Mac,
The use of the term "analemmatic" for this dial is discussed in two
articles I did for the BSS Bulletin:
"Of Analemmas, Mean Time and the Analemmatic Sundial - Part 1" Bulletin of
the British Sundial Society, Jun 1994, 94(2):2-6.
"Of Analemmas, Mean Time and the Analemmatic Sundial - Part 2" Bulletin of
the British Sundial Society, Feb 1995, 95(1):39-44.
These are reprinted in SciaTheric Notes - I, available from the North
American Sundial Society. The articles cover a good deal of ground about
the analemmatic dial. The following is a relevant extract:
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There is an interesting irony in the fact that the analemma ('figure 8')
curve has become a familiar feature on the classical sundial over the last
century and a half, but has only rarely been seen on the analemmatic
sundial. One might expect the similarity in names to suggest more of a
kinship between the dial and the curve. The purposes of the present
article are to consider this irony - a consideration which requires
something of an etymological journey - and to elaborate on the design of a
standard-time analemmatic sundial which reinforces the kinship by reuniting
the dial and the curve."
In order to proceed, we need to understand the concept of the analemma in a
more general setting. Not only is the word analemma seldom used today
outside of the 'gnomonic community', but when it is used, its meaning tends
to be only a narrow derivative of its original sense:
"The word analemma means much the same as lemma; the analemma is for
graphical constructions what the lemma is for geometrical demonstrations;
it is a subsidiary figure which is taken up to shorten and facilitate the
construction of the principal figure. "
The particular analemmas which in ancient times proved to be of most use in
the design of sundials appear in the works of Vitruvius and Ptolemy.
Writing in the first century B.C. in De Architectura, the Roman engineer
Marcus Vitruvius Pollio noted that "in order to understand the theory of
these dials, one must know [the theory] of the analemma". However, the
analemma to which he referred was not the now familiar curve relating
apparent and mean time. What Vitruvius alluded to was a graphical
procedure equivalent to what is known today as an orthographic projection.
Although he did not provide instructions for its use, Vitruvius made it
clear that the analemma was at the core of the ancient practice of
sundials.
Early in the second century A.D., Claudius Ptolemaeus wrote De Analemmata,
a more detailed presentation of a method for projecting the principal
circles of the celestial sphere onto a plane - the projection being from a
point at an infinite distance along a line perpendicular to that plane.
After describing the coordinate system resulting from his projection,
Ptolemy presented two distinct methods for determining the coordinates; one
method was trigonometric, the other was nomographic - basically, he
invented an instrument. This instrument - Ptolemy's analemma - was
composed of two pieces: a carpenter's square and a plate of wood or metal
with inscribed scales and curves. It allowed one to read values of
coordinates directly from the analemma diagram by use of the carpenter's
square as a straight-edge.
The analemma is thus also an instrument which implements a graphical
procedure. This sense of the word is apparent in such references as
Regiomontanus' 15th century introduction of a "universal rectilinear
analemma" - now generally implemented as an altitude dial on a card; St.
Rigaud's publication of his version of that dial as a New Analemma, and
John Twysden's 1685 Use of the Great Planisphere called the Analemma. Note
also Valentin Pini's 1598 discussion of Ptolemy's work, in which he
introduced his own analemma - a simple armillary dial.
The analemmatic sundial we know today was probably invented some time in
the period between 1532 and 1640. The timing could not have been more
unlikely for the introduction of a modern sundial based on an ancient
analemma:
"[The ancient] type of dial has fallen into disuse, since we stopped
dividing the day into temporary hours. The Ptolemaic theory would
therefore be perfectly useless to us today, if his constructions could not
be equally adapted to the new system.... When the book of the Analemma was
published for the first time by Commandin, in 1562, gnomonics had already
been founded on totally different principles. See the Horologiographia of
Munster, of which the first edition is of 1531, and the second of 1533. "
Whoever invented the dial managed to combine the three senses of analemma
into a single accomplishment which not only bridged the centuries but
transformed an old concept so that it made sense in a world of equal hours
- the new paradigm of time measurement.
"[The analemma was] applicable to the ancient dials which , as everyone
knows, have their style perpendicular to their face. It had lost all
practical utility with the modern dials, based since the 15th century on
the inclination of the style parallel to the axis of the world. But the
analemmatic dial, with perpendicular style, appearing in the texts of the
17th century, revived the use of the analemma through its geometric
construction."
The analemmatic dial is little else than the graphical procedure we know as
orthographic projection turned into an instrument to tell time. Its
ellipse of hour-points results from an orthographic projection of the sun's
path from the pole onto the horizon circle. Authors ranging from Vaulezard
in 1640 to Lalande, more than a century later, derived its distinctive
declination scale for the placement of the vertical gnomon directly from
the traditional analemma drawing.
