International Gnomonic Bulletin

International Gnomonic Bulletin
Digital Bulletin created by Nicola Severino on October 2003
Number 9
May 2004
Spherical roman sundial from a archaeological site of Paestum (Salerno), Italy.
In this number: Oughtred by Alessandro Gunella
Sundials in the gardens, castles & internet curiosity, by N. Severino
IInntteerrnnaattiioonnaall G
Gnnoom
moonniicc BBuulllleettiinn
By Nicola Severino
nicolaseverino@libero.it
www.nicolaseverino.it
OUGHTRED
By Alessandro Gunella
Preface: This article is the essay explained in the Italian Seminario di Gnomonica of March 2002. In
April of the same year it was published in the spanish magazine Analema N° 34. I don’t claim the
authorship of the method, because it must be attributed to Agostino Dal Pozzo, a 17th century man.
Give to Caesar…..
The diagram of Oughtred (1636) completes 365 years happily, but that aura of mystery
stays, so that it rests practically unknown by the most part of the writers of gnomonics. With any
small exception, if we refer to 17th century:
about at 1660, the Jesuit Andreas Tacquet of
Antwerp, explainig the general problem of the
Astrolabe, remembered the diagram of
Oughtred, but he did not name the inventor.
The book “Gnomonices biformis” of
Agostino Dal Pozzo (1679), doctor “in utroque
iure” and "mathesiphilus" uses the diagram to
develop the normal Wall-sundial. He refers to
the work of a predecessor, Father Salodius.
(On Agostino Dal Pozzo I could add, but with a
scarce deal for the economy of this article, that
probably he was my countryman).
How does the dial of Oughtred to be built?
Let start from the Analemma of Vitruvius (Fig. 1) in the ZRN circle, and follow
same technique that is worth for the astrolabes: from the Nadir N, let project
circles of the Zodiac signs on the plane of the horizon: this is represented by the
line (and, after a turnover, by the same ZRN circle): on it we project, at first,
equinoctial plane AB, getting the A'
and B' points: from them will pass the
circle that, being a maximum circle,
will also pass in the extreme points of
the ZN diameter. The "diurnal" part
of it is NA'Z, and the nighttime part is
ZB'N.
the
the
SR
the
If we repeat the joke for C and D,
extreme points of the Cancer tropic,
we get the passing circle per C'D'
(projections of the two extreme points
from N). Here it is worthwhile to
observe that the perpendicular line to
SR, passing per X, is the line of intersection between the plane of the tropic and the
horizon circle ZRN.
That suggests a method to avoid tracing many lines to get the other circles to be
projected: the diurnal arc of the Capricorn tropic passes per E' (projection of E from
N) and per the two extreme points of the perpendicular. The figure 1 doesn't illustrate
the construction of the other arcs (relative to the
beginnings of the zodiac signs) for don't make
illegible the sketch.
And here we must thank the CAD systems allowing to
trace these figures with facility, that in other epochs
required biblical times.
Let now find the hour lines (Fig. 2): find the
projections P' and Q', of the poles of the earth on
the horizon plane; the hour meridians are maxima
circles that must pass per such projections.
Following one of the possible techniques (the
same used to divide, in the astrolabe, the circle of the zodiac) we divide the ZNR
circle in 24 parts, and project the subdivisions from P' on the equinoctial circle. I
don't stay to explain why, otherwise this should be an essay on the polar projections.
The hour circles of the equal hours pass per 1, 2, 3 points etc. on the equinoctial line.
The final result of the operations until here explained is visible in the figure 3, in
which I have traced the remarkable parts of the hour lines and the arcs of circle of all
the zodiac Signs.
The diagram for the Italic and Babylonian hours
I took advantage from the relative legibility of the Fig. 3 to make an addition: the WR
line represents the limit circle of the stars "always visible" on the Vitruve Analemma.
His projection on the plane of the horizon is the W'R circle.
The hour circles of the Italic hours and Babylonians, if we refer to the Analemma, are
maxima circles passing per the same hour points of the equal hours in the equatorial
circle, and tangent to the limit circle WR of above.
In the figure 4 are represented two maxima circles of these two hour systems (Italic
and Babylonic), passing per the equal hour "1" in the equatorial circle. I think not
necessary of dwell in worth.
In the figure 4/bis, pleasant to be seen, but absolutely illegible, the whole procedure
is illustrated for get all the hour lines of the two systems (Italic and Babylonic). From
the diagram the projection of the opposite circle also results, that of the "always hide
stars". Obviously, the tangent planes to the circle of the "always visible" are tangent
also to his opposite.
The Fig. 5 illustrates the final result. Modifying the latitude, the form of the diagram
changes.
Agostino dal Pozzo and the wall dial.
The "colleague" Agostino dal Pozzo wrote around 500
pages in Latin for illustrate the gnomonics under two
appearances: the graphic one, and the analytical.
He is perhaps the first, in Italy, to have applied the
Logarithms to the trigonometric relationships that
regulate the diagrams of the dials. But he thought it was
hit duty to furnish to the reader the parameter tables to
trace on the vertical walls (for the latitudes of the
Padana Lowland) the italic dials, on the base of the
length of the perpendicular stylus, without necessity of
making complicated calculations.
In that epoch the Colomboni tables were just printed;
whith them Agostino owed concourse also.
At the end of the book, he added a small essay, in
Italian, in which he illustrates a method for get the dials
on the walls from the Oughtred diagram. He begins affirming, justly, that the diagram contains all
the data of the tables, and that enough arrange with it to trace a correct dial. However the example
he adopts to teach the method is very wrong, starting with the exposure of the method to construct
the diagram; so much to give the impression that he doesn't know at all the matter of which he
writes…
The general idea stays, that has given me anyting to think over.
I have therefore abandoned the exposure of my (probable) countryman, and elaborated again the
problem, looking for a solution relatively simple and "logic."
Therefore, in this article, I will bore the reader, but only within some limits: I will expose the knowhow to build the horizontal equal hours dial and the vertical one (in the North part of Italy the
equal hours were said "French" or "Ultramontane", and in the South part "as the Spanish
manner"); I then will explain how to do the Italic horizontal and vertical dial, and after stay there,
because it needs have the sense of the limit (or do I know only how to do those? I won't confess it
ever)
As in other occasions, I will correctly remember that these "graphic acrobatics" must be classified
as curiosity: the time and the use have settled easier methods to explain and to be applied.
This method could enter the number, because the "conversion" is always very simple. But any
problems of "quality" of the result exist, above all for the extreme and the central hours, and any
true limitations, that induce to discard the
hypothesis of a practical use.
How much useless things in the life!
The equal hours horizontal Dial
Let consider (Fig. 6) the vertical
Stylus in the S center of the polar
Oughtred diagram; SV is his length,
and let build the gnomonic triangle
CVM. The AM straight line will be
the equinoctial line, and the C point
the center of the horizontal dial.
Let consider now the h hour line on the polar diagram, and in it the H point on the
equinoctial line: projecting it from the S point, H' on the AM line is found.
The h hour straight line of the dial will be therefore CH'; if on it the E and I points of
the Oughtred diagram are projected, the length of the hour line (the Heliodrome,
according to Kircher) will be E'I'. Obviously the operation must be repeated for all
the hour lines, and we will meet any small difficulty e. g. when defining the extreme
points of the meridian line CM. I leave the reader to find how overcome it.
The declining vertical dial
Let capsize (Fig. 7) the horizontal
plane toward the top (or toward the
lower part, it is indifferent: but to the
top gives less trouble) around the
horizon line, so that the OAS angle is
equal to the declination of the wall. The
OS distance will be the projection of
the stylus on the horizontal plane. Let
build the gnomonic triangle CVM, in
which VO= OS.
C is the center of the clock; the
equinoctial line is MA.
The figure explains how the 2 line of
the afternoon is built: the three points
(those "important" of the hour line) are
projected on AV, the trace of the
horizon plane, finding H' I' and E.' Let trace the vertical line from H', finding H" on
the Equinoctial line.
The hour line will be CH"; to find his extreme points of the so-called Eliodrome sink
the vertical lines from the I' and E' points.
Why the vertical lines? elementary, Watson: the clock of Oughtred is "azimuthal",
and the planes coming from S are all "Vertical."
The Italic horizontal dial
Between the methods I elaborated, I think the simplest it is the following (Fig. 8):
Let find the equinoctial line through the triangle VMC (as in the figure 6, obviously),
the SV length of the vertical stylus, and the V position of the gnomonic point.
Now we must modify the diagram of the figure 5, extending the arcs of circle until to
the circle limit of the diagram (see always Fig. 8).
We find now the H' point on the equinoctial line, correspondent of H point, and we
trace the Azimuth ST.
Since the correspondent of the T
point is to the endless distance,
the hour line in examination
will be certainly a passing
straight line per H' and parallel
to ST. The limits of the solar
field will be found by the
projections of I and E points
from S.
The Italic Vertical declining Dial
The considerations on the Italic horizontal clock, and particularly on the ST direction,
also are worth for the vertical clock; but now the line of horizon is here, above the
quadrant, and not to endless distance. For the rest, we will undergo the operation like
for the vertical equal hours dial.
Let make the same way, and hoop the correspondences, rather than the differences.
(Always two points must be found for each hour line).
We capsize the diagram toward the top (in the sketch in fact it is "inverted" because
seen from the under) exactly like we
did for the other vertical clock; we
find, like for the preceding vertical
clock, the gnomonic triangle relative
to the meridian line, because the
diagram of Oughtred of which we
arrange is relative to the latitude of
the place and therefore must be
referred to the meridian line, and not
to the substilar line.
The perpendicular line SS' to the
horizontal plane will be the length of
the perpendicular stylus to the wall
(in the italic clocks it is important).
Let project now, on the line of horizon, the H equinoctial point, of the 19th hour line
taking in examination: and then from H' find H" on the equinoctial line, as done for
the other clock. If now we prolong the ST up to T' , on the horizon line, we have a
second point of the hour line 19 on the wall: this will be therefore T'H".
The extreme E" and I" of the hour line are found as for the precedent vertical clock.
Conclusion
I want to make notice the reader a singleness, inviting it to compare the "classical"
construction of the vertical dial with the method explained here: to build the vertical
clocks graphically,declinaning or not, an equatorial dial is used usually, that is
capsized around the equinox line of the future dial. From the turnover we find the
hour points above the equinox line, and from them the rest of the work. As it
concerns the extreme points of the hour lines, it needs apply to a supplementary
construction (avoided by the French builders, with the use of the so-called
"sciaterre"). For the italic lines the more used method is the known one as "method of
the half hours", while the determination of the extreme points of the hour lines is
done usually superimposing the "italic" diagram to one "French" built before.
With the method exposed above, we capsize the diagram of Oughtred around the
horizon line, and on it the extreme points of the hour lines are projected; the method
now is indifferent for the equal hour lines, the Italic and Babylonians, and allows to
determine directly and always with the same criterion the extreme points of the hour
lines.
The unique true "difficulty" consists of the degree of graphic attainable precision, that
depends on the dimensions of the diagram, on the distance between the center of the
clock and the horizon line, on the dimensions of the threads to throw directly on the
wall for find the projection points, on the number of "hours" can be traced in fact, etc.
These are the reasons for which above I affirmed that we are in front to a suggestive
theory, but not easy to be applied.
Sundials in the gardens, castles and internet curiosity, by N. Severino
Warrnambool Botanic Gardens
Sundial
This newly restored sundial was donated by Mayor Hickford in 1906. It has a slate face and bronze
gnomon. Few sundials remain in public gardens today due to vandalism.
Warrnambool, Victoria, Australia
Sotterley Plantation is located on Route 245 in Hollywood, Maryland.
It is accessible from Richmond (110 mi.), Washington D.C. (60 mi.), Baltimore (90 mi.) and
Philadelphia (130 mi.).
Eleanor and Mabel Satterlee at the sundial in the garden (early 1900s)
School children visiting Sotterley at the sundial (2002)
History of Cranbury Park, Hampshire by Michael Ford
CRANBURY
PARK
The Home of Sir Isaac Newton
The Chamberlaynes came to live at Cranbury Park around 1800 and are still in residence. The
pleasure grounds were laid out in 1815 and are thought to be by Papworth. The sundial in the
garden displays the Conduitt coat of arms and was calculated by Sir Isaac Newton himself.
The Garden of Cranbury Park is normally open for one day only in June. Enquire locally for
details.
The gift of time
Roger Littge’s interest and enthusiasm for the Student
Experimental Farm translated into this sundial in the garden area
near the farm’s office.
What makes this replica of the ancient solar timepiece special is
that "it automatically corrects for the earth’s orbital eccentricity
and the obliquity of the ecliptic, or tilt of the axis of rotation
relative to the orbital plane," says Littge, a postgraduate
researcher in the Department of Mechanical and Aeronautical
Roger Littge designed this 4-foot-tall
sundial for the Student Experimental
Engineering (photo, right).
Farm.
Debbie Aldridge/Illustration Services
The sundial was built over four months in 1998, largely by
volunteers such as Carol Hillhouse, director of the Children’s’ Garden Program and ecological
garden coordinator. Hillhouse is looking for an area artist to decorate the outside of the sundial with
a tile mosaic.
The 4-foot-high sundial, made of mortar, steel and wire, is located in the ecological garden directly
in front of the Plant Science Teaching Center and the Student Farm Fieldhouse.
Herstmonceux Castle UK
staffi.lboro.ac.uk/~copal/pal/biography/rgo/castle.htm
We were fortunate to be there the year after the Tercentenary and and this huge sundial in the
garden was one of the special commemorative pieces on the site.
The Secret Paintings of Clementine Hunter - Part 1
Background on Whitfield Jack, Jr.,
Owner of Clementine Hunter's "Bowl of Zinnias"
Whitfield Jack, Jr. was born in 1936 in Alexandria, Louisiana, about forty-five
miles from Melrose Plantation. In 1944, when Whitfield was eight years old,
Mrs. Cammie Henry, owner of Melrose, gave his grandparents, Blythe White
Rand and Dr. Paul King Rand of Alexandria-- friends of Mrs. Cammie's since
the mid 1930's -- a one-hundred year lease for $1.00 on a parcel of land for a
fishing camp on Cane River. The camp, named Happy Landing, was located
just across the cotton fields and down the road from Clementine's house.
From the time he was eight years old, until Mr. Jack was in his late teens, he
visited Melrose frequently with his grandmother -- sometimes staying at
Happy Landing for several weeks at a time -- and became a good friend of
both Clementine Hunter and Francois Mignon, the resident guardian, care
keeper, and director of social life at Melrose. Mr. Jack maintained his
friendship with Francois until the latter's death in 1980 and is one of the few
people still alive today who was actually there during the early years when
Clementine first began painting.
Site: http://www.clementinehunterartist.com/SECRET-1/secret-1.html
Whitfield Jack Jr.'s grandmother, Blythe Rand, (far right) and Francois
Mignon (second from left) with a group of visitors c. 1944 in the garden
at Melrose beneath the giant sundial. Francois referred to the flocks of
tourists as "pilgrims".
El Paso Solar Energy Association
Solar Cook Off '97
EPSEA's Solar Cook Off coincided with Eath Day Festivities in El Paso on April 20. On a beautiful
Solar Day, EPSEA not only conducted the cook off but also set up working solar displays which
included; PV water pumping, solar distillation, concentrated solar energy, a stirling engine and the
"Human Sundial". Thousands of people visited our booth and left with information about the
equipment displayed as well as solar design, hot water and more.
The Human Sundial
Once laid out the human dial holds their hands slightly apart and turns until there is no shadow on
either palm.
Lilly Ojinaga, Program Coordinator for Renewable Energy, State Government of Chihuahua,
Mexico demonstrates just how easy it is to tell time.
Curiosity
Sundial of 1959 at Carleton University, Ottawa, Ontario, Canada
Presented to Alois (Louis) Anton Raffler commemorating 30 years of outstanding service.
The sundials at Aberdour Castle, Scotland
The Fragrance Garden, Maryland
Examples of all types of roses can be found in this garden including hybrid tea, rugosa hybrids, grandiflora,
English, miniature, floribunda, shrub, groundcover, polyantha, climber, Gallica, hybrid musk, and the garden
rose. Other plants of interest in this garden are crape myrtle or Lagerstroemia x 'Apalachee', Amsonia
hubrechtii or blue star, Fagus sylvatica 'Rohan Obelisk' or upright purple beech. Look for the many All
American Rose Selections awarded by the American Rose Society and a new sundial in this garden.
Cleone Gardens Inn. Canada
Sundial at Nathan Phillips Sq. – Toronto Canada
Armillary sphere sundial
Australian National Botanic Gardens, Canberra
Located beside the Main Path near the Rock Gardens, beside a spacious lawn, is a fine example of
an armillary sphere sundial. Made from silicon bronze, the sphere is 0.5m in diameter, and is
mounted on a rock for easy reading. An adjacent plaque gives the time correction needed and
instructions for reading the sundial. The precise geographic coordinates for the dial are Latitude 35°
16' 45" S, Longitude 149° 06' 26" E.
The dial was presented by the Friends of the Australian National Botanic Gardens in November
1999 and was made and installed by Sundials Australia in Adelaide. The dial is shown on the
Visitor Guide map of the Gardens and is about 300m north of the Visitor Centre. The walk to the
summit of Black Mountain starts nearby.
Armillary sphere sundials, modeled on the celestial or terrestrial sphere, are constructed from three
or more interlocking rings which provide support for the rod-like gnomon, which forms the axis of
the sphere, and casts the time-telling shadow on the equatorial ring. In the case of the ANBG
sundial this equatorial ring interlocks with a meridian and polar ring.
The equatorial ring carries hour lines marked at 10 minute intervals from 5a.m. to 7 p.m., the
approximate time (Australian Eastern Standard Time) of earliest sunrise and latest sunset
respectively in Canberra. The gnomon is set at an angle of 35° to the horizontal (corresponding to
the latitude of Canberra) so that its upper end points at the South Celestial Pole.
Another fine armillary sphere in Canberra can be seen in the north corner of Parliament Drive
outside Parliament House.
Sundial around Melbourne, Australia
Ohio. USA- The class of 1905 donated a sun dial mounted on a marble column. This was placed
on the 40th parallel south of University Hall (Bldg. 088). In October 1926 the Sun Dial was moved
to the intersection circle in the Long Walk nearest to the Library [Bldg. 050] (Lantern, October 5,
1926). Maps of the period indicate that the center of the circle was 400 feet east of the Library. Four
years later, it was returned to its original location (Lantern, June 5, 1930). In 1981, the Sun Dial was
incorporated into the Sphinx Plaza. http://www.rpia.ohio-state.edu/facility_planning/ovalmirror/SEC7-2.HTML
San Juan, near Dublino, Ireland
Sundial at Portmarnock beach
Sundial
Bronze sundial mounted on Chelmsford granite pedestal
Height: 18' Diameter: 10’
In process for Massachusetts General Hospital Nurses Alumnae
Bulfinch Lawn
Sundial Sculpture:
To Honor Alumnae Nurses at the Massachusetts General Hospital
I would like to tell you about the sculpture that I have created to honor not only the alumnae nurses at the MGH but the nursing
profession as a whole. The green space in front of the Bulfinch building seemed a perfect place for a sundial.
The earliest known sundial has been dated at about 1500 BC. Evidence of their existence has been found in Babylonia, Greece, Egypt
and China at about that time. Although the formal profession of nursing is much more a modern notion, nursing as a concept is as old
as the oldest civilization known. The sundial represents that timelessness and further the 24 hours, 7 day a week spent by nurses doing
their job.
The bronze dial is 7 feet in diameter. It is round and represents the cycle of life. Nurses of today are at the beginning of life and at the
end. This diameter also represents the seven days many perceive it took to create the earth. This sundial will also, indeed, tell time!
There is room at the bottom of the Gnomon* for a saying or a quote, possibly of some famous person like Florence Nightingale. That is
the part of the dial that represents night. Somewhere along the sundial an exact bronze replica of an MGH cap will be serendipitously
found.
The figures in the Gnoman represent past, present and future. They also represent growth as each figure shown is larger than the last.
The first figure (past) is shown carrying a lamp, indicating Florence Nightingale and the beginning of nursing as we think of it today.
The second figure (present) is shown holding a book, indicating the important educational and intellectual changes in the profession.
The third figure (future) is shown carrying a Globe indicating the multiracial nature of nurses. Also, nurses travel more and more all
over the world, helping and teaching. They will do it in reality and virtually through the internet. The Institute for Health Professionals is
a major vehicle to that end.
I have used the Greek goddess as the image for these three figures. Examples are: Athena (Minerva) who was the goddess of wisdom.
Aphrodite (Venus) who was the goddess of love and beauty. Artemis (Diana) who was the goddess of hunting, but protected young
creatures and looked after maidens in childbirth.
The granite pedestal that holds the sundial is 10 feet in diameter and made from Chelmsford granite, a native stone having a thermal
finish. It is 18 inches high, a height for telling time with ease, for sitting or for sitting on the grass and leaning against.