The Compendium 16-1 March 2009 - North American Sundial Society

Transcription

Volume 16 Number 1
March 2009
Journal of the
North American Sundial Society
ISSN 1074-3197 (printed) ISSN 1074-8059 (digital)
The
Compendium*
It is eternity now. I am in the midst of it.
- Richard Jeffries
* Compendium... "giving the sense and substance of the topic within small compass." In dialing, a compendium is a
single instrument incorporating a variety of dial types and ancillary tools.
© 2009 North American Sundial Society
NASS Officers
President & Editor: Frederick W. Sawyer III
8 Sachem Drive, Glastonbury, CT 06033
nass_president@sundials.org
Vice President: Don Petrie
462 Millard St., Stouffville, ON L4A 8A8 Canada
nass_vicepresident@sundials.org
Secretary: Roger T. Bailey
Treasurer: Robert L. Kellogg
10158 Fifth Street, Sidney, BC V8L 2Y1 Canada
nass_secretary@sundials.org
10629 Rock Run Drive, Potomac, MD 20854
nass_treasurer@sundials.org
Annual membership in the North American Sundial Society includes 4 issues of The Compendium. The
Compendium is published in both print and digital editions; the digital edition (in pdf format) may be
received either on CD or by Internet download. To join NASS, contact Fred Sawyer at the above address.
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The North American Sundial Society, Inc. is a not-for-profit 501(c)3 educational organization
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Contents
Sundials for Starters: The Sundial Registry
Sidereal Time For The Homogeneous Analemmatic Sundial
A Vertical Declining Cast Concrete Sundial
Indian Circles – Again
A Simple Trick For Reading Analemmatic Dials
The New Time – A Poem Trilogy (1896)
Quiz Answer: Nicole’s Reflections
Quiz: Bob’s Design Parameters
Ecliptical Planetary Hours
Sisters Of Charity Of Ottawa Sundials
The Vertical Sundial Of The Leimonos Monastery
Digital Bonus
A Derivation Of Formulae For Elevation And Azimuth
Patron Saint Hildevert
The Tove’s Nest
A Projected Bury St. Edmunds EOT Curve
Robert L. Kellogg
Hendrik J. Hollander
Mac Oglesby
Alessandro Gunella
Bill Gottesman
Anonymous
Fred Sawyer
Ortwin Feustel
Fer J. de Vries
Bailey & Seguin
Efstratios, et al.
Herbert O. Ramp
Fred Sawyer
Kevin Karney
1
3
5
8
9
11
13
14
15
27
30
33
34
36
39
Cover
Sundials for Starters – The Sundial Registry
Robert L. Kellogg (Potomac MD)
Since the establishment of the North American Sundial Society in 1997, NASS has pledged to locate and
catalog existing or historical sundials in North America. The result is the NASS Sundial Registry, created
from dial information submitted by members such as you and the interested public.
The first sundial reports were diligently filed in envelopes with photographs, drawings, letters of
correspondence, and an occasional newspaper clipping. For several years the Registry was nothing more
than a collection of several hundred envelopes stored in a small box rarely seeing the light of day. As
more dials were reported, NASS published a list of these dials with a brief description. Many of these
early dial Registry entries were (and still are) devoid of photos.
I was involved in the first “modernization” of the NASS Sundial Registry, where a number of significant
things occurred: First was the creation of an electronic database using Microsoft Access. We limited the
database entry to one 600 x 400 photo, but did incorporate all of the data fields from the Registry
Submission Form. Older photographic prints were scanned and, with all new digital camera images,
placed in an Image Archive for use with the Sundial Registry. The form asked contributors to look to
closely at public dials for who created them, when, who was the designer, and of course dial description
and inscription. In many cases additional details
of the dial were available through correspondence
with the contributor.
Fig. 1 Burning Man dial #439 - Pyrolarium
Two of my favorite dial entries are exciting:
Victor-Charles Scafati’s Burning Man dial NASS
#439 (Fig. 1) used Fresnel lenses to set off tubes of
black powder every hour of the day as his entry
into the annual pyro festival. Scafati explained, “I
was lecturing to a group of people about the
Pyrolarium’s theory and construction. They didn’t
give me the least bit of perimeter as I explained
that the sculpture before them was charged with a
total of two pounds of black powder. They did,
however, give me a wide berth when I accidentally
set fire to my shirt while I was demonstrating the
aiming mechanism of the Fresnel lens.”
Dial #259 (Fig. 2) was a brass horizontal dial
commissioned by the Rev. Thomas Clagget in
thanksgiving for being called as the first [Episcopal]
Bishop consecrated on American soil on September
17, 1792. The dial sat in front of the church for 200
years, then “the sundial was stolen from the church,
but a quick-thinking parishioner got word out to
every antique store within 100 miles and several
days later it was recovered. A replica was created
and now sits outside the church on a pedestal.”
The second significant modernization step was to
get the NASS Registry onto the web. Thanks to
Bob Terwilliger, NASS webmaster for over a
decade, sundial images and brief text were posted in
The Compendium - Volume 16 Number 1
Fig. 2 Clagget Thanksgiving dial #259
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March 2009
Page 1
a virtual spiral bound “Register” accessible to the public with a click of the mouse. In 1997 the Registry
received a marvelous gift of photographic updates of 113 sundials across the United States from Chi Lian
Chiu. This significantly enhanced the quality and quantity of sundial photos. Today, sundial submitters
are requested to provide multiple, high-resolution digital images of dials they want to register. The
Registry Image Archive now holds nearly 3000 digital images of some 650 sundials. Many of these
photos are available for viewing at www.sundials.org.
Since 2004 Larry McDavid has served as NASS Sundial Registrar. In November 2008, Larry took the
third significant modernization step by creating PDF files of the complete NASS Registry database (with
the exception of several private dials that have restricted access). For each dial, the complete Microsoft
Access database entry is made available to sundialists and to the public. Unfortunately this means only
one 600x400 photo of the dial per PDF file entry. For most dials registered since 2004, Larry now has
multiple digital photos that he has carefully trimmed and light-balanced. NASS is now working hard to
establish an extended web Registry with full dial information, all suitable dial images, and any additional
documents (scans of newspaper articles, drawings, etc.).
One of the hardest things has been establishing latitude and longitude for the dials. Ten years ago few
people had GPS devices and many dials did not record their coordinates. As the internet grew, we used
early versions of “map quest” sites to convert road intersections into degrees, minutes and seconds of
location. Now of course we have Google Earth.
Can we make the Registry better? Roger Bailey is investigating the geo-tagging sundials using GPS
data. Precise latitude and longitude data saved as a GPS waypoint can be shared with others as a waymark
or as Google Earth KML files allowing sundial locations on an internet map. Roger hopes that “with this,
we could go to a new location and rapidly find the sundials it that area. This would allow us to target sites
of interest. All the technology now exists, in individual devices and now in sophisticated 3G devices with
GPS camera, cell phone, internet and programs all in one hand held package. All we need is the GPS
waypoint data for sundials". Roger encourages people to enter and update registry entries with the latitude
and longitude data from GPS devices. (I recommend using the GPS format DDDº mm.mmm').
Other dial registries and galleries are maintained around the world. French dials are available at
http://pagesperso-orange.fr/blateyron/sundials/gb/galerie.html, while British Dials of Distinction may be
found at http://www.sundialsoc.org.uk/. Canadian dials are listed in the catalog at the website
http://cadrans_solaires.scg.ulaval.ca/. The tool to provide sundials by location can be found at
http://www.waymarking.com/ that exists to provide interesting locations on the planet, and by selecting
the category of sundials, geo-positioning of sundials around the world is instantly available. For example,
you can go to http://www.waymarking.com/waymarks/WM5CM0 to see the Trois Rivieres sundial at the
monastery of the Ursulines.
As you travel, we ask that you seek sundials not shown in our Registry on-line, gather the appropriate
detail information and digital pictures and submit the dial for registration. If you visit a dial that is already
registered, please check on-line to see if we already have good pictures; if not, you and your digital
camera can help improve our NASS Sundial Registry. The on-line submissions form is at
http://sundials.org/registry/newform/. Further information can be obtained by contacting Larry McDavid
using the email address nass_registrar@sundials.org
These registries and galleries are not only “Sundials for Starters”, but are inspiration to dialists of all
experience levels. You can examine dial form and structure to see the multitude of combinations of
science and art. Hopefully these dials, as well as being a record of telling time by the sun’s shadow, will
give you inspiration for creating your own dial.
Robert L. Kellogg, 10629 Rock Run Drive, Potomac, MD 20854
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March 2009
rkellogg@comcast.net
Page 2
Sidereal Time For The Homogeneous Analemmatic Sundial
Hendrik J. Hollander (Amsterdam, Netherlands)
The Homogeneous Analemmatic Sundial has a homogeneous distribution of the hour lines. It indicates
the local solar time for a place on earth. Because the sundial has to be adjusted to the sun when read, it is
easy to indicate the sidereal time with the sundial. This principle is discussed in the text below.
The Homogeneous Analemmatic Sundial
An example of a homogeneous analemmatic sundial¹ is shown in Figure 1. The sundial is aligned to the
north and next, the disc with the gnomon is rotated until the shadow intersects the date on the yellow disc.
While rotating the gnomon disc, the yellow central disc moves. This movement deforms the ellipse of the
analemmatic sundial to a circle with homogeneous hour lines.
Sidereal time
The sidereal time equals the hour angle of the
vernal equinox. The vernal equinox is a fixed
spot in the celestial sky. After a period of 24
(star-) hours the vernal equinox has returned to
the same place in the sky. Just as the local
solar time refers to the place of the sun (the
sun is south at 12 o’clock solar time), the
sidereal time refers to the place of the stars
(the vernal equinox is south at 12 o’clock
sidereal time).
Figure 1: The homogeneous analemmatic sundial. The small
arrow indicates the solar time.
Figure 2: start of spring, at 12.00 solar time
and 0.00 sidereal time, the sun and the vernal
equinox join south
The configuration of 0.00 sidereal time and 12.00 solar
time at the start of Spring is shown in Figure 2. The
vernal equinox (indicated with A) is south at 0.00 sidereal time. At the start of Spring the sun is also
south.
Figure 3: approx. 20th of April, 0.00
sidereal time, the sun is east of the meridian
Figure 4: approx. 20th of April, 12.00 solar
time, the angle u indicates the sidereal time.
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March 2009
Page 3
Considering the location of the sun around 20th of April at 0.00 sidereal time we will find the sun east of
the vernal equinox, see Figure 3. The angle α is called the right ascension.
A bit later, at 12.00 solar time, the sun is south and the vernal equinox is rotated α degrees to the west, see
Figure 4.
The angle α equals the hour angle u and therefore the sidereal time². Apparently, the solar time and the
sidereal time differ by the angle α (and an additional 12 hours). So we can add a circle with the dates to
the sundial to indicate the sidereal time.
Indication of the sidereal time
The sidereal time is implemented with dates on the disc with the gnomon, see Figure 5. In fact, the right
ascension is drawn for each day with reference to the vernal equinox around the 20th of March. Besides
the month, the 10th and 20th day of each month is indicated. The gnomon is placed in the small circle at
the vernal equinox. The shadow in the figure is 20th April, 0.00 sidereal time.
Figure 5: the sidereal time is read at the date of today, the solar time is read at the small arrow as usual. The shadow
shown is 0.00 sidereal time (some minutes after 10.00 solar time), April 20th.
Considering the configuration of Figure 2, the shadow of the gnomon intersects the date on the yellow
central disc and 12.00 solar time is read at the small arrow. At the indication of March 20th on the disc
the sidereal time 0.00 is read. With the configuration of Figure 4 around April 20th, the arrow indicates
12.00 solar time again and at April 20th the sidereal time is read: approx. 2 o’clock. The principle of a
scale which is able to rotate with the dates to indicate sidereal time can be used on every homogeneous
sundial. The homogeneous analemmatic sundial however has to be adjusted to the sun to read the solar
time so the indication of the sidereal time does not introduce any additional steps.
Notes:
1. See Dutch Sundial Bulletin 97, May 2008 and The Compendium 15(2), June 2008 and www.shop.analemma.nl
for article and a small movie.
2. Actually: -α=u.
Hendrik J. Hollander
hendrik@analemma.nl
De Breekstraat 35 1024 LJ Amsterdam, Netherlands
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March 2009
Page 4
A Vertical Declining Cast Concrete Sundial
Mac Oglesby (Brattleboro VT)
Fig. 1 -- The finished sundial, showing about 5 hours 40 minutes until sunset. The latitude of the building is
42.85 degrees north. Of course, longitude does not matter.
On August 29, 2008 we installed a concrete
"hours until sunset" sundial onto the southwestfacing (48.6 degrees west of south) wall of
Brattleboro's Municipal Center.
To create this sundial, I first measured the
declination of the wall, then used Fer de Vries'
program zw2000 and DeltaCad to create
presentation pictures and a model, and started
seeking permission. A key feature of my proposal
was that this dial would be free to the town,
thanks to the Sawyer Dialing Prize. Still, it took
almost four months to get a decision.
strips. The gnomon, a blunt post of 1/4 inch
threaded stainless steel rod, would be locked in
place by a 7/8 inch long coupling nut buried in the
slab. Of course, all of the mold elements had to be
placed in reverse. Positions of the hour lines were
given by my spreadsheet, but I double checked
with zw2000, so that incorrect values would not
be set in stone.
After the Town's officials agreed to accept a
donated sundial, I met with Richard Holschuh,
owner of Concrete Detail, a local company which
crafts and installs concrete counter tops. He
agreed to the challenge of making a 48 by 30 by 1
inch dial. I purchased rubber letters and numerals
and researched methods of creating the hour lines.
The decision was to use 1/4 inch triangular wood
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March 2009
Page 5
Fig. 2 -- A final step before casting was waxing the wood strips for easier release from the concrete. Notice the
coupling nut (for the gnomon) just right of the T in VT. The rubber letters, numerals and hour lines were glued
in place with silicon caulk.
Fig. 3 -- The concrete mix was carefully poured into the mold. The initial mix was placed by hand on top of the hour
lines, to avoid any possible displacement. The four black cylinders have central knock out dowels to accept the
mounting bolts. No reinforcing steel was used, but there are tiny fibers in the concrete.
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March 2009
Page 6
The actual casting was delayed for several months
until the mounting frame was in place, for it was
deemed foolhardy to cast mounting holes without
knowing the exact locations of the bolts. After
casting, the concrete cured for a week and the
inevitable surface blemishes were repaired. We
never weighed the slab, but two men easily lifted
and carried it, and were able to handle it once it
had been hoisted to the top of the scaffold. Now
came an exciting part, the first trial fitting of the
concrete slab onto the bolts.
Fig. 5 It fits! Rich and Jesse Holschuh, father and son
who cast the dial, show their pleasure as it slides on.
The dial was carefully shimmed to make certain it
was plumb and flat against the mounting spacers
used to keep it slightly away from the wall. The
gnomon was gently threaded into its socket,
checked for length and secured.
On the next sunny day, August 31, the Dialist's
Companion showed sunset at 7:21:05 pm for
Brattleboro. I took a photo at 12:21 and then
others every 60 minutes (give or take a few
seconds) until 6:21 pm to satisfy myself that the
sundial was working properly, at least on that
date. The results were excellent. A passerby
commented, "It's a pity the wall isn't as elegant as
the sundial."
One final note -- I wish to acknowledge that vital
assistance with the sundial's installation was
provided by employees from Brattleboro's Public
Works Dept.
[For a 7 min. YouTube video of the installation:
http://ru.youtube.com/watch?v=0og0Xn25XQg]
Mac Oglesby
43 Williston Street
Brattleboro VT 05301
oglesby@sover.net
Fig. 4 -- Three men hoisted the dial to the top of the
scaffold. The black mounting frame, which holds four
1/2 inch bolts, is visible on the wall.
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March 2009
Page 7
Indian Circles – Again
Alessandro Gunella (Biella, Italy)
In the last issue of The Compendium 15(4):22, a brief article illustrates a problem set by a Japanese
teacher to 12 year old students. Barry Duell, the author of the article, reminds us clearly that it concerns
the Indian Circle construction. This construction, known by all dialists from their beginnings, is relevant
because it allows us to find the meridian line with facility and good approximation. Recently it has
enjoyed a kind of revival, because the French dialist Paul Gagnaire has realized that the method of
Zarbula for drawing vertical declining dials is based substantially on the application of the Indian Circle
to vertical declining planes.
I want to linger over the term "Indian Circle", and remind my colleagues that the word Indian is
borrowed. The Indian circle is not at all Indian, but it belongs to the Greek-Alexandrine culture of the
period from the IIIrd century BC to around the IInd century AD. So the notion of the method came to
Indian astronomers through the Greek scientists, and is not original with them.
Vitruvius (Ist century B.C.), in Book One, Chap. 6,
describes a method to find the directions to be chosen,
and those to avoid, for tracing the streets of a new city,
that resembles very much the Indian circle technique.
Al-Biruni, well-known Arabic mathematician of the
10th century AD, attributes the invention to Diodorus
Alexandrinus (1st century AD) but the Greek text is
lost.
Instead, what has come down to us is the text
"Constitutio Limitum "1 of Hyginus Gromaticus, a
surveyor of the IInd century AD, whose job probably
consisted of the so-called "centuriatio", that is in the
subdivision of lands to be colonized, or in the
preparation of the military camp sites.
(Fig. 1- drawn from a medieval manuscript)
He describes the method for finding the meridian line with these words:
It is proper to find the shade of the hora sexta, and begin to trace boundaries starting from it, so that they always
will be oriented according to the meridian line. It is obvious that then a line going to east or to west crosses them
perpendicularly.
Let us first trace a circle in the earth, in a flat place, and in its center set a gnomon, whose shade enters the inside
of the circle during a certain period of the day. This method is surer than finding the East and West points (with the
Sun).
Wait now while, beginning from the dawn, the shade of the gnomon shortens: when it joins the circumference, mark
the crossing point; wait now as the shade goes out from the circle, and mark the second crossing point.
Once the points in which the shade enters and goes out are marked, trace a straight line from one mark to the other,
and find its middle point.
The line from the center to that point is the meridian line….
Alessandro Gunella, Via Firenze 21, I-13900 BIELLA, Italy
agunellamagun@virgilio.it
1
See Hygin l’Arpenteur- l’Etablissement des limites- Hygini Gromatici Constitutio Limitum - Text in Latin and
front translation into French - 1996 Office des publications officielles des Communautés Européennes, L-2985
Luxembourg.
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March 2009
Page 8
A Simple Trick For Reading Analemmatic Dials
Bill Gottesman (Burlington, Vermont)
Analemmatic sundials are crowd pleasing family friendly sundials, but typically are difficult to read with
precision. Even when a person correctly stands on the proper spot, his/her broad shadow limits the dial’s
readability to maybe a quarter hour or so; and raising one’s hands over one’s head often seems to worsen
the situation.
Figure 1. 16 foot analemmatic granite sundial inside 42 foot stone circle, Burlington, Vermont.
I recently observed that a person’s legs make a sturdy vertical triangle that permit a knife-like beam of
light to accurately illuminate the time. This narrow beam is now my preferred method for reading an
analemmatic sundial.
The 42 foot stone circle Earth Clock in Burlington, Vermont (www.circlesforpeace.org; The Compendium
15.1 (2008): 30-34) recently installed a 16 foot (major axis) analemmatic granite sundial. They also
posted the corrections for longitude and the Equation of Time. Adding an Equation of Time graph to an
analemmatic dial is impractical unless the dial can be read with precision.
Casting a narrow beam between one’s legs, the dial can realistically be read to within 5 minutes, rather
Figure 2. See text.
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March 2009
Page 9
than the 15 minutes or so I commonly encounter from a broad body shadow (figure 2). Visitors to the
Burlington Earth Clock, when shown this, are typically delighted that the time, when corrected by the
EoT/longitude graph, agrees with their watch.
When using the light between one’s legs to illuminate the time, the beam must originate centered over the
current date (figure 3).
Near mid-day, the light beam will not reach the dial’s numbers, but will still point the way. Earlier or
later, when the sun is lower in the sky, the beam often extends beyond the dial’s boundary.
Figure 3. Date is November 24.
Figure 4. Beam is narrow, distinct, reliable.
Figure 5. Even a child can do it.
Bill Gottesman, 100 Overlake Park, Burlington VT 05401
!
March 2009
billg@precisionsundials.com
Page 10
The New Time – A Poem Trilogy (1896)
Anonymous
THE NEW TIME. - A STRAIGHT TALK BY THE SUNDIAL.
The General Manager of Railways has recently issued a circular to local bodies throughout the Colony,
urging the adoption of a uniform time for all South Africa. Under this arrangement, if accepted, the
proclaimed time in Cape Town will be no less than 46 minutes in advance of the actual hour. Such a
condition of things is naturally calculated to upset the equanimity of the venerable Sundial in the
Municipal Gardens, which accordingly launches forth as follows:
A hundred years I've faced the sky upon my pedestal,
And with my finger's shadow shown the hours of day to all;
And though some scars of age I bear, I challenge any man
To say my record's less correct than when I first began.
And still with my old friend the Sun the time I might be telling
When all who read my face to-day have reached a sunless dwelling;
And now some meddling idiots a new-fangled fad have started,
Which'll turn me to a laughing-stock, and leave me broken-hearted.
We let the wretches have an inch, and now they ask an ell,
And what they'll want before they stop is more than I can tell;
I quite expect to see a law gazetted very soon,
That all must rise at sunset, and go to bed at noon.
Ah, Hamlet! if you lived to-day, your luck you well might curse,
For the time's already out of joint, and these would make it worse;
They'll tinker with the compass next, or "cook" the calendar,
Till simple folk begin to feel they "dunno where they are."
O Elliott, Mr. Elliott, deep the grudge to you I owe;
And did your fate depend on me, I guess you'd have to go.
For I am not deluded by a subtlety sublime
Which seeks to show its up-to-date by being out of time.
Besides, if one hour everywhere is a necessity,
Then, surely, Cape Town should dictate what that one hour should be;
And Durban and Johannesburg and Delagoa Bay
Should come to us - to ME - to learn the proper time of day.
Of course, the clocks won't mind the change - that wretched servile race,
Each with hands for ever sneaking round and round its foolish face.
You can turn a key inside them (so I’m told) and make them say
That it's half-past nine to-morrow when it's really six to-day.
But we sundials have got consciences, and listen to them too;
We just say what the Sun tells us, and of course that must be true.
And a hundred Gills and Elliotts cannot "square" us though they try,
For it takes a man like Joshua to make us tell a lie.
So all ye Railway Managers, ye Governments beware !
And trifle with the Sun-appointed hours if ye dare;
For a clock to strike is nothing, but you don't know what it's like
When an honest, earnest Sundial goes fairly out on strike.
But stay, I must be prudent, for if Rhodes gets on my track,
All my century of service might be ended with the sack;
So I'll smother my annoyance, and declare my fixed intention,
Of sending in my papers and applying for a pension.
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March 2009
Page 11
THE TRUE TIME - A REPLY TO THE OLD SUNDIAL FBOM THE TRANSIT INSTRUMENT OF
THE ROYAL OBSERVATORY.
A hundred years you've faced the sky upon your pedestal,
A hundred years and you have seldom told the truth at all.
Your record, true, is as correct as when you first began.
But oh, the lies that you've been telling poor confiding man.
In your old friend the Sun, my boy, it does not do to trust,
I think it really time that you were resting in the dust;
If you so very truthful were, you would most plainly see,
I should not have to watch at night, there'd be no work for me.
From day to day you vary so, I think it very wrong,
Sometimes you make the day too short, sometimes again too long;
And those who put their faith in you will much regret to hear
That you are only quite correct just four times in the year.
In February you will be some fourteen minutes slow,
But now you're sixteen minutes fast - is that the way to go ?
'Tis I must regulate the time, 'tis I must tell it right,
And so I keep a steady watch upon the stars at night.
THE NEW TIME. - LAST WORDS BY THE SUNDIAL.
(A Rejoinder to the Transit Instrument.)
O sneering Transit Instrument! I call it more than mean,
That you for my discomfiture should dare to intervene,
The wrath of Time-reformers I should really scarce have felt,
But you have fairly floored me with this blow below the belt.
We might have worked together and upset the hateful scheme,
But in your spiteful hope to score, you've spoilt that happy dream,
For now the people know their Time-physicians don't agree,
They'll set their clocks to suit themselves, and sack both you and me.
I know the Sun goes wrong at times, it is my secret sorrow,
But if he lags behind to-day, he sails ahead to-morrow;
And so I thought twixt this and that, my time was as correct
As any erring mortal was entitled to expect.
But now, of course, the game is up, the fat is in the fire,
And naught remains for me to do but gracefully retire.
But ah, you sneaking reptile, could I get at you to-night,
Such stars as you have never seen would dance before your sight!
Turner, H.H. et. al.
The Observatory – A Monthly Review Of Astronomy
Taylor & Francis, London, Mar. 1896, 18(no.238):142-143.
http://tinyurl.com/3vrogq
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March 2009
Page 12
Quiz Answer: Nicole’s Reflections
Fred Sawyer (Glastonbury CT)
Nicole enjoyed spending her
vacations in this cottage. She
and her siblings had inherited it
from her grandparents. Her
favorite spot was the large
sunroom – it held many
memories.
The rectangular
room had a long, (roughly)
southwestern back wall, 24 ft.
wide and 8 ft. high with three
windows. Grampa had set a
small horizontal mirror on the
sill of one of the windows (3 ft.
above the floor) and then had
drawn hourlines for a reflected
sundial on the flat ceiling and
side walls. She remembered
having a date every afternoon
with Grampa to see “The Great
Fall” – that’s what Grampa
called it. They watched the
spot of sunlight creep across
the ceiling until it reached the
4pm (local apparent time) hour
line. At that time, each and every day, the spot seemed to give in to the pull of gravity and start its long
fall down the side wall. Throughout the summer, Great Fall began at 4pm; and Nicole and Grampa were
there to watch it!
Last year she and her family refreshed the paint on the hourlines in this special room. She gave her
daughter the same assignment that Grampa had given her when she was in grammar school and the dial
was first laid out. She remembered that Grampa made a mark where the 11am line hit the top of the side
wall. He then gave her the marking pencil and told her to mark the 10am line where it hit the top of the
side wall, measuring exactly halfway from the back wall to his 11am mark. It was important to Nicole
that her daughter could repeat her same contribution to the original dial. Silly thoughts? Perhaps. But
these memories were important to Nicole. They contributed as much to the room’s warmth as the
sunbeams that still streamed through the windows.
Questions: What is the latitude of the cottage, the exact orientation of the room, and the position of the
mirror on the windowsill?
Correct solutions to this quiz were submitted by Rolf Wieland (who went so far as to create a 3
dimensional cardboard rendering of the room, complete with hour lines drawn in) and by Ortwin Feustel
(who provided the graphic that we show here). Both Rolf and Ortwin used the provided information to
create an equation for φ which required an iterative approach to solve. However, there is an approach that
uses an old dialing trick to produce an equation that is directly solvable. I have referred to this trick a
couple times in the past – in a digital bonus ppt file in our last issue and in an article in The Compendium
for Dec. 1997, where it shows up as William Emerson’s Proposition XXIV.
Refer to the figure. Note that the right wall coincides with the 4pm hour line. The left wall is parallel to
the 4pm line and is intersected by the 10am hour line - 6 hours earlier. This point of intersection is
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March 2009
Page 13
therefore a point of symmetry for the intersection of lines with the left wall; i.e. since the distance from
the back wall to the 10am point equals the distance from the 10am to 11am points, we know from this
symmetrical placement that the corner must be the intersection of the 9am hour line with the left wall.
H is the site of the mirror; F is the dial center. Angles AFH and BFH are respectively θ1 and θ 2 where
tan θ 1 = tan 60 o sin ϕ = 1.732051 sin ϕ , tan θ 2 = tan 45 o sin ϕ = sin ϕ . The effective height of the ‘stile’ is
5 feet (i.e. 8-3 ft), so HF = 5 / tan ϕ and AF = HF cos θ 1 = 5 cos θ 1 / tan ϕ . BAF is a right triangle and AFB
is an acute angle. Trigonometry now gives the following for the 24 ft. wall BA:
BA = AF tan (θ 1 + θ 2 ) =
5 cos θ 1 tan (θ 1 + θ 2 )
tan θ 1 + tan θ 2
5
5 ⋅ 2.732051 sin ϕ
=
⋅
= 24
=
tan ϕ
tan ϕ 1 + tan 2 θ 1 1 − tan θ 1 tan θ 2 tan ϕ 1 + 3 sin 2 ϕ 1 − 1.732051 sin 2 ϕ
(
Set k = sin 2 ϕ , so cos ϕ = 1 − k and
)
5 ⋅ 2.732051 1 − k = 24 1 + 3k (1 − 1.732051k ) . Squaring both
sides and simplifying yields the equation: 27.780972k 3 − 22.818380k 2 − 0.432577k + 2.086775 = 0 .
Now, a cubic equation can be explicitly solved. Instructions on the algorithm can be found at
http://www.1728.com/cubic.htm, but more importantly this site allows us to sidestep the algorithm by
providing a calculator. This equation has 3 real roots: k ∈ {− 0.269627, 0.407740, 0.683254} . But since
k = sin 2 ϕ , we know k must be positive – eliminating one possibility from consideration. Also, since
AFB is acute, we have θ 1 + θ 2 < 90 o ⇒ 0 < tan θ 1 tan θ 2 < 1 ⇒ 1.732051 sin 2 ϕ < 1 ⇒ k < 0.577350 .
We now have only one possible value for k: k = 0.407740 ⇒ ϕ = 39.683426 o
ϕ = 39 o 41'
Once we have the latitude, the other items sought are easily produced. The exact orientation of the room
is known if we specify the angle AFH= θ 1 . We know that tan θ 1 = tan 60 o sin ϕ , so θ 1 = 47 o 52′52′′ . The
(outside) back wall of the room declines 47 o 52′52′′ west of south.
The position of the mirror on the wall is given by specifying its distance AH from the right wall.
AH = AF tan θ 1 . We established earlier that AF = 5 cos θ 1 / tan ϕ , so AH = 5 sin θ 1 / tan ϕ = 4.46987 and
we know that the mirror is 4 ft. 5.64 in. from the right wall.
Fred Sawyer, 8 Sachem Drive, Glastonbury CT 06033
fwsawyer@aya.yale.edu
Quiz: Bob’s Design Parameters
Ortwin Feustel (Glashütten, Germany)
Bob has a villa at a small hill with a wonderful panorama up to the horizon. He enjoyed time and time
again beautiful sunrises and sunsets. On the beginning of February 2009 he has decided to make a vertical
sundial (for Local Apparent Time). He knows that he needs the design parameters geographical latitude φ
as well as the wall declination d .
On February 4th, he observed that the illumination of the wall in question began at 9:00am (LAT); the
sun’s rays left the wall eight hours later. The whole day it was a totally clear sky.
Which values for latitude and wall declination did Bob calculate?
Ortwin Feustel, Heftricher Straße 1d, D-61479 Glashütten, Germany
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March 2009
feustel_gnomonik@t-online.de
Page 14
Nicola Severino Finds Important News About
Ecliptical Planetary Hours
Fer J. de Vries (Eindhoven, Netherlands)
Introduction.
For many years I have been interested in planetary hours and in 1992 I published two notes 1) about this
subject in the bulletin of De Zonnewijzerkring (The Dutch Sundial Society). In the course of the years I
got help from several gnomonists and in 2007 I got extra information from Mario Arnaldi of Italy, who
found some interesting texts in old literature. For me this was a reason to write an article 2) in our bulletin
and I wrote a note 3) on the website of De Zonnewijzerkring.
Except for a picture in the scholarly book by Joseph Drecker 4), 1925, in which it is shown how
(ecliptical) planetary hourlines look on a horizontal sundial, I never have seen an image in older literature.
This is changed now.
Nicola Severino of Italy recently (Oct. and Nov. 2008) found three pictures in some old literature. One
image shows the pattern for a horizontal sundial in which one such hourline is seen and the other images
show tympans for an astrolabe with the (ecliptical) planetary hourlines. These new images are the main
reason to write this article.
What are planetary hours?
The photo below shows one of the two beautiful sundials on the front of the Ratsapotheke in Görlitz,
Germany. The emphasized hourlines are for the antique hours, also named as temporal, Jewish or
unequal hours, and are based on the diurnal arc.
These hours are the 12th part of the time between sunrise and sunset and are equal in one day but change
in length during the seasons. In the Northern Hemisphere, these hours are long in summer and short in
winter.
Sundials on the front of the Ratsapotheke in Görlitz, Germany
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Symbols for the planets are drawn between the hourlines and because of that these hours are also called
planetary hours. There are more sundials with these planetary hourlines, and in old and new literature as
well we may read that the planetary hours are the same as the antique hours.
However, in the book by Drecker it is written that this is an error. Drecker points in a footnote to
Sacrobosco 5), around 1230, who had written: Hora naturalis est spatium temporis in quo medietas signi
peroritur. (A natural hour is the space of time in which half a sign rises.) These hours then are not based
on the diurnal arc but on the ecliptic. According to Drecker, Sacrobosco’s definition should be used for
the planetary hours.
There are more sources which refer to Sacrobosco and an example is in the book by Maurolicus 6) where
we may read: Bene igitur dixit Ioannes Sacroboscus, cum diffinivit horam naturalem, hoc est inaequalem,
sive temporalem, esse spacium temporis, quo peroritur dimidium signi in zodiaco.
Another source, also recently found by Nicola Severino, is an English translation7), 1651, of a Latin book
by Agrippa8), printed in 1533. A certain paragraph has as its title: Of the true motion of the heavenly
bodies to be observed in the eight sphere, and of the ground of planetary hours. In this paragraph we
may read:
… so also in planetary hours the ascensions of fifteen degrees in the Eclipticke constituteth an unequall
or planetary hour, whose measure we ought to enquire and find out by the tables of the oblique
ascensions of every region.
The full text of this paragraph is added in an addendum.
So far we have different names and different definitions of planetary hours but we may conclude that at
least a time system, based on the rise of half a sign of the ecliptic, was known in older times and we
continue our story with the name Ecliptical Planetary Hours.
Characteristics of ecliptical planetary hours.
The definition of an ecliptical planetary hour now is the rise of half a sign of the ecliptic. A sign is 30º, so
half a sign is 15º; and one ecliptical planetary hour therefore is the rise of 15º of the ecliptic. The
counting starts with sunrise and, as with the
antique hour, the first hour starts then. Just
as with the antique hours we think in periods
of time, not in moments of time.
There are always 6 signs of the ecliptic
above and 6 signs below the horizon. This
means that in the time between sunrise and
sunset there are 12 ecliptical planetary
hours, just as with the antique hours. In the
course of a year the length of an ecliptical
planetary hour as well of an antique hour
changes because the length of the time
between sunrise and sunset changes with the
seasons.
Figure 1
But the length of the hour changes within
one day because the time needed for a sign
to rise is different. Sometimes a sign rises
fast; another time a sign rises slowly. So the
length of an ecliptical planetary hour also
changes in one day while an antique hour is
constant in one day.
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With an astrolabe, one of the most beautiful instruments in astronomy, it is rather easy to show how the
length of an ecliptical planetary hour changes in one day 9). As an example here this is shown for the first
day of spring or 0º Aries.
At the start set the rete with the point for 0º Aries on the horizon at the left side. Also set the regula at this
spot. This position is drawn in figure 1.
The regula shows that the sun rises at 6
o’clock with an hourangle of 90º before
noon.
Now turn the rete and the regula together
until the point of 15º Aries is on the
horizon left.
Now one ecliptical
planetary hour has past.
Repeat this step for each next 15º of the
ecliptic to rise until the point of 0º Aries
is on the horizon at the right side where
the sun sets.
This position is drawn in figure 2, and in
the day 12 ecliptical planetary hours
have passed.
All the regula positions are drawn and it
is seen that the hours change in length
from short in the morning to long in the
afternoon.
Figure 2
The bottom image now shows the
astrolabe in the position where on the first day of autumn, 0º Libra, the sun rises. If we repeat the
sequence as above we get the same hourlines but mirrored, with long hours in the morning and short
hours in the afternoon.
How do ecliptical planetary hours look
on a sundial?
Now that we have insight into the
characteristics of the ecliptical
planetary hours, we are able to draw a
sundial with these hourlines. In the
past this would have been a monkish
work, even if an astrolabe would have
been available, but in our time a
computer program such as ZW2000 10)
can do the job in a minute.
In the figure 3 a horizontal dial for
latitude 52º North is shown. For clarity
the drawing is cut in two parts; for the
lengthening days and shortening days
separately.
No datelines are added so the shapes of
the lines are not disturbed by other
lines.
Figure 3
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The first image found by Nicola
Severino.
In a Latin book from 1644 by Ioanne
Caramvel Lobkowitz 11) this picture of a
horizontal sundial is found.
In this dial we see seven datelines for
the shortening days, labelled with the
signs for Cancer to Capricornus.
Further we see straight lines for local
apparent time. But for us the other
curved lines are of importance.
These lines are labelled with Roman
numbers in the sequence VI, V… II, I,
(noon), I, II...V, VI.
Figure 4
Finally, we see a pin gnomon as
well as the location where this
gnomon should be placed.
Being busy with studying what
these curved lines could mean I
discovered I had to mirror the
picture. Therefore the rest of the
figures of this dial are drawn with a
mirrored image. The reason for
mirroring the picture I will explain
at the end of this paragraph.
In the book by Lobkowitz several
times the latitude of 52º was
mentioned and for that reason a
horizontal sundial for that latitude
and with the same lines was
calculated, drawn and scaled to the
Figure 5
dimensions of the image from
Lobkowitz. The pattern was placed on
top of the image from Lobkowitz and
the result is shown in three steps.
Figure 6
In the mirrored figure 5, the datelines
are added and the lines for the solstices
and equinoxes fit well.
In figure 6 the lines for local apparent
time are added. The center of the
hourlines is not precisely placed but the
direction of all the hourlines fits very
well.
In figure 7 the ecliptical planetary
hourlines are added. The double line in
the center fits very well with the end of
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March 2009
Page 18
the 6th ecliptical planetary
hourline. The other curved lines
do not fit.
We may conclude that the result
we now have found shows at least
one of the ecliptical planetary
hourlines on a sundial and we are
very pleased with this result.
But what do the other curved lines
mean?
For two dates the intersection
points of the datelines and the
curved lines are accented in figure
8.
Figure 7
Further, a table from the book by
Lobkowitz in the same paragraph
in which the dial is presented, is shown here as figure 9.
Looking closer at the pattern of the dial
it is seen that the accented points on the
equinox lie, in the time system for the
local apparent time, all one hour apart.
This is confirmed in the table where the
series of times is: 10:17, 11:17, 12:17
…
So the other curved lines show the
number of hours before or after the end
of 6th ecliptic planetary hourline as may
be seen in the sequence VI, V, …, II, I,
(noon), I, II, ..., V, VI of the
numbering.
The same is due for the second series
of points for the sign of Scorpius where
the series reads as 10:11, 11:11, 12:11
… and also the other series in the table
show one hour difference.
Figure 8
Here we have a strange combination of one
ecliptical planetary hourline, for the end of
the 6th hour, which is the starting point for
counting in equatorial hours of 15º.
In the table we may also see that
Lobkowitz names the end of the 6th hour
“medium cæli”.
Now it is obvious why I needed to mirror
the picture from Lobkowitz.
Figure 9
Without the image mirrored, the values in the table did not correspond with the local apparent time on the
dial.
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March 2009
Page 19
Also if I had not mirrored the image I would have had to calculate the ecliptic planetary hourlines for the
lengthening days while on the dial the labels at the datelines are for the shortening days.
The second image found by Nicola Severino.
In a book around 1508 – 1520 by an unknown author 12) an image of a tympan for an astrolabe for a
latitude of about 48º North is found. On this tympan all the ecliptic planetary hourlines are seen, not only
for the day hours but also for the night hours.
For the same latitude such a tympan is drawn with a computer program and it is seen that all the lines
match very well. (Fig. 10)
In this book many more drawings are published but hardly any text.
Figure 10
The third image found by Nicola Severino.
In a book by Oronce Finé 13), 1553, the image of the tympan below (Fig. 11) is found. Here only half of
the ecliptical planetary hours are drawn. This is more convenient in use but now two tympans will be
needed. As mentioned in the book the tympan is for a latitude of 48º 40´ N. In the upper part the
hourlines for the day are drawn, in the lower part for the night.
Overlaying the tympan with calculated ecliptical planetary hourlines, as I did before, shows that the lines
fit very well and it is concluded that Oronce Finé did a very good job. However, I discovered that the day
hours are for the period from Capricornus to Cancer with lengthening days and the night hours are for
Cancer to Capricornus with shortening days.
Assuming that his image is for Capricornus to Cancer it is seen that for 0ºAries the first night hour is
short. But this hour should be long as may be seen in figure 12.
Did Oronce Finé make an error? Not necessarily. It is possible to distribute the needed patterns in the way
he did but in use this is less convenient.
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March 2009
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Figure 11
Tables for ecliptical planetary hours.
Another important find by Nicola Severino is a
German book by Eliam Crätschmairum 14), 1626.
In the main part of this book tables are found with
values for the start time for each of the 24
ecliptical planetary hours for each day in a year.
These start times are expressed in local apparent
time, all for the latitude of 50º 48´ North.
In the tympan for that latitude (Fig. 13) all the
ecliptical planetary hours for the shortening days
are drawn. For the arbitrary date of the 1st of
November the declination circle is added and all
the regula positions through the intersection
points of the hours with the date circle are drawn,
so we can read all the times for the start of the
ecliptical planetary hours.
For the day and the night hours the counting starts
on the horizon with hour 1.
Figure 12
For the start of the day hours 2, 3, 7 and the night hours 5, 9, 11, values are added as I read on a larger
version of this tympan.
The values of all the 24 hours for this date are compared with the appropriate tables. A part of these
tables is seen here.
The table (Fig. 14) at top is for the day hours (Tagstunden), the lower part is for the night hours
(Nachtstunden).
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March 2009
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Figure 13
For all the 24 hours the difference
between my reading and the value in the
tables is less than two minutes.
Such a comparison is also done for 0º
Aries, Libra, Cancer and Capricornus
and the values are also within 2 minutes
as I read on the tympan.
It appears that the tables are well
calculated.
Very important is the naming of these
hours by Crätschmairum.
On the Latin title page of the book (Fig.
15) we already read the words
Tabulæ ... horarum planetariarum ....
And on several places he names these
hours
Planetenstunden,
Planeten
Tagsstunden, Planeten Nachtsstunden
and Zodiacalstunden.
In English, this translates as:
“planetary hours, planetary day
hours, planetary night hours and
zodiacal hours.”
So in this book the planetary hours
are based on the rise of 15º of the
ecliptic, as defined by Sacrobosco,
and not on the unequal or antique
hours.
Also we read in the book: weil er
(Zodiacum) der Führer aller
Planeten (ist).
In English: “Because the ecliptic
is the ruler for all planets.”
For the planetary rulers we copied
(Fig. 16) the scheme as found in
Crätschmairum’s book.
For Sunday we read the sequence
Figure 14
for the day hours 1 to and with 12 as:
Sun, Venus, Mercury, Moon, Saturn, Jupiter,
Mars, Sun, Venus, Mercury, Moon and Saturn.
Comparing this sequence with the planetary
rulers in the sundial in Görlitz on the first page
of this article, we see the same sequence at top
near the winter solstice.
Figure 15
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March 2009
Page 22
Planetary Hours Table
Day hours
Saturday
Thursday
Tuesday
Sunday
Friday
Wednesday
Monday
Night hours
Figure 16
Conclusion.
Considering the finds by Nicola Severino discussed here, we may conclude that besides planetary hours
based on the diurnal arc, it is really true there is a system in which the planetary hours are based on the
ecliptic. We are very pleased with all the finds by Nicola Severino, who shared all of this with us and
who gave us permission to publish about this important material in the website of Nicola Severino, in The
Compendium, and in the Bulletin of De Zonnewijzerkring.
Thanks go to Mac Oglesby for reading and improving the English text. The website of Nicola Severino
is: http://www.nicolaseverino.it/
Literature and notes.
1 Fer J. de Vries, Planetenuren, Bulletin of De Zonnewijzerkring, nr. 92.1, January 1992.
2 Fer J. de Vries, Hora naturalis: antiek of planetenuur?, Bulletin of De Zonnewijzerkring, nr. 08.1,
January 2008.
3 Website of De Zonnewijzerkring, article of the month, archives 2007, month 07-12.
http://www.de-zonnewijzerkring.nl
4 Joseph Drecker, Die Theorie der Sonnenuhren, 1925. See also addendum.
5 Johannes de Sacrobosco, Tractatus Sphaera, about 1230. See also addendum.
6 Franciscus Maurolicus, Computus ecclesiasticus, 1575.
7 The sphere of Sacrobosco, Lynn Thorndike, 1949.
8 Heinrich Cornelius Agrippa, De occulta philosophia, 1509-1520, printed in 1533, book 2, chap 34. See
also addendum.
9 A small file with a demonstration of the ecliptical planetary hours on an astrolabe is added to the
electronic version of The Compendium and is available for download as a powerpoint file at
http://www.de-zonnewijzerkring.nl/downloads/hora-naturalis-eng.zip
10 ZW2000 is available for download at the website of De Zonnewijzerkring:
http://www.de-zonnewijzerkring.nl. links: calculate and construct, flat sundials-extensive version,
download computer program.
11 Ioanne Caramvel Lobkowitz, Solis et artis adulteria, 1644.
12 Author unknown, Astronomische Zeichnungen, 1508-1520.
13 Oronce Finé, De duodecim caeli domiciliis, & horis inaequalibus, libellus non aspernandus, 1553. See
addendum for title page of the book.
14 Eliam Crätschmairum, also Elias Kretzschmayer, Kretschmar or Kretschmer, Horologium Zodiacale,
1626.
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March 2009
Page 23
Addendum.
Sacrobosco.
An English translation of Sacrobosco's Tractatus Sphaera by Lynn Thorndike, 1949, is at
http://www.esotericarchives.com/solomon/sphere.htm
In chapter 3 we may read Sacrobosco’s definition: … a natural hour is the space of time in which half a
sign rises. The complete text of chapter 3 is cited below.
RIGHT AND OBLIQUE ASCENSIONS.
It is to be noted that the six signs from the beginning of Cancer through Libra to the end of Sagittarius
have their combined ascensions greater than the ascensions of the other six signs from the beginning of
Capricorn through Aries to the end of Gemini. Hence those six signs first mentioned are said to rise erect,
but the others obliquely. Wherefore the verses:
They rise aright, oblique descend from Cancer's star
Till Chiron ends, but the other signs
Are prone at birth, descend by a straight path.
And when we have the longest day of summer, when the sun is in the beginning of Cancer, then six signs
rise vertically by day but six obliquely at night. Conversely, when we have the shortest day of the year,
when the sun is in the beginning of Capricorn, then those six signs which rise by day do so obliquely, but
by night the other six rise vertically. When, moreover, the sun is at either equinoctial point, then by day
three signs rise vertically and three obliquely, and at night the same.
For the rule is: However short or long the day or night may be, six signs rise by day and six by night, nor
because of the length or brevity of day or night do more or fewer signs rise.
From these facts it is gathered that, since a natural hour is the space of time in which half a sign rises,
there are twelve natural hours in each artificial day, and so also in the night. Moreover, in all the circles
which parallel the equator to north or south, days or nights are lengthened or shortened according as
more or fewer signs rise vertically or obliquely by day or night.
Some other readings.
1) Charles-Henri Eyraud and Paul Gagnaire, Le Ore Planetarie, translated in Italian by Riccardo
Anselmi for magazine Web Gnomonices, n. 3, February 2004, available for free download at:
http://www.nicolaseverino.it/riviste.htm (Download WG n. 3.)
In French the article is published in the revue of the ANCAHA, nr. 97, 2003.
2) A. Gunella, A. Nicelli, Un libro di Oronzio Fineo astrologo ed una polemica sulla suddivisione delle
case celesti e sulle ore ineguali, magazine GnomonicaItaliana, anno II, n. 5, giugno 2003.
3) N. Severino, Ancora sulle ore Canoniche, Temporarie e Planetarie, in Gnomonica, n. 2, January, 1999.
Drecker.
From the book Die Theorie der Sonnenuhren by Joseph Drecker, 1925, the figure with the ecliptical
planetary hourlines is copied. The relevant German text in this book about this subject is translated into
English by Ruud Hooijenga and his text follows below.
In close relationship with the ascendant lines are the planetary hours, which are those periods of time in
which, according to Astrology, one planet rules. Erroneously, the expression planetary hours is also used
for the unequal, antique hours. Here, the following should be noted.
Two great circles on the celestial sphere can be used, because of their apparent diurnal rotation, for the
division of the day into hours: the equator and the ecliptic.
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Selecting the equator results in equal hours; one such hour is the time between the rises of two points
which are 15° apart on the equator.
Selecting the ecliptic, however, one hour is the time that passes between the rises of two points which are
15° apart on the ecliptic.
Since each day and each night half of the ecliptic rises, one obtains 12 daily and 12 night hours. That is
what the ecliptic hours have in common with the antique hours, which are derived not from a great circle,
but from a diurnal arc of the sun, and therefore considered less self-evident, or natural.
The ecliptic hours on the other hand are called natural hours. They differ however substantially from the
antique hours by the fact that they are of unequal duration even in the course of a single day.
Reasonably, then (“ratio postulate”, says Maurolycus), only the ecliptic hours can make claim to the
name of planetary hours.
Serious dialists recognize this fact, but they also point out the conflicting opinions of modern astronomers
and astrologers. The confusion between the true planetary hours and the antique hours has its origin in
their partial similarity, but also in a desire to avoid the difficulties in the construction of the first.
Agrippa.
On the next page is the title page of an English translation of the books by Heinrich Cornelius Agrippa.
This translation was written in 1651 by J.F. Agrippa’s book was written from 1509 to 1510 and printed in
1533.
Below chapter xxxiv from book 2 is cited.
Chap. xxxiv. Of the true motion of the heavenly bodies to be observed in the eighth sphere, and of the
ground of Planetary hours.
Whosoever will work according to the Celestiall opportunity, ought to observe both or one of them,
namely the motion of the Stars, or their times; I say their motions, when they are in their dignities or
dejections, either essential or accidentall; but I call their times, dayes and hours distributed to their
Dominions. Concerning all these, it is abundantly taught in the books of Astrologers; but in this place two
things especially are to be considered and observed by us. One that we observe the motions and
ascensions and windings of Stars, even as they are in truth in the eight sphere, through the neglect of
which it happeneth that many err in fabricating the Celestiall Images, and are defrauded of their desired
effect; the other thing we ought to observe, is about the times of choosing the planetary hours; for almost
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all Astrologers divide all that space of time from the
Sun rising to setting into twelve equall parts, and call
them the twelve hours of the day; then the time which
followeth from the setting to the rising, in like manner
being divided into twelve equall parts, they call the
twelve hours of the night, and then distribute each of
those hours to every one of the Planets according to
the order of their successions, giving alwayes the first
hour of the day to the Lord of that day, then to every
one by order, even to the end of twenty four hours; and
in this distribution the Magicians agree with them; but
in the partition of the hours some do different, saying,
that the space of the rising and setting is not to be
divided into equall parts, and that those hours are not
therefore called unequal because the diurnal are
unequal to the nocturnall, but because both the diurnal
and nocturnal are even unequall amongst themselves;
therefore the partition of unequall or Planetary hours
hath a different reason of their measure observed by
Magicians, which is of this sort; for as in artificiall
hours, which are alwayes equall to themselves, the
ascensions of fifteen degrees in the equinoctiall,
constituteth an artificial hour: so also in planetary
hours the ascensions of fifteen degrees in the Eclipticke
constituteth an unequall or planetary hour, whose
measure we ought to enquire and find out by the tables
of the oblique ascensions of every region.
The complete text of the translation is at:
http://www.esotericarchives.com/agrippa/ or directly to book 2 at:
http://www.esotericarchives.com/agrippa/agripp2c.htm
Oronce Finé.
The 28th of November 2008 Nicola Severino found a book
by Oronce Finé, dated 1553. This was within two months
of the other finds we are discussing in this article. This
book is not a new discovery but the image of the tympan
still was unknown to us. The title page of the book is seen
here. The book is in Latin and has about 75 pages.
Fer J. de Vries
Van Gorkumlaan 39
5641WN EINDHOVEN
Netherlands
ferdevries@onsneteindhoven.nl
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Page 26
Sisters Of Charity Of Ottawa Sundials
Roger Bailey & Sister Louise Seguin SCO
When I travel, I look for sundials. This focus can offer an interesting perspective on the local history and
culture. With this point of view, let’s visit Ottawa, the Capital of Canada, an interesting city with
remarkable history. Ottawa is at the confluence of three rivers. The Ottawa River was the original route
west across Canada. At Ottawa the Gatineau River comes in from the north (Quebec) and the Rideau from
the south. These rivers were the trade routes that determined the development of Canada as a nation and
Ottawa as its capital. Everyone sees the rivers, Parliament buildings, government infrastructure, museums
etc. but visitors often miss other interesting details.
Let’s start our quick tour at Parliament Hill. Just to the east is the Rideau Canal from Kingston on Lake
Ontario and St Lawrence River. Proceed past the canal and the Chateau Laurier, a classic railroad hotel,
and turn left onto Sussex Drive passing the bunker of the American Embassy, the fragile glass of the
National Art Gallery, the fortress of the War Museum and the castle of the Royal Mint. Sussex Drive
carries on to the residences of the Prime Minister and Governor General but we are going to stop at the
Royal Mint as an entry in the Mayalls’ book Sundials: Their Construction and Use mentions a pair of
sundials at the mint. This reference was an early entry in the NASS registry.
1. Sisters of Charity of Ottawa Motherhouse
2. Allard’s Corner Sundials
But there are no dials on the mint. Look across the street to Lower
Town, the historic French part of Ottawa to a limestone heritage
building, the Motherhouse of the Sisters of Charity of Ottawa. What
drew my attention there was the pair of large sundials on the corner
above the entrance. These sundials, very much in the French tradition,
seemed to be original, accurate and unique. At the time of my visit
(mid 90’s) I just took a few pictures and sent the information along to
the NASS Registrar. This was primarily to correct the misinformation
in the Registry noting corner dials on the Mint. The Mayalls got it
wrong. The dials are across the street on the Sisters’ Motherhouse. I
had no further information so the registration remained incomplete.
The sundials are remarkable and there must be an interesting history
but I was a shy visitor and did not enquire further.
From our sundial perspective, let’s review the history of Ottawa. The
initial settlement was across the river in Quebec. This shore offered an
easier portage past the falls and rapids than the south side for the
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explorers like Champlain, LaSalle, and the Jesuit missionaries to Huronia almost 400 years ago and fur
traders of the North West Company 200 years ago. Around 1800, the first lumberjacks arrived in the area
and set up a bush camp on the south side of the river. In 1826 Colonel John By established a construction
camp called Bytown at the northern end of the Rideau Canal. To provide a time reference, in 1828 a
sundial was erected at this location on what is now Parliament Hill. The dial pictured is not the original
but a 1919 replacement.
In the early years the pioneer community had a population of 6,000 inhabitants from England, Scotland,
Ireland and the province of Québec. The army defending the strategic waterway, the navies building the
Canal and the lumbermen made Bytown their favorite meeting place. Bytown soon developed a rather
bad reputation, the site for disorderly conduct and fights initiated by racial and religious arguments.
Abuse of alcohol together with a lack of policemen to maintain order meant that Bytown was not a
pleasant village to live in, certainly not to raise families in. The lack of schools and hospitals made the
situation even worse. This is why Msgr. Phelan, Bishop of Kingston and Pastor of Bytown, called upon
Msgr. Bourget, Bishop of Montréal, requesting Oblate Priests and Grey Sisters of Montreal to come and
help civilize Bytown.
February 20, 1845 marked the arrival of Élisabeth Bruyère, SGM (Soeurs
Grises de Montréal – Grey Nuns of Montreal). She and three other Sisters,
one postulant and one aspirant, came from Montreal by sled on the Ottawa
River. Élisabeth was only 26 years old when she became the Founder of
The Grey Nuns in Bytown. Within a year the Sisters had established a
school, hospital and shelter. In 1847 they cared for victims of the Typhus
epidemic among the Irish immigrants fleeing starvation due to the potato
famine. The Sisters survived and prospered. In 1850, the Motherhouse was
completed. In 1857, Bytown, now called Ottawa become the Capital of the
United Provinces of Upper and Lower Canada due to its strategic, secure
location on the major trade routes. Confederation in 1867 brought into
Canada the rest of what is now ten provinces and three territories from sea
to sea to sea.
The Grey Nuns, including the Sisters of Charity of Ottawa, are well known and respected across Canada
for civilizing the frontier communities. There are still Grey Nuns’ hospitals and schools across Canada,
into the US and now in missions around the world.
In 1850, Father Jean-François Allard, OMI (Oblate of Mary Immaculate) became the Chaplain of the
Mother House, built in 1850 at the corner of Bruyère Street and Sussex Drive. He was the Sisters’
spiritual director and he taught science in the new school. We owe to him the design of the two sundials
that have faithfully told the time of day for so many years. Fr. Allard grew up near Briançon, in the heart
of the Zarbula Zone of France. The dials he constructed here are simple elegant corner dials, very much in
the French Tradition. These dials are the oldest example of this type of
sundials in North America.
To our knowledge, only one other pair of similar historical corner dials
survived, the 1883 dials designed by l'abbé Raymond Caisse, Prefect of
Studies at the St. Joseph Seminary, 858 rue Laviolette, Trois Rivieres,
Quebec.
Are Fr. Allard’s designs correct for the location and wall declination? Do
they tell the correct solar time? To check, I used modern computer
techniques, Fer de Vries “Zon 2000” and “Delta CAD”, to draw a
modern design. This was then superimposed on pictures of the actual
dials. The wall declination was estimated to be about S 31º W for the
afternoon dial and S 59º E for the morning dial using Google Earth. This
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agreed with the architect’s drawing provided by Sr. Louise showing 31.8º and 58.2.
The large afternoon dial facing Sussex Drive is gnomonically correct. The hour lines are right however
the overlay for S 59º W fits better than 58.2º. The gnomon is unusual as it is in the meridian plane. The
advantage is the co-latitude angle with the wall is true. The disadvantage is it is more difficult to set and
keep correct than the normal perpendicular
gnomon of the “substyle height” canted at the
substyle distance.
The narrow morning dial on the east side street is
also gnomonically correct with the best fit being
S 31º E. This dial is narrow as it is constrained by
the corner and the windows. The circle is
distorted to an ovoid shape. This dial faces onto a
side street with little traffic. Most people passing
the corner on the main street would have a full
view of the narrow dial and a narrow view due to
perspective on the wider afternoon dial. The
design artistically compensates for perspective
for the typical viewer. Again the gnomon is
mounted in the meridian plane parallel to the
other dial around the corner.
The time stamps on the photos show they were taken on 3 Jan 08 at
2:44 and 2:46 pm EST. On that date the Equation of Time was 4’25” and the longitude correction for 75.6978º is -2’47” giving
solar time as 2:38 to 2:40. This agrees with the shadows on the
sundials as closely as they can be read from the photos. The
morning dial may be a bit off as the gnomons did not look to be
perfectly parallel. Mounted as they are in the meridian plane, the
gnomons could be easily bent and difficult to correct.
We conclude that the dials were correctly designed and
constructed. Modern techniques are no better for designing such a
sundial. Fr. Allard demonstrates an excellent artistic sense as the
subdued colors and lack of ornamentation are correct for the
convent location. The narrow dial on the side street is appropriate
to balance the perspective.
This is a fine example of the science and art of sundial design and
provides a link to Canada’s history, culture and development.
Sister Louise Sequin SCO, provided the information and pictures
on the history of the SCO sundials. Stephen Blakeney took the
excellent photos and Roger Bailey contributed the technical analysis for this article and presentation at the
NASS Conference in 2008.
References:
1. Mayall, R. Newton & Mayall, Margaret W., Sundials: Their Construction and Use, New York, Dover
Publications, 2000.
2. André E. Bouchard, “Les cadrans verticaux déclinants du Québec”, Le Gnomoniste, Aug 2004,
Commission des cadrans Solaires du Québec. http://132.203.82.104/v08-08-04/pdf/VIII-1-p2-7.pdf
Roger T. Bailey, 10158 Fifth Street, Sidney BC, V8L 2Y1 Canada rtbailey@telus.net
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The Vertical Sundial Of The Leimonos Monastery
Efstratios Theodossiou, Petros Mantarakis, Vasillios N. Manimanis, and George Giouvanellis
History Of The Monastery
The still inhabited patriarchal Monastery of Leimonos (Moni Leimonos, which means “Monastery of the
Meadow”) is located near the centre of the island of Lesbos, at a road distance of 14 km to the west of
Kaloni town. Lesbos lies in the Eastern Aegean Sea, at geographical coordinates 39º 15´ 5´´ N , 26º 10´
10´´ E. It is the largest monastery on the island, and is a scaled down copy of Aghion Oros, the monastic
community on Mount Athos. The origin of the monastery dates back to the 16th Century. The fertile small
basin where it lies was then a part of the land belonging to Emmanuel Agallianos, a major land-owner of
the region. After his death the property passed to his son, the monk (and afterwards saint of the Orthodox
Church) Ignatios Agallianos.
On the Agallianos property resided an old Byzantine church and monastery that had been operational
until 1462 when the Ottoman Turks occupied the island. From 1523 to 1526, Ignatios restored and
expanded the old Byzantine Monastery of Pammegistoi Taxiarches (“The Most Great Archangels”) and
founded a new monastery named Leimonos Holy Monastery (Fig. 1).
In 1530, Ignatios was ordained a
bishop (of the territory of
Mithimna on Lesbos). Bishoprics
fell under the jurisdiction of the
Ecumenical
Patriarchate
in
Istanbul rather than local
diocesan control. Therefore,
Ignatios was able to secure a
patriarchal sigillium recognizing
both the Leimonos Holy
Monastery and another nearby
monastery as stavropegiakes
(patriarchal monasteries), and
thus they were under the
protection of the Patriarchate.
Although Lesbos was under
Ottoman rule, Ignatios managed
Fig. 1 Moni Leimonos
(because of his good relations
with the sultan – the legend says
that Ignatios had cured the sultan’s son from some disease) to get an imperial decree (firman) granting
protection from any local authority excesses. Thus, the Leimonos Monastery flourished, and with
Ignatios’ help and contributions revitalized learning and religion on the island. With his money he created
schools of copying, calligraphers and singers of Byzantine religious music in the monastery, as well as the
famous “Leimonias School”, the only cultural institution on the island during the Ottoman rule, with
famous teachers such as Pachomios Roussanos. The School remained active until 1925.
Today, after almost 500 years, this imposing and large monastery still keeps numerous historical objects
and a very large archive of religious texts. The Leimonos Monastery celebrates St. Ignatios Day annually
on 14 October. It owns more than 40 churches and the present bishop plans to raise the number to 365, so
that one church would be honoring the saint on any given day.
At present, the library of the monastery has 20,000 books (the oldest dating from 1498) and 516
manuscripts (the oldest dating from the 9th Century), and a Gospel handwritten with golden-yellow ink.
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The monastery also operates a museum of religious and popular art, and, since 1990, a geology museum.
All of the above, together with the exquisite Byzantine icons, make Leimonos Monastery an important
post-Byzantine monument of Greece and a major attraction for tourists, pilgrims and scholars. Its
philanthropic action includes the operation of a house for the aged.
The main church (“Catholicon”) of the monastery was restored in 1526 and it has since been repeatedly
repaired. It is a three-aisled basilica with the roof of the middle aisle higher than the other two and a
double narthex. It is decorated with interesting frescoes of the late 16th and early 17th Century. Also
worthy to mention is the wooden carved separator between the main part of the interior and the sanctuary,
partly covered with gold. On its southern wall there is the vertical sundial of the monastery, probably the
only one on the island of Lesbos.
The Vertical Sundial Of The Monastery
The Leimonos Monastery is decorated with
a quite simple vertical sundial dating from
the beginning of the previous century (Fig.
2).
We report its existence because of its
uniqueness as well as for being one of the
few vertical sundials (less than twelve)
mounted on Orthodox churches of the postByzantine period in the whole of Greece.
To be exact, our team has located the
following sundials: 1 on St. Paraskevi of
Galaxidi; 1 on St. Charalambos of
Mylopotamos, Cythera island; 1 on St.
Apostoloi (Apostles) of Chrysanthio,
Achaia; 2 in Tinos island; 2 in Kythnos
island; 1 on St. Ioannis (St. John) of Myloi,
Euboea island; 1 on the Analepsis in Paxoi
island; 1 in the Taxiarches Monastery near
Melissia village of Egio.
The simple vertical sundial of the
Leimonos Monastery, constructed in the
beginning of the 20th century, has been mounted on the southern wall of the main church of the
monastery. It does not bear traditional hour lines, but instead some carvings for the morning and the
afternoon hours. These begin with the 6th morning hour and end with the 6th evening hour. Carvings can
also be discerned for the half-hour intervals, a notable characteristic for such a simple (almost naïve)
sundial. Looking at the photograph it appears to be a rather badly executed example of a mundane vertical
south dial. The year 1912 is carved on its plate, under the twelfth hour. It is known that the sundial was
mounted on the wall on December 8th of that year, to celebrate the end of centuries of Ottoman rule.
Folklore states that that day was selected because it was especially sunny for the winter season and the
inhabitants wished to honor the light-giving Sun.
Fig. 2 Leimonos Sundial
The role of the monastery in the minor local battles between the Greeks and the Turks in 1912 (WW I)
was essential, since it operated as a first-aid center for the wounded and prisoners-of-war, as well as a
headquarters for Greek officers. The monument for the dead on the nearby Tyrranydiou hill is a reminder
of the roughness of the battles.
The installation of the sundial, according to the present abbot of the Monastery Archimandrite Nikodemos
Pavlopoulos, symbolized the beginning of a new free life for the Lesbos populace. The abbot of the
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Page 31
monastery at the time when the sundial was constructed and placed was Fr. Hadjiserapheim (1886-1928),
whose lay name was Eustratios Nianiadelles; he served as an abbot for just a short interval (some months
in 1912).
The sundial was constructed by marble artisans of the Hadjidiakos family, some descendants of which
still carve marbles today. They did not have any special knowledge of gnomonics, a fact that resulted in
this naïve construction:
They carved on a rectangular plate 50 × 40 cm and 4 cm thick, made of pure white marble, three
concentric circles. The middle circle was not colored with black ink. In the first ring, which is formed
between the inner and the middle circle, there are only the carvings of the whole and half hours. In the
second ring, which is formed between the middle and the outer circle, there are the numbers of the whole
hours: 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5 and 6. The plate was mounted on the wall by drilling two holes on
it, one at the upper part and one at the bottom (but above the carving of the year 1912), and passing two
large nails, one of which (rusted) is clearly visible in the photograph. They also added, probably later on,
two more nails to the right-hand side and the left-hand side in order to fix the plate better.
The actual polar-pointing gnomon is missing – one can see its origin where the 6am-6pm lines would
intersect – and all that is left is the small hole in the mentioned intersection and the iron gnomon
supporter projecting from the center of the face. This slender rusted supporter completes the sundial.
Despite its simplicity, this vertical sundial was used continuously, as the monks told us, till the
destruction of the gnomon some years ago. For that reason the abbot Nikodemos asked for our help to
reconstruct the dial. However, looking on the plate, a number of questions were raised. Of course the
6am-6pm lines ought to be horizontal for a normal dial as the modern dial in Utrecht (52°05´N, 5°08´E),
taken by us during Christmas period last year, when we were in the Netherlands (Fig. 3). That dial, which
looks like the Leimonos’ sundial, is well designed and correct; it is painted on the south wall of the
National Museum von Speelklok (Nationaal Museum van Speelklok tot Pierement) in Utrecht-Holland.
On the street’s corner is written: Steenweg 6. Buurkerkhof gebied om de Buurkerk 11e eeuw
Museumwartier.
So, the question is: Was the Leimonos dial designed to show time in some system other than the standard
equal hours of local solar time? That would be rather surprising for 1912! Or, was it just meant to be a
symbol dedicating the beginning
of a new free life for the
populace? If someone wants to
help in the reconstruction, he must
stay for some days at the Convent
to measure all the hour line angles
and to analyse how the design was
done mathematically to support
any description.
The abbot Nikodemos told us that
he plans the construction of an
additional sundial in the future,
probably in the year 2012, when
100 years will have passed from
the installation of the first one.
We note that at the period in
which
the
sundial
was
constructed, the monastery started
to operate one of the first steam-
Fig. 3 Sundial in Utrecht
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Page 32
powered olive-pressing machines on the island, participating in the industrial development of the region.
Also, in the library of the monastery there is a manuscript of an astronomical book of the known
astronomer and geographer of the late 17th and early 18th Century Ioannes Skylitzis, entitled Eisagoge eis
tas Kosmographias kai epistemas kai technas (Introduction to the Cosmographies, the Sciences and the
Arts), which was probably consulted as a source by the abbot and the marble artisans for the construction
of the sundial. The Greek scholar Ioannes (John) Skylitzis taught mathematics, astronomy and physics in
the island of Chios and in Istanbul between the years 1650 and 1735.
Bibliography
1. Spanos, A.: Synoptiki istoria tis ieras Monis Leimonos (Concise History of the Holy Leimonos
Monastery). Akritas Editions, Athens 2002.
2. Spanos, A.: Iera Patriarchiki kai stavropigiaki Moni Leimonos (The Holy Stavropegian and
Patriarchal Leimonos Monastery). Akritas Editions, Athens 2003.
Acknowledgements
The authors express their thanks to the University of Athens for financial support through the Special
Account for Research Grants (Programm 70/4/7671).
Efstratios Theodossiou, Vasillios N. Manimanis and George Giouvanellis
Department of Astrophysics, Astronomy and Mechanics, School of Physics
University of Athens, Panepistimiopolis Zographou, GR 157 84, Athens, Greece
etheodos@phys.uoa.gr
Petros Mantarakis, 22127 Needles St. Chatsworth, California zanispetros@socal.rr.com
Digital Bonus
[Available to all NASS members, including those with Print Only subscriptions]
The digital edition of this issue of The Compendium includes 4 bonus items.
First: Hora Naturalis - a demonstration of the ecliptical planetary hours on an astrolabe to supplement Fer
de Vries’ article.
Second: Some notes for the use of an astrolabe – an additional article by Fer de Vries detailing the
various parts and the use of an astrolabe equipped with the ecliptical planetary hours.
Third: Sisters Of Charity Of Ottawa Sundials – a copy of the presentation given by Roger Bailey at the St.
Louis conference covering the dials described in the article by Roger and Sister Sequin.
Fourth: Excalibur Programmable Scientific Calculator – “Excalibur is a full featured RPN calculator for
Windows 32-bit operating systems. It was designed exclusively as a Reverse-Polish-Notation (RPN)
calculating machine and is crafted for both the beginner and the advanced user. Logical banks of
functions cover everything from scientific calculations to business formulas to computer science logic.
The calculator also provides a robust programming mode which allows you to save time by automating
number entry, formulas and computational algorithms. But don’t let the vast features of Excalibur cause
you to worry - beginners will also feel at home with Excalibur.” This program is freeware and is
completely portable – not requiring installation on your computer. I have found it ideal for use on a USB
flash drive. The fact that it is easily programmable makes it quite useful.
The homepage for Excalibur is: http://www.geocities.com/dbergis/freeware.htm.
[For a limited time, these files are available to all members at http://drop.io/NASSbonus1.
password: 161.]
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March 2009
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Page 33
A Derivation Of Formulae For Elevation And Azimuth
Herbert O. Ramp (Vienna, Austria)
In The Compendium 1(3):8, ‘Solving the Spherical Triangle’, Fred Sawyer presented derivations of the
equations for elevation and azimuth of the sun. I offer another way of deriving these equations, which
also shows the connection between the equator and horizon coordinate systems.
For the design of sundials (which also show date hyperbolas), three fundamental parameters are required.
They are: geographic latitude ϕ, the sun’s declination δ (day of the year), and the hour angle τ (hour of
the day). These parameters enter into equations for the sun’s elevation (also called altitude) and the sun’s
azimuth. Elevation and azimuth are part of the design equations for sundials. The derivation of the
equations for elevation ε and azimuth α are given below.
The definitions for ε and α as used in this paper are:
ε … angle at which the sun is seen in a vertical direction from the location of the sundial.
ε = 0° → horizon; ε < 0° → below horizon.
α … angle at which the sun is seen in a horizontal direction from the location of the sundial.
α = 0° → culmination of the sun, south; α < 0° → before (local) noon.
Other variables used in this paper are:
λ … geographical longitude
ϕ … geographical latitude
δ … sun’s declination (range ±23.44°)
τ … hour angle (τ = 0° local noon, local culmination of sun, < 0 before noon, 15°/hour, range ±180°)
The following nomenclature is used (all Greek letters, because all magnitudes are angles).
Horizon-system:
Ordinate (zenith-nadir great circle) … η
Abscissa (horizon circle) … ξ
Equator-system:
Ordinate (north-pole south-pole great circle) … ϕ Abscissa (equator) … λ
Assume we are given a sphere with radius = 1 and a point Po on its surface. The position of the point Po
in the horizon coordinate system is given by:
ξo = -cos ε ⋅ cos α ηo = sin ε where cos ε is the radius of the circle parallel to the horizon at elevation ε.
Using the equator coordinate system, the position of Po is:
λo = -cos δ ⋅ cos τ ϕo = sin δ where cos δ is the radius of the circle parallel to the equator at declination
δ.
Rotating the north-south axis into the zenith-nadir axis, using the equations below:
ξ = λo⋅cos(90°-ϕ)+ϕo⋅sin(90°-ϕ) η = -λo.sin(90°-ϕ)+ϕo.cos(90°-ϕ)
where (90°-ϕ) is the angle of rotation. (ϕ … local latitude)
It follows:
ξo = -cos δ ⋅ cos τ ⋅ sin ϕ + sin δ ⋅ cos ϕ = -cos ε ⋅ cos α
ηo = cos δ ⋅ cos τ ⋅ cos ϕ + sin δ ⋅ sin ϕ = sin ε
From the equation for ηo:
From the equation for ξo: (1)
ε = arcsin[cos δ ⋅ cos τ ⋅ cos ϕ + sin δ ⋅ sin ϕ]
α = arccos[(cos δ ⋅ cos τ ⋅ sin ϕ - sin δ ⋅ cos ϕ)/cos ε] ⋅ sign τ
Using cos δ ⋅ cos τ from the equation for ηo, α can be written as:
(2)
α = arccos[(sin ε ⋅ sin ϕ - sin δ)/(cos ε ⋅ cos ϕ)] ⋅ sign τ
Multiplication with sign τ resolves ambiguities – but runs into trouble with τ = 0°. The trick of adding
10-6 (or another small quantity) to τ takes care of that problem. (With hardly any effect on the numerical
results)
Setting horizon-system and equator-system in relation, by using the spherical sin law, one gets:
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sin(90°-ε)/sin τ = sin(90°-δ)/sin(180°-α)
Expanding:
α = arcsin[sin τ ⋅ cos δ / cos ε]
(3)
Combining equations above and forming sin α/cos α = tan α, one gets, after lengthy transformations:
α = arctan[sin τ / (cos τ ⋅ sin ϕ - tan δ ⋅ cos ϕ)]
(4)
The ambiguity problem for case (4) can be resolved by using arctan2. [The function arctan2(x,y)
calculates arctan(y/x) and returns an angle in the correct quadrant.]
α = arctan2[cos τ ⋅ sin ϕ - tan δ ⋅ cos ϕ, sin τ]
(5)
Below are graphs of all five variants of the azimuth equation. All are for ϕ = 40° and δ = 23.44°.
140
120
(1), (2), (5)
100
80
60
40
20
-200
-100
(3)
-200
-100
α
Variants 3 (below left) and 4 (below right) can
both produce incorrect values if care is not taken to
change the quadrant of the value that the
unexamined equation produces for certain inputs.
τ
0
-20 0
-40
-60
-80
-100
-120
-140
140
120
100
80
60
40
20
0
-20 0
-40
-60
-80
-100
-120
-140
Variants 1, 2 and 5 (to the left) always return
correct values (i.e. there is no ambiguity in the
determination of the correct quadrant of the
resulting value).
100
200
Herbert O. Ramp
Joachim-Schettl-Gasse 29
A-1140 VIENNA, Austria
horamp@aon.at
α
(4)
τ
100
200
-200
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March 2009
-100
140
120
100
80
60
40
20
0
-20 0
-40
-60
-80
-100
-120
-140
α
τ
100
200
Page 35
Patron Saint Hildevert
Fred Sawyer (Glastonbury CT)
Virtually every human activity or condition has a patron saint. There are patron saints of dairymaids,
dentists, distillers, ecologists, editors, embroiderers, fiddlers, fruit dealers, grave diggers, hosiers,
jugglers, librarians, mathematicians, nail makers, old-clothes dealers, pencil makers, potters, reformed
prostitutes, sawyers, spelunkers, vinegar makers, waitresses - and the list goes on and on. Yet there is no
‘official’ patron saint of dialing. That is not to say that, as an activity, dialing has no redeeming qualities.
It just seems that there has been an oversight somewhere!
If I recall correctly, a number of years ago some of our Italian dialing colleagues petitioned the Vatican to
determine what would be required to arrange a patron saint assignment. They were told that there was not
yet a patron saint of dialing and that to correct the oversight they would have to establish that any
proposed patron had in fact been involved in dialing as an activity or had at least actively encouraged
dialists in some way. At first blush, this would seem to be a perfectly reasonable requirement. However,
how then, one might ask, did St. Clare of Assisi, who lived in the 13th century, become the patron saint of
television!? And perhaps even more perplexing – how did St. Isidore, living in 7th century Spain,
become the patron saint of the Internet? Surely there must be some sort of double standard going on here.
Of course, even with this requirement, it would be possible to point to a number of possible patrons. The
first that comes to my mind is the Venerable Bede, the 8th century Father of English History. Bede wrote
about timekeeping and his work on how to use one’s shadow length to tell the time of day has been
discussed in The Compendium (see the June 1997 article by Bob Kellogg). A recent conference of the
British Sundial Society featured a tour stop at Durham Cathedral where Bede’s remains have been
interred in the Galilee Chapel since the 11th century.
But, frankly, adopting Bede as patron would be establishing a new tradition – and what I am more
interested in is recapturing an existing tradition. Perhaps as dialists we could fit into the purview of an
existing patron by making an argument that another group should be more inclusive in defining its
membership. Perhaps we could legitimately claim St. Barbara since she is the recognized patron of
mathematicians. But this might be stretching things a bit. How about St. Hubert of Liège – he is the
patron of precision instrument makers. This affiliation might work – but it would still be creating
something new.
What I am interested in is finding a patron saint who, at some point in history, was adopted as such by an
identifiable group of dialists. From my perspective, an established tradition is of more interest than trying
to justify any new assignment.
St. Hildevert
In St. Hildevert, dialists have a patron who satisfies this requirement:
“In the VXIIth century, dialists (cadraniers) formed a brotherhood in Holy Cross parish with the combmakers, tabletiers and marqueters, that met on St. Hildevert’s Day, May 27th” [Apel/Pytel, p.21]
The brotherhood met at the church of the Holy Cross in Paris which was situated near the corner of Quai
de la Corse and rue de la Cité [Gagnaire, ch.3. Some of the saint’s relics were here Apel/Pytel, p.21].
So who was Hildevert? He was the 7th century Bishop of Meaux. He died on May 27, 680 and was
buried in the church at Vignely that he had had constructed. Following centuries of reports of miracles
occurring at his tomb, he was declared a saint and his remains were removed to Meaux. In the late 11th
century, when veneration of a saint’s relics played a considerable role in the economy, Hildevert’s
remains were removed from their resting place and taken on a tour of villages around France. At each
stop, the faithful were allowed to visit the saint’s relics and listen to stories of his life and the miracles
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March 2009
Page 36
attributed to him. Donations were collected; a portion of the
treasure was left in the village to fund good works and the
remainder stayed with the priests who were directing
Hildevert’s posthumous tour.
After passing through several dioceses, the grand tour arrived
in Gournay-en-Bray, where the faithful were once again
invited to venerate the relics. However, on the morning that
the troupe was scheduled to leave, it was discovered that the
casket had suddenly become extremely heavy – almost as
though it had been filled with rocks! [Devarenne, p.15] After
much thought, it was decided that Hildevert was making it
known that he wished to remain in Gournay-en-Bray.
This idea did not sit well with Hugues III de Gournay, the
seigneur of the place. Suspecting trickery, he attempted to
set the casket on fire but was astounded when the flames
refused to burn the container. He was quickly converted, had
a silver casket made for the saint’s relics, and ordered that a
Church of St. Hildevert, Gournay-en-Bray
new church be built in honor of Saint Hildevert. [Full
disclosure! F. Sawyer is a direct descendant in the 27th generation from Hugues III de Gournay.] That
church still stands today and houses the saint’s relics.
Over the centuries, Hildevert became well-known as protector against the ravages of fire. This
association arose from an event in 1375. A major fire threatened to reduce much of Gournay to ashes –
after all else failed, a procession of priests laid the saint’s relics before the fire and, so the legend goes, the
flames were extinguished. Gournay also became a center of pilgrimage by those afflicted with nervous or
mental disorders. Hildevert proved to be an important saint in the middle-ages.
In the 17th century a new industry developed in the region; the area around Gournay-en-Bray became a
center for tabletiers – those who make and sell chess-boards, dominos, snuffboxes and other products of
ivory or ebony. Tabletterie had started simply as a trade that prepared tablets of ivory or wood to be
marked up for notes or keeping accounts. Over the centuries it grew to include the manufacture of small
luxury handheld items for personal use. In this era, any new fraternity of craftsmen would find validation
for itself in a variety of ways – one of which was the adoption of a patron saint.
Exactly how Hildevert became patron of the tabletiers is not known, but at least one writer [Devarenne]
has conjectured that the adoption might have resulted from sponsorship by a very well-known, influential
woman of the time: Anne Geneviève de Bourbon-Condé (1619-1679), Duchess of Longueville. In 1658,
she was given a finger, a few pieces of the skull, and a small piece of a rib from the saint’s skeletal
remains – to aid her in her devotion! [Devarenne, 18-19]. As a privileged member of the royal court, and
as one who was particularly interested in the prospects of Gournay and Méru, both of which were in her
domain, the duchess could well have been the instigator of the saint’s patronage, helping to obtain royal
recognition of the corporation of tabletiers.
The corporation of tabletiers grew quickly. Soon it incorporated the évantaillistes (makers of fans – in
ivory) as well. So the focus of the saint’s patronage shifted in this era from nervous disorders to the
manufacture of small luxury items in ivory and wood. Besides working in ebony, tabletiers also used
boxwood, walnut tree, wild cherry tree, and olive-tree. And St. Hildevert quickly became the patron as
well of wood turners and carvers. Combmakers came under his purview, as did also marqueters.
A close examination of the 1870 lithograph by J. Tallon [Devarenne] shows St. Hildevert standing at a
table on which we can see a fan, dominoes, dice, a brush and comb, and wood turned items – the makers
of all of which came under his patronage at some point in time. Indeed, this is the telltale sign that
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March 2009
Page 37
identifies the subject as St. Hildevert – it is
customary in images of christian saints to include
some allusion to an event in the saint’s life or to the
subjects of his/her patronage.
Unfortunately, there is no sundial on the table; and
yet, we know that dialists did indeed come under the
burgeoning influence of this patron saint. It is not
clear exactly how this came about, but the fact that it
did should not be surprising. St. Hildevert clearly
seems to have become the patron saint of those who
make small ‘luxury’ items of ivory or wood. In the
17th century, the tabletiers of Dieppe (France)
became famous for their marvelous creations –
including ivory diptych sundials which rivaled those
for which the German city of Nuremberg was
justifiably famous.
“It is quite probable that those of the tabletiers who
specialized as dial-makers remained very tied to
their fellow-members within the same corporation
and did not go to seek another patron.” [Gagnaire,
ch.3]
So be it. However it came about, there is historical precedent (more secular and capitalistic than
religious) for St. Hildevert to be the patron saint of dialists. On May 27, the feastday of St. Hildevert, I
will join the celebration in spirit and acknowledge our patron.
Bibliography
Devarenne, Anatole, Saint Hildevert - patron des tabletiers, Editions du Thelle, Meru-en-Thelle (Oise)
France, 1948.
Opizzo, Yves & Gagnaire, Paul, Hildevert, notre saint patron,
Le Rêve d'une Ombre, Éditions Burillier, Vannes France, 2007,
p.29.
Apel, Jacques
Christian,
domestiquée
cadraniers et
solaires du
Bonnefoy, La
France, 1990.
& Pytel,
L'ombre
Les
Cadrans
Perche,
Mesniere
Fred Sawyer
8 Sachem Drive
Glastonbury CT 06033
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March 2009
A St. Hildevert sundial by Pierre
Joseph Dallet.
Photo by P.J. Dallet
Page 38
The Tove’s Nest….
A Universal Capuchin Dial
Fer de Vries
ferdevries@onsneteindhoven.nl
In The Compendium 6(1), Mar. 1999, William S. Maddux, Mac
Oglesby, Warren Tom and I wrote an article with the title: A
"Universal" Capuchin Dial (or The Sailing Wooden Shoe).
This dial was developed by Jan Kragten in 1992. We had never
seen a universal Capuchin dial before, but now we have. Nicola Severino sent me two images: one from
a 1535 book ([Collectio figurarum], Eine reiche Sammlung von Kupferstichen u. Holzschnitten, welche
Sonnenuhren u. andere astronomische Instrumente darstellen) by Georg Hartmann (Bayerische
Staatsbibliothek, Munich, Germany), in which a mirrored example is seen; and one from a 1562 book
(Gnomonice Andreae Schoneri) by Andreas Schöner (Instituto e museo di storia della scienza, Florence,
Italy). Attached are images of both dials.
Fred Sawyer
An 18th Century Innovation
At the Italian sundial conference in 2002 Riccardo Anselmi introduced a novel sundial that is a vertical
direct east/west dial whose traditional hourlines on each face can be used throughout the day – using the
gnomon’s shadow for half the day and a reflected sunspot for the other half. This idea was developed so
that it works with a variety of vertical decliners by Silvio Magnani at the 2004 Italian conference. The
idea was generalized to inclining/declining dials by Gianni Ferrari in Sundials with a double system to
show the hours in The Compendium (Dec 2006, 13(4):27-34). However it is not unusual in modern
dialing to find that some ideas we believed to be truly novel in fact first appeared some centuries ago;
such is the case here. While working on another research project, I recently came across a 1731 talk that
the French mathematician Augustin Danyzy (1698-1777) gave to the Société Royale de Montpellier,
France. The (translated) title of the talk was: A way to make a vertical declining dial function even when
the plane is not illuminated, by placing a small mirror on the extremity of the stile so that the image of the
sun reflected on the dial falls on the same hour lines which had already been traced. Danyzy begins by
presenting Anselmi’s idea almost as a given and he moves on to the design of Magnani’s dial. The full
original French text of the talk can be read at http://tinyurl.com/da88m7.
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March 2009
Page 39
Old Quiz
Rene Vinck
rj.vinck@skynet.be
A note on the solution of the Quiz "Ancient sundial location" in Compendium 15(4): the Italian book
Orologi solari by G. Fantoni gives a simple and instant solution for the slope of the asymptote as a
function of the sun's declination and the elevation of the style which in this case is the complement of the
latitude. See fig. 56 on page 79 and form. 26 on page 80. See also footnote 46 on page 110.
Sundials in the Adirondacks
Martin Jenkins
m.a.jenkins@ex.ac.uk
Dear NASS friends. My wife Janet is a very keen gardener and while visiting her family in Queensbury,
NY last year we purchased a copy of Gardens, Adirondack Style by Janet Loughrey, Down East Books,
Camden, Maine, ISBN: 0-89272-623-7.
Now you may ask “What has this to do with sundials?” Well, the book documents how people have
overcome the area’s rugged mountain climate to create beautiful gardens for the past 150 years, and some
of these gardens contained sundials which may still be there.
On page 33 there is a photo of Horace Inman (© Adirondack Museum collection) showing him standing
next to a horizontal dial mounted on a very ornate pedestal. He was a manufacturer and inventor from
Amsterdam NY, who purchased Round Island on Raquette Lake in the 1890s. Interestingly, according to
the book the island is still owned by the family, so the dial may still be extant!
Another dial is shown in a photograph of the Knapp Estate gardens on Shelving Rock. The photograph (©
Jesse Wooley) on page 57 shows a pedestal mounted horizontal dial in the foreground. Apparently the
Knapp mansion was destroyed by fire in 1917 and never rebuilt. The gardens lasted until the 1930s. After
WW2 most of the property was sold to the state of NY and is now a state park but the Knapp family still
retain a lake shore home. So maybe the dial is still ‘alive and well’, who knows!
Maybe a member in the region would like to pass a few hours researching into these dials with a view to
recording them for NASS, if they still exist. The fact that these dials were from the 1890s and owned by
relatively wealthy people would imply that the dials would be of quality and thus of significant interest
historically. Happy dial hunting, please let everyone know via The Compendium how you get on.
The Bury St. Edmunds Curve for 25 Centuries Fred Sawyer
In 2005, John Davis reported finding an interesting 1870 graphical Equation of Time on a sundial in Bury
St. Edmunds, England (“More On The Equation Of Time On Sundials”, BSS Bulletin, Jun 2005,
17(ii):66-74). Later that year I provided the mathematical basis for the graph (“The Bury St. Edmunds
Curve”, The Compendium, 12(3):29-31), showing that it allocates the exact same curve length to each day
of the year, and does so in an absolute minimum of length. I subsequently turned the curve upside down
and used its resemblance to a flame as part of a design element in a new sundial (“An Osculatory
Sundial”, The Compendium, 14(1):13-16). Kevin Karney, who has done a considerable amount of work
on the history and theory of the equation of time, liked the image and decided to project it for 25
centuries. That’s 2500 versions of the curve, one following after the other, varying slightly in position
from year to year. With Kevin’s permission, we have reproduced the figure on the inside back cover.
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March 2009
Page 40
The Bury St. Edmunds Curve of the Equation of Time Projected for 25 Centuries – Kevin Karney

The Compendium 16-1 March 2009 - North American Sundial Society

Transcription

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