from
which the values were taken and references to related values. Kennedy
included parameters found in a fairly high number of important primary
sources as well as much of the relevant secondary literature.
Only two physical
copies of the parameter file exist: the original
Prof. Kennedy, who is now retired in Princeton, USA, and a photocopy
some new additions under the care of Prof. D.A. King at the Institute
History of Science in Frankfurt am Main, Germany. During a research
in Frankfurt am Main, sponsored by the Alexander von Humboldt
from September 1997 to February 1998, a preliminary computer version of
Kennedy's parameter file was developed by Benno van Dalen. It is this
version that is introduced on this page.
PARAMS consists of a single executable PARAMS.EXE and a
library file C4DLL.DLL, which is copyright protected but may be
together with the executable (for the precise conditions, see the file
LICENSE.TXT, in which "licensee" refers to the developer of PARAMS and
"sublicensee" to the users of the program).
database actually consists of the following six separate
The advantage of
this set-up is that changes to entries for associated
astronomers, primary sources and secondary sources can be made
from the entries for the parameter values themselves. For instance, if
a typo in the name of an astronomer is corrected, the correction will
once be visible in all parameter entries associated with that
Or, once the specification of a primary source has been entered, it can
be accessed by selecting it with the mouse from a so-called combobox
without having to type a single letter.
- PARTYPES for the names of all types of parameters
- ASTRONOM for the name, location and time of the astronomers with
the parameter values in PARAMS are associated
- SOURCES1 for the primary sources (title, author, shelfmark) from
parameter values were taken
- AUTHORS for the names of modern scholars
- SOURCES2 for the secondary sources (title, author, place and year
from which parameter values were taken
- PARAMS for the actual parameter values.
For each of the six
databases listed above you will need two files,
one with extension .DBF, the actual database file, and one with
.MDX, the index file which contains all sorting information. A
memo file PARAMS.DBT contains the extra information saved with each
value. If one of the thirteen files described above is not present, the
program PARAMS will not be able to execute properly. The files are all
in DBASE format, which means that it should also be possible to access
them directly from DBASE (version 4.0 or later). However, in that case
you yourself will be responsible for various functions that are
performed by the program PARAMS, such as entering the sexagesimal form
of the parameter values correctly and maintaining the links between the
To get started,
copy all 16 files contained in PARAMS16.ZIP into a
directory (suggested name: Params or, in Windows 95, Parameters) and
PARAMS.EXE, if desired after linking it to an icon on the desktop. The
main screen of the PARAMS program will then display the complete data
a single parameter value. You may try out the combobox lists and other
ways of entering and modifying data after switching to Edit Mode
Options, Edit Mode). However, note that in PARAMS, as in most
programs, changes to entries are saved automatically whenever you
to a different entry or perform a query, search, or other command.
on the Undo key (or type Alt-U) to undo any changes you have
Contents of this
Editing records, GoTo, Query,
programs provide some type of "navigator", a set of
with which the user can step through the database and perform other
operations such as undoing changes, deleting and undeleting records,
adding or duplicating records. In all six databases which can be
within PARAMS the navigator is set up vertically on the right of the
Each button indicates a certain operation, which you can perform by
on the button, pressing the RETURN key when it is selected, or pressing
its accelerator key (or hot key) Alt-X, where X stands for the first,
letter of the command name as indicated on the button. The scroll bar
the right of the navigator is intended to indicate the place of the
parameter entry within the whole database or the current selection, but
its operation has not yet been implemented, partially because it would
be too slow on 486 machines.
The ten navigator
buttons in PARAMS provide the following functions:
- First (Alt-F): Jump to the first record in the database
current selection, using the current sort order (see below under Sorting).
- Previous (Alt-P): Move to the previous record in the
in the current selection, using the current sort order.
- Next (Alt-N): Move to the next record in the database or
current selection, using the current sort order.
- Last (Alt-L): Move to the last record in the database or
current selection, using the current sort order.
- Add (Alt-A): Add a new, empty record to the database.
the data of this record, see below under Editing
and Fields. Note that you can not give the
"Add" when you are already adding a record: you first have to save the
newly added record with the command Write or by moving to any other
before you may add another entry.
- Copy (Alt-C): Add a new record to the database and fill
the data of the current record. This may be useful if the new entry
resembles the current one, for instance because it comes from the same
primary or secondary source.
- Mark (Alt-M): Mark the current record for deletion. A
will indicate "DELETED", but the entry will physically remain part of
database until the database files are «packed» (see below
under Other commands).
- Recall (Alt-R): Recall (or Undelete) the current record.
field indicating "DELETED" will disappear. Undeleting can also be
by clicking on the "DELETED" field of a record marked for deletion.
- Write (Alt-W): Write the current record to disk. In most
will not be necessary to give an explicit Write command, because
is done automatically whenever you move to a different record or
some other command. However, if you want to check the validity of the
you have just entered without moving to a different record, in
when you are adding a new record, "Write" may be useful.
- Undo (Alt-U): Undo any changes you have made to the
All data will be reread from disk. In case you are in the process of
a record, the addition will be canceled and you return to the previous
When you start
PARAMS, the program is in View Mode (indicated in the
of each window). If you want to make changes to existing records, you
to switch to Edit Mode by toggling the menu item Options, Edit Mode.
Alternatively, you may use the commands Add and Copy (see above under Basic
database commands), which will
automatically switch to Edit Mode in
order to allow you to edit a new record.
In Edit Mode you
can use the TAB key or a limited number of
keys to move between the various fields for each database (see below
a complete description of these fields). In some
fields, such as Confidence, Ref, and Extra Info you may type any text
like. In many other fields, however, the validity of the text you type
will be checked. In the Parameter Value field, for instance, you have
enter a correct sexagesimal number; input such as 1s30, 0;60 and 100,25
will not be accepted.
The fields Method
and Entered By provide a so-called combobox list,
indicated by the small boxed arrow on the right side of the field. You
may select a value from the list by clicking on the arrow or pressing
down-arrow and up-arrow keys repeatedly. For these two fields the
of the input is not (yet) checked: you may also enter other values than
those in the lists.
For the remaining
fields with a combobox list, Parameter Type,
Astronomer, Primary Source - Title, and Secondary Source - Title, the
is different. The easiest way to specify input for these fields is
to select it from the combobox lists. Since these lists are quite long,
a combination of some key strokes with a click on the boxed arrow or a
press of the down-arrow key usually provides the quickest way of
the desired data. For instance, to enter the Khâqânî
Zîj, you may select the Primary Sources - Title field and type Kh
followed by a single press of the down-arrow key (in other cases, some
more presses may be needed).
If the text you
want to enter is not present in the combobox list,
can simply type it in the edit box. When you have finished the whole
and try to save it, PARAMS will let you know that it has not been able
to find the text you typed and will give you the possibility to add it
to the database concerned. In the case of a new astronomer, you will
be able to specify its location and time, for a primary or secondary
you can enter its author using another combobox list and the library
or publication data in any format you like. Once you have thus updated
the underlying databases, the new record in the main parameter database
can finally be saved to disk.
From the above you
will understand that if you want to modify the
for a parameter type, astronomer, or primary or secondary source, you
have to go to the respective databases rather than making the changes
the main window. In the latter case PARAMS will assume that you want to
add a new entry rather than only modify an existing one. In order to
the underlying databases, select them from the Databases
In each of the
six databases accessible through PARAMS you can use the
command GoTo (click on the GoTo button or type ALT-G) to jump to a
of your choice. In the main parameter database you will be asked to
a parameter value, which, for the time being, has to be in the format
the Parameter Value field, i.e. with a semicolon at the place of the
point (cf. the complete field descriptions
In the other databases you may select the entry you want to go to from
a combobox list. Note that it is not necessary to enter the complete
specification: if you type "0;59,8,19", the first Parameter Value
with those characters will be selected, also if it has a larger number
of sexagesimals. In the Primary Sources and Secondary Sources database,
GoTo lets you only specify the title of the source; if you want to move
to a certain source by specifying its author, you may use a query
Query, available in the main database as well as in the
Sources and the Secondary Sources database, lets you select all entries
in these databases with a particular parameter type, associated
historical author (i.e., author of primary source), title of primary
modern author (i.e., author of secondary source), or title of secondary
source. Thus it is possible to select all values of the obliquity of
ecliptic contained in the complete database, all entries which were
from Caussin's edition of the introduction of the Hâkimî
or all parameter values associated with .Habash al-.Hâsib.
Performing a query
is very easy: in the main database you select the
field you want to base your selection on from the Queries menu.
Here Historical Authors stands for the author of the primary source,
Authors for the author of the secondary source. In the Primary Sources
and the Secondary Sources database you click on the Query Button (or
Alt-Q). In each case the Query window appears and allows you to type
name or title you want to select or to draw it from a combobox list.
clicking on OK (or typing RETURN or Alt-O) the specified selection will
be made and its first record displayed. Note that the title of the
now indicates that you are in Query Mode.
You can step
through your selection as you would through the whole
You can even perform a GoTo without losing the selection: after the
you want to go to has been displayed, the next move brings you back in
your selection. If you want to have access to the complete database
you need to «undo the query» by selecting Queries, Undo
Query or pressing Alt-G again and checking the "Undo Query" check
in the Query window. Later you can retrieve your selection by calling
Query" in the same way as "Undo".
As is explained
in more detail in the field
below, the main parameter database can be sorted in at least two ways.
As a default, the contents of the Parameter Value field, i.e. the Greek
representation of the parameter with decimal integer part, semicolon
the sexagesimal point, and sexagesimal fractional part, is used for
the parameter entries. By toggling the Sort, Use Parameter
menu item, the sorting method can be changed to use the Parameter Sort
Key field, i.e. a purely sexagesimal representation without semicolon.
The latter is particularly convenient if you do not know the type of
parameter you have encountered and hence the place of its semicolon.
following table shows the effect of the two different ways of sorting
a small set of six arbitrary parameter values:
The menu item Sort, Complete Sort
to select the respective keys of all six databases for sorting the
In general such a key sort corresponds to the order in which the
have been added to the database. Except when entering large amounts of
data while constantly checking existing entries for references and
key sort will not be particularly useful for the general user.
| Parameter Value
|| Parameter Sort Key
0; 0, 0, 4,21
- Options, Font enables the user to specify the font used
text in all windows. The default font is System, bold-face, 10 pt.
- Options, Scale is an expedient for graphical systems on
windows of PARAMS are not correctly scaled (the main window should fill
the whole screen as a default). This command will only be needed in
- Options, Pack rewrites all database files and the memo
to disk, physically deleting all records marked for deletion and their
Extra Info fields. After packing, no previously deleted records can be
recovered any more. In normal situations it is hardly ever necessary to
pack. You may do so if you have deleted a large number of records and
disturbed by their continued appearance between the other records.
The data for
every single parameter value are displayed in the
fields on the main screen of PARAMS:
- Parameter Type: the type of the parameter. By
the parameter type combobox list (in order to be able to do that, you
to be in Edit mode), you can select one of the names of the parameter
entered in the separate database PARTYPES. In order to modify these
you will have to select Databases, Parameter Types; if you
a name in the Parameter Type field of the main screen, PARAMS will
that you want to add a new name to the PARTYPES database instead of
an existing one.
All names of planetary parameters start with the name of the planet
concerned ("Solar ..." and "Lunar ..." for the sun and the moon),
of certain periods with "Length of ...", etc. Mean motions have been
per day as well as in Arabic and Persian years. Base positions of the
motions have been entered for the Hijra and Yazdigird epochs. Types
occur very rarely (e.g. planetary base positions for a date not equal
the epoch of the Hijra or Yazdigird calendar) are entered as "Other"
are fully described in the Extra Info field.
- Parameter Value:
the parameter value in so-called
i.e. with a decimal integer part and sexagesimal fractional part. The
point is denoted by a semicolon, sexagesimal digits are separated by
You may enter the contents of this field in any sexagesimal format you
like: 5,59;45,44 and 11s29;45,44 will both automatically be converted
the Greek form 359;45,44.
- Parameter Sort Key: the parameter value in a
purely sexagesimal notation. This field will be filled in
whenever an entry with a new parameter value is saved to disk. For
a Parameter Value 359;45,44 will appear in the Parameter Sort Key field
as 5,59,45,44. This system, used by Kennedy in his original parameter
and in the parameter indexes of many of his publications, has the
that parameter values of unknown type can be looked up without knowing
the place of the sexagesimal point. As a default, PARAMS uses the
Value field for sorting the parameter database. By toggling Sort,
Parameter Sort Key the field used for sorting can be changed to the
Parameter Sort Key field (see also above under Sorting).
You can see the effect of the two different ways of sorting by stepping
through the database with the commands Next (Alt-N) and Previous
described above under Basic database operations.
For the time being, the GoTo commands (see above)
operate with Parameter Values and not yet with Parameter Sort Keys.
- Method: the method by which the Parameter Value was
In principle, the following abbreviations are used in this field:
Confidence: the (numerical) confidence that can be
Parameter Value. This entry usually gives an interval around the
Value, where the last digit of the Confidence field agrees with the
digit of the Parameter Value. Thus a value 0;59,8,20 with confidence
indicates the interval of values from 0;59,7,0 to 0;59,9,40. The
of the Confidence field depends on the contents of the Method field as
- q indicates a direct quotation from a primary or
- dc stands for direct calculation, i.e. a simple linear
as is used, for instance, to convert a mean motion per year to a daily
- c signifies a more complicated type of calculation,
the daily mean solar motion from the length of the tropical year;
- sq means «squeezing», the determination of
parameter by dividing a particular mean motion by the number of days of
the period concerned;
- lne, the least number of errors criterion, is a more
of squeezing a parameter, which makes use of the information in all
- ls is a least squares estimation, which uses
to determine the accuracy of the obtained estimate of an unknown
(both the least number of errors criterion and the method of least
are described in my doctoral thesis, for which the reader is referred
my list of publications).
Associated Astronomer: the name of an astronomer to
Parameter Value concerned is explicitly attributed in a primary or
source. The names of a large number of medieval astronomers can be
drawn from the combobox list. You may open the ASTRONOM database
(select Databases, Astronomers) to see which astronomers have
and, if desired, to make modifications to the astronomer data.
- For a direct quotation, the confidence field will always be
the entered parameter value is precisely what is found in the source.
- For a directly calculated, calculated, or squeezed parameter
field indicates the range of values that the parameter may have if we
that the number from which it was calculated or squeezed is not exact
was rounded to its number of sexagesimal places. For instance,
a source gives a mean motion of 9;51,23° in 10 days, we assume that
this value was rounded from a more accurate value and actually lies
9;51,22,30° and 9;51,23,30° (in the notation used for the
field this would be written as 9;51,23,0 ±30). By dividing by
we obtain a daily mean motion which should lie between 0;59,8,15°
0;59,8,21°. This we will enter as 0;59,8,18 ±3, i.e. the
field will contain ±3.
- For the least number of errors criterion, the Confidence field
the range of parameters for which the largest number of tabular values
is correctly recomputed.
- For the least squares estimate, the Confidence field will give
95 % confidence interval, an interval which contains the parameter
with a probability of 95 %.
All long vowels in Arabic and Persian names have been entered as ANSI
characters â, î and û. In case an Arabic letter
a dot under it in the transliteration, this dot has been placed in
of the letter, e.g. .h and .s. I have as much as
used the forms of the names that are most common, e.g.
.Habash al-Hâsib, Abû al-Wafâ´, Ibn
As a result, some congestion of names takes place under al-, Ibn,
etc. Special entries have been added for parameters that cannot be
to a particular astronomer. Examples are: "Babylonian tradition",
tradition", and "Modern value".
Note that in the current version of PARAMS long vowels and dotted
are not alphabetically ordered as would be preferable: names starting
a dot (e.g., .Habash al-.Hâsib) appear at the very beginning,
starting with a `ayn or a long vowel (e.g., Âryabha.ta) at the
of the alphabetical listing. Location: the place where
the Associated Astronomer
The contents of this field change automatically depending on the
astronomer. You can only edit the contents of the Location field in the
ASTRONOM database (select Databases, Astronomer).
Time: the period in which the Associated Astronomer
worked. The contents of this field change automatically depending
the entered astronomer. You can only edit the contents of the Time
in the ASTRONOM database (select Databases, Astronomer). If
the dates of birth and death are indicated in the form "1393-1449".
abbreviations include obs. for "made observations in".
Primary Source - Title: the title of a primary
the Parameter Value occurs or from which it can be derived. Names
zîjes containing the word "Zîj" are given in an "English
such as "Shâmil Zîj" or "Sanjufînî Zîj".
Other titles are given in a transliteration of the Arabic or Persian,
out initial words like "Kitâb". If necessary, an indication
brackets specifies the source more closely, e.g.
Zîj (London)" and "Îlkhânî Zîj (Paris)"
two different manuscripts of al-.Tûsî's work.
You can select a previously entered primary source from the combobox
list. In order to modify existing entries for a primary source (title,
author, or shelfmark), you will have to open the SOURCES1 database
(select Databases, Primary Sources). Primary Source -
Author: the author of the primary
which the Parameter Value was taken. The contents of this field
automatically depending on the entered primary source. You can only
the contents of the Primary Source - Author field in the ASTRONOM
(select Databases, Astronomer). The changes you make there will
be visible in the Associated Astronomer as well as in the Primary
- Author fields, since both draw their data from ASTRONOM.
Primary Source - Shelfmark: the library and
of the primary source from which the Parameter Value was taken. The
contents of this field change automatically depending on the entered
source. You can only edit the contents of the Primary Source -
field in the SOURCES1 database (select Databases, Primary Sources).
Primary Source - Ref: the folio number and other
for finding the precise place where the parameter occurs in the primary
Secondary Source - Title: the title of a secondary
which the Parameter Value occurs or from which it can be derived. I
have always used complete titles, even though this means that a large
appears under "The ..." and various under "The astronomical ...". This
still seemed preferable to abbreviated forms, which are clear for
works, but not for less important ones. Abbreviated forms have been
for additional references in the Extra Info field (see below). You can
select a previously entered secondary source from the combobox list. In
order to modify existing entries for a secondary source (title, author,
or publication data), you will have to open the SOURCES2 database
(select Databases, Secondary Sources).
Secondary Source - Author: the author of the
from which the Parameter Value was taken. The contents of this
change automatically depending on the entered secondary source. Note
in case of a publication with two or more authors only the first author
has been entered. You can only edit the contents of the Secondary
- Author field in the AUTHORS database (select Databases, Modern
Secondary Source - Published: the place and year of
of a book, or journal name, volume number, year, and pages for an
Journal names have generally been entered as abbreviations, of which
for the Vierteljahrsschrift der Naturforschenden Gesellschaft
probably is one of the less obvious ones. The contents of the Published
field change automatically depending on the entered Secondary source.
can only edit the contents of the Secondary Source - Published field in
the SOURCES2 database (select Databases, Secondary Sources).
Secondary Source - Ref: the page number and other
for finding the precise place where the parameter occurs in the
Extra Info: all relevant additional information
Parameter Value and its sources. This field is often used to
additional astronomers using the Parameter Value and additional primary
and secondary sources that contain the value. Furthermore, relations
other parameters will be given, such as the value from which a given
was derived or other values which can be derived from it. Common
for this type of relations are mean motions which are given per day as
well as in an Arabic or Persian year.
Key: an internal number attached to each new entry.
you will not deal with the key, although it can be used to sort the
in which case the parameters are arranged in the order in which they
Entered by: the initials of the person responsible
of the parameter. In most cases, this is ESK (E.S. Kennedy). Other
abbreviations include BvD (Benno van Dalen), DAK (D.A. King), and MCa
Castells). If you add entries of your own, you may here insert your
instead of the default ESK. This may be useful, for instance, when
newly added entries, facilities for which will be provided in later
Date: the date of the last modification of the entry.
is entered and adjusted automatically whenever you add or change an
Note that the
relation between the parameter information in the various
fields is not always the same. For instance, if a parameter is
with a certain astronomer, the mention of that astronomer may occur in
the primary or the secondary source or even in another source indicated
in the Extra Info field. Sometimes the primary and secondary sources
to a manuscript and edition of the same work, in other cases they may
completely unrelated and even deal with astronomers from different
and periods. Although this way of entering the data may occasionally
to some confusion, it seemed preferable as far as efficiency and search
(query) possibilities are concerned. If needed, additional explanations
of the relation between parameter value and sources are given in the
version of PARAMS is a preliminary one and still needs a
number of improvements and additions. The To Do list contains at least
the following items:
- Addition of the remaining parameter data.
- Context-sensitive help system and all help commands.
- Additional queries: combined queries (for example, select all
values listed in the .Hâkimî Zîj of Ibn Yûnus),
query on library / shelfmark information of a primary source.
- Possibility to write all data fields of the selected parameters
- Provisions for the use of multiple copies of PARAMS at the same
the moment it is save to use one copy for editing and one or more
for look-ups, but some safety has to be provided in particular for
adding records in two different copies.
January 3, 2011.