Re: Railways and Sundials

[Warren Thom]

Thank you John, for posting your pictures.  I find your skills and artistic
work fascinating. Nice job.

I am glad to see you are posting again.

Warren


On Fri, Jan 4, 2013 at 11:37 PM, John Carmichael
wrote:

> *Hello All:*
>
> * *
>
> *Bare with me, this email will eventually relate to sundials (as Roger
> says, everything eventually does…)*
>
> * *
>
> *I sheepishly must admit that I have been unusually quiet on the list for
> one year. Let me explain…*
>
> * *
>
> *It wasn’t for lack of interest in all your postings which I have been
> reading, it was because I was so deeply involved in a giant project which
> consumed all my time and undivided attention. It took over my life for one
> year (and helped me to escape the horrible state of world and national
> affairs.  I literally made my own little world and never left town). I
> have been working non-stop all day, every day for thirteen months on this
> project. Without the encouragement and support from my family and friends,
> it would not have been possible.*
>
> * *
>
> *I have been making sundials for twenty years.  But had a crazy dream
> festering in the back of my head for just as long.  Ever since they were
> invented in Germany in the 1980s, I’ve wanted to design and build a Garden
> Railway. They can be magical and most satisfying things.  I figured that
> I’m starting to get old and if I waited any longer I physically wouldn’t be
> able to do it.  So I bit the bullet and made a big decision to temporallyhalt 
> my sundial business, retool my shop, and make the railroad.
> *
>
> * *
>
> *Then along came the letter from Gianni Ferrari on Railway Sundials, and
> it woke me up and I realized that sundials do relate to everything. (
> thanks Roger).  Well, Gianni’s letter also gave me an idea…*
>
> * *
>
> *Many years ago, NASS gave me the Sawyer Dialing Prize which was a
> beautiful and sturdy little brass equatorial dial made by The Great Tony
> Moss himself.  Sadly, it has set on my shady workbench, much loved but
> unused for all these years.  I had no sunny window available and no good
> place outside- until now!  I thought what a great idea!  I’ll use my
> Sawyer Dialing Prize Sundial as a miniature monumental sundial on the
> railroad.  So I glued it on top of a stone pinnacle by the Trolley
> Station.  Looks great and works just fine.  Thanks Tony and Gianni!  Everybody
> loves it.*
>
> * *
>
> *I’m back at dialing again and have orders.  The break was good, but I’m
> happy to be dialing again.*
>
> * *
>
> *Here is a Flickr set of the new railroad, including the railroad
> sundial: http://www.flickr.com/photos/jlcarmichael/sets/72157632430552837/
> *
>
> *I didn’t have time to write descriptions under each photo, so you’ll
> just have to guess what you are looking at.*
>
> *All aboard!*
>
> *John*
>
>
>
>
>
>
>
>
>
>
>
>
>
> John L. Carmichael
>
> Sundial Sculptures
>
> 925 E. Foothills Dr.
>
> Tucson AZ 85718-4716
>
> USA
>
> Tel: 520-6961709
>
> Email: jlcarmich...@comcast.net
>
>
>
> *My Websites:*
>
> (business) *Sundial Sculptures:* http://www.sundialsculptures.com
>
> (educational) *Chinook Trail Sundial: *
> http://advanceassociates.com/Sundials/COSprings/
>
> (educational) *Earth & Sky Equatorial Sundial:*
> http://advanceassociates.com/Sundials/Earth-Sky_Dial/
>
> (educational) *My Painted Wall Sundial:*
> http://www.advanceassociates.com/WallDial
>
> (educational) *Painted Wall Sundials:*
> http://advanceassociates.com/WallDial/PWS_Home.html
>
> (educational) *Stained Glass Sundials:*
> http://www.stainedglasssundials.com
>
> (educational) *Sundial Cupolas, Towers & Turrets:*
> http://StainedGlassSundials.com/CupolaSundial/index.html
>
>
>
> *From:* sundial [mailto:sundial-boun...@uni-koeln.de] *On Behalf Of *Gianni
> Ferrari
> *Sent:* Saturday, December 01, 2012 4:02 AM
> *To:* LISTA INGLESE
> *Subject:* Rrailways and sundials
>
>
>
> Maybe someone is interested in the group of monothematic sundials that
> Italian gnomonists Giacomo Bonzani and Guido Dresti have designed on the
> walls of the stations of a small mountain railway (52km)  which connects the
> town of Domodossola (Northern Italy) with nearest Switzerland.
> Greetings
>
> Gianni Ferrari
>
> LInk:
>
>
> http://lnx.vigezzonews.it/index.php?option=com_content&view=article&id=750:la-valle-dal-tempo-dipinto&catid=38:la-valle-dal-tempo-dipinto&Itemid=62
>
>
>
> -
> Ing. Gianni Ferrari
>
> Lat.44;38,18.5N
> Long. 10;56,05.3E
> gfme...@gmail.com
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
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Re: "Everything relates to sundials"

[Warren Thom]

Mac,

 I like your ramp walking sundial.  The video was cute.   I too think,
everything relates to sundials.

When you first said a "ramp walking" sundial, my first thought was about
the equinox steps of the Mayan ruins which act like a snake moving up
during sunset on the equinox.  I do think such steps could be oriented to
"shadow crawl towards"  ANY time and on ANY date the sun is out.  Unlike
the stopped clock that is correct twice a day, such a ramp would only be
correct time twice a year.

Warren

On Sat, Jan 5, 2013 at 7:13 PM, Mac Oglesby  wrote:

>
> Dear Friends,
>
> Not to compare, in any way, my insignificant efforts with John
> Carmichael's wonderful railway project, his comment about everything
> relates to sundials reminded me that such was my situation recently.
>
> Several months ago I became interested in ramp walking toys and made a few
> (even designed a couple) before I hit upon the fun idea of trying to design
> and make a ramp walking sundial.
>
> For the benefit of list members who don't receive The Compendium, a very
> brief video is available at:
>
> http://www.youtube.com/watch?v=WMo5Cpy64sY
>
> (This video was made just a bit after 11:00 AM on November 10, 2012.)
>
> Best wishes,
>
> Mac
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
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Re: Passion - Shall we change this to "End of Life Plans"?

[Warren Thom]

Over the last two weeks, I have given a little thought to having my  
parent's tombstone modified to include a sundial.  It faces East and a few  
designs would look nice.  (I have also spent several hours reading about  
cutting in stone that John Carmichael and others have so interestingly  
promoted.)


On the appropriateness of the topic: Our minister gave a service one time  
on death.  The focus was on making plans, not on the afterlife.  She made  
a planning form available.  It included hymns for a memorial service and  
other wishes.  Some in the congregation thought it was inappropriate and  
some thought it practical.  No one thought it was funny.  Well she gave a  
few culturally used synonyms for death like, kick the bucket, sell the  
farm etc. that drew a few chuckles.


With many different cultures represented on this list and the limits of  
expression in the written word, reading the list requires that we not make  
hasty assumptions about others intentions.  I interpreted the questions  
below to be about personal plans and actions resulting from our unique  
interest.  I assume the best of intentions unless proven otherwise with  
expanded discussion.


The question of what to do with an accumulation of sundial items is a good  
one.  Some items have value only to a few people.  Since I plan to be  
cremated, I don't really want a dialing item to be destroyed.  I mentioned  
this question very briefly at a NASS meeting either last year or the year  
before.  I don't recall the outcome.  I do plan to leave my intentions  
with my wife or children including the desire to sent some of the items to  
NASS to be given away in the silent auction. Are there other plans that  
others would share on the list?


No tattoos for me.  I have more than enough distinguishing marks on my  
body already and none are tattoos.


Warren Thom (42 N, 89 W)



Do any of you plan to have a sundial on your gravestone?

Do any of you plan to be buried with a sundial?

Do any of you have a sundial tattoo?




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Re: Hemicyclium dials

[Warren Thom]

I built this hemisherium from a clear 4" plastic Christmas ornament.  The  
location of the center, the radius and the circles draw was an experience  
greater than one can have from looking at a model or viewing pictures.   
Thank you Fer for providing the directions.


Warren Thom


On Tue, 26 Oct 2010 14:01:59 -0500, fer de vries  
 wrote:



Phil,

On this address

http://www.dse.nl/~zonnewijzer/hemisph.htm

you find a pocedure I once wrote to construct a hemisherium.

Best wishes, Fer.

Fer J. de Vries

De Zonnewijzerkring
http://www.de-zonnewijzerkring.nl

Molens
http://www.collsemolen.dse.nl

Eindhoven, Netherlands
lat.  51:30 N  long.  5:30 E

  - Original Message -
  From: Phil Walker
  To: sund...@rrz.uni-koeln.de
  Sent: Tuesday, October 26, 2010 6:48 PM
  Subject: Hemicyclium dials


  Hi diallers,

  I am considering a model cube dial with  E. S and W  faces, each with  
a concave hemisphere on it. It would have a pin gnomon with a ball nodus  
at the end, at the centre of the hemisphere. I understand that this is  
based in the Greek" hemicyclium"  but there.are a few 16th century cube  
dials of this type in England and Scotland.


  I've two questions,

  What are the dial equations for the hour- and day-curves for a  
hemicyclium-based dial? Do they require some spherical trigonometry?


  How' in practice, could I draw/paint/scribe etc the said curves onto  
the concave shapes?


  Your help would be appreciated,

  Phil Walker
  52N2W (ish)
  http://www.sundial.pwp.blueyonder.co.uk/





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Re: Fwd: how italian hours

[Warren Thom]

All,

I have enjoyed the discussion about Italian hours.  My first dial was an  
hours to sunset dial on my garage door done in the 1970s.  Mac Oglesby's  
models and dials are inspiring to me.  I had a globe parallel to the earth  
in the 1980s that I liked to view on a sunny day.  I could observe where  
on earth the sun was overhead and where the sun was setting at that very  
moment.  About six years ago I worked on a design that would cast a shadow  
 from a nodus onto a map that would show where on earth the sun was  
directly overhead.  It was an ugly confusing map.  My question is:

Hour and prayer lines are fine.  Is there other information, that uses  
Italian hour calculations (or solar declinations) , that would be of  
interest to a broad audience?  Fred Sawyer created a universal dial of  
modern hours based on a world map.  Is it possible to create a "map" dial  
that would show where the sun is setting at that moment?  What could it  
look like?  Would it require a line shadow casting instead of a point?   
Any thoughts?

Thank you -- Warren Thom


On Sat, 03 Apr 2010 06:33:11 -0400, Gianni Ferrari   
wrote:

> In Ottoman Sundials we find often the Italic hours because these hours  
> give
> the time  to the sunset, when the Muslims  must say the Prayer Maghrib.
>
> These hours are given not from 0 (sunset) to 24 (sunset of the next day),
> but, as Roger has written, in two cycles of 12 hours and  are called  
> Ezanic
> hours.
>
> So at sunset we have the end of the 12th hour of a cycle and the  
> beginning
> of the 1st of the next.
>
> In such a way only at the equinoxes at noon the  Ezanic, Modern (French),
> Babylonian and Temporary hours have all the value 6.
>
> In different days this is not true as you can see in the table attached.
>
>
>
> In Ottoman Sundials  generally we don’t find Babylonian hours, while we  
> have
> often the lines of the Solar Time that give to the Muslims the time to  
> noon,
> that is the time to the Zuhr prayer.
>
> These hours are not numbered as in our clocks or sundials, but,  
> generally,
> with the number of hour to noon (in the morning) or after it (in the
> afternoon). So  : 5, 4, 3, 2, 1, noon, 1, 2, 3, 4, 5.
>
>
>
> They use “Arabic numbers” or, in oldest sundials, numbers written with
> “letters” ( Abjad method)
>
>
>
> Gianni Ferrari
>
>
>


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Re: DeltaCad Sundial and Dialling Related Macros

[Warren Thom]

Thanks Carl

A lot of effort can be seen in the Delta CAD macros by each of the authors. 
It is nice to see them presented with examples so a dialist can compare the 
different results.

Nice job of presentation-

Warren


- Original Message - 
From: "Carl & Barbara Sabanski" <[EMAIL PROTECTED]>
To: "Sundial Mailing List (E-mail)" 
Sent: Sunday, January 20, 2008 7:31 PM
Subject: DeltaCad Sundial and Dialling Related Macros


> Sunny Day!
>
> With the permission of Simon Wheaton-Smith I now have a web page providing
> an overview of his many DeltaCad sundial and dialling related macros. 
> Thank
> you Simon!
>
> The Sundial Primer is now host to a total of 63 DeltaCad sundial and
> dialling related macros written by a number of diallists.  If you don't 
> have
> them yet come and visit and get them while they're hot.
>
> http://www.mysundial.ca/tsp/deltacad_sundial_macros.html
>
> Happy Dialling!
>
> Carl Sabanski
> www.mysundial.ca
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 

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Re: Does Refraction Affect Azimuth? / Re: sundial Digest, Vol 24, Issue 17

[Warren Thom]

Hi Bill,

If I recall your comments at the NASS meeting correctly,  while azimuth might 
be unaffected by refraction, because the "real time" of sunset  is later due to 
refraction, the azimuth at a later time needs to be calculated. That is, for us 
at North latitudes the sunset is further North than a normal calculation of 
sunset would give.  Assume no objects on the horizon.   Did I miss something?

Warren


  - Original Message - 
  From: Bill Gottesman 
  To: Mashallah Ali-Ahyaie ; sundial@uni-koeln.de 
  Sent: Thursday, December 27, 2007 11:12 AM
  Subject: Re: Does Refraction Affect Azimuth? / Re: sundial Digest, Vol 
24,Issue 17


  Mashallah,

  I believe you are correct about azimuth and time of transit being unaffected 
by refraction.

  "Astronomical Algorithms" by Jean Meeus has a good section on calculating 
effects of refraction and the sun's semi-diameter.  Also a valuable section 
about how to correct for the effects of Nutation.  I'm not so sure about the 
other topics you mention.  I would guess parallax of the sun from the 
perspective of the earth's diameter is covered in surveying books, or perhaps 
one of the astronomical trigonometry books by Smart.

  -Bill Gottesman
- Original Message - 
From: Mashallah Ali-Ahyaie 
To: sundial@uni-koeln.de 
Sent: Thursday, December 27, 2007 4:24 AM
Subject: Does Refraction Affect Azimuth? / Re: sundial Digest, Vol 24, 
Issue 17


Dear Mr Gianni Ferrari,

   Greetings, happy new year and Merry Christmas to you and all members.

   As I recall, the azimuth of a body and its time of transit are not 
affected by refraction. Please kindly do comment.

   Also, I would like to have a good and applied article on astronomical 
corrections (Refraction, Parallax, Dip of Horizon and Semi-Diameter.) I wonder 
if any respectful member could help. 

Best regards,

Mashallah Ali-Ahyaie


On Dec 26, 2007 2:30 PM, <[EMAIL PROTECTED]> wrote:

  Send sundial mailing list submissions to
 sundial@uni-koeln.de 

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  Today's Topics:

1. R: Re: Azimuth of Sunrise - Sunset ( [EMAIL PROTECTED])


  --

  Message: 1
  Date: Tue, 25 Dec 2007 22:58:32 +0100 (GMT+01:00)
  From: " [EMAIL PROTECTED]" <[EMAIL PROTECTED]>
  Subject: R: Re: Azimuth of Sunrise - Sunset
  To: 
  Message-ID: <[EMAIL PROTECTED]>
  Content-Type: text/plain;charset="UTF-8"


  And the air refraction ?

  Because of refraction, the sun is already 
  below the horizon when we observe
  the upper limb kiss the horizon. In
  this moment the altitude of the Sun?s center is  about
  ?(34+14) = -48?
  (the refraction at 0? degree is about 34?)
  The Azimuth of the point 
  where we begin to see the Sun (limb) is then different from the
  theoretical and geometrical value, also if the differences are small at
  mean latitudes.

   With Lat = 45 on  Winter Solstice,  the Azimut of the 
  Sun?s limb (when it appears)  is about 56.8 degree ; the Azimuth of the
  Sun?s center 56.4? and the theoretical Azimuth 55.8?.
  The differences
  increase when Latitude increases.
  With Lat.= 66?. the Sun?s limb 
  appears with an Azimuth about 7 degree more than the theoretical value
  (18.8 and 11.9?)

  My best wishes for a sunny New Year !
  Gianni Ferrari




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  End of sundial Digest, Vol 24, Issue 17
  ***




-- 
Mashallah Ali-Ahyaie 





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Re: Winter Solstice at Newgrange, Ireland

[Warren Thom]

Hi Frank,

At the 2007 NASS conference, Bill Gottesman had several comments about 
calculating sunrise/sunset for the purpose of viewing these observations. 
He was consulted in the building of an observation area.  These were some of 
his comments if I recall correctly.

(1)  Get a panoramic view of the area because hills, buildings, and trees do 
effect sightings.

(2) Use the last quarter of the sun setting, not the center, to calculate 
the azimuth at sunrise and sunset.

(3) Refraction of the air does alter the observation time and azimuth.  This 
needs consideration in calculations.

I am sure he will say more when he sees this topic being discussed.

Warren Thom

- Original Message - 
From: "Frank King" <[EMAIL PROTECTED]>


> Dear Jack,
>
> There is another little thing about sunrise and
> sunset at the solstices that you might enjoy
> knowing.  It was, I believe, known in prehistoric
> times so this isn't a recent research result...
>
>  The point on the horizon where the sun rises at
>  the winter solstice is directly opposite the point
>  on the horizon where the sun sets at the summer
>  solstice.  [And vice versa of course.]
>
> To see this from the formula you need to use the
> two-argument inverse-tangent function.  In Excel
> the formula for the azimuth at sunrise is:
>
> ATAN2(sin(dec), +sqrt(cos(phi+dec)*cos(phi-dec)))
>
> The formula for the azimuth at sunset is:
>
> ATAN2(sin(dec), -sqrt(cos(phi+dec)*cos(phi-dec)))
>
> [Everything is in radians not degrees by the way.]
>
> If you reverse the sine of dec the argument of the
> square-root function doesn't change but sin(dec)
> does change sign.  Of course you have to reverse
> the sine of the square-root result when going
> from sunrise to sunset.
>
> Accordingly, going from sunrise at one value
> of dec to sunset at the negative of that value
> of dec takes you 180 degrees round the compass.
>
> This is because you are going from:
>
>  ATAN2(arg1, arg2) to  ATAN2(-arg1, -arg2)
>
> I hope you aren't wishing you had never asked
> the question!!!
>
> Best wishes
>
> Frank King
> Cambridge, U.K.
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 
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Re: God's Longitude and the Lost Colony of Virginia

[Warren Thom]

Subject: God's Longitude and the Lost Colony of Virginia


  At the BSS meeting in Cambridge this spring. Frank King outlined the problems 
assigning a unique date to a mark on a sundial. With our Gregorian calendar and 
leap year cycle the date for any given solar declination can vary over four 
days. He showed how a calendar based on a 33 year cycle devised by Omar Khayyam 
 could reduce this spread to 24 hours. He then pointed out that for one 
specific longitude, the date of the first day of spring would always be the 
same. He mentioned that this was called God's Longitude and left it for us to 
figure out where that was as a homework exercise.

  I've done my homework and discovered a remarkable story, one that just had to 
be told at the NASS Conference in Virginia, at the 400th anniversary of the 
Jamestown colony of 1607. Fred Sawyer agreed to work with me as co-author and 
to present at the conference the story of  "God's Longitude and the Lost Colony 
of Virginia". It is a great story of the birth of science in Elizabethan 
England, the global conflicts of religion and empires and a secret agenda for 
the English protestants to occupy the new world at longitude 77ºW, God's 
Longitude.

  I have posted the presentation as Fred presented it at this personal website 
for you to download and enjoy. 
http://www3.telus.net/public/rtbailey/GodsLongitude/ It is a 5.7 MB PowerPoint 
presentation. If you do not have PowerPoint, download the free viewer from 
Microsoft. This will allow you to view the presentation but not the speakers 
notes that go alone with it.

  I would like to thank Frank King for the inspiration, Simon Cassidy for doing 
the historical research and uncovering the secret agenda, and Duncan Steel for 
publicizing it in his book "Marking Time: The Quest for the Perfect Calendar".

  Enjoy,

  Roger Bailey
  www.walkingshadow.info  



Great presentation (via Fred Sawyer) Roger.  I enjoyed your topic very much and 
I have retold the story 3-4 times.  Nondialist people find it of interest.  
Thank you Roger, Simon Cassidy and Frank King.

On the topic of the McLean - 2007 NASS meeting -- congratulations to Mac 
Oglesby as recipient of the Sawyer Prize,  and thanks to Fred for all his 
organizational efforts, to Jack for hosting, to the British contingent for 
their insights, and all in attendance for their contributions.  I ordered from 
Lulu.com and received within a week "A Treatise of Gnomonicks."  It had the 
answer to the question -- "Why is a horizontal dial at the North pole called 
equatorial and one at the equator called a polar dial?"  Answer in the Ozanam 
book says the name comes from the plane of the dial.  At the North pole, the 
plane of the dial is parallel to the equator and the one at the equator has a 
plane that "intersects" both the poles.  

I have a question related to time/calendar relationships -- Is it possible to 
show the day of the week (Monday, Tuesday etc...) by a shadow on a dial face 
good for only a rather short range of years and knowing the relationship of the 
current year to the last leap year?  

Thanks again,

Warren Thom
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Re: simultaneous sunset

[Warren Thom]

Dear Mr. King,

I have really enjoyed this problem.  In one sense it is simple because it 
not about hours, but about events.

In a recent post you said:

From: "Frank King"
Subject: Re: simultaneous sunset
>
> One of the many nice features of this puzzle is that there
> is no need to know the time of sunset (or sunrise) and, in
> consequence, you can lay any understanding of hour-angles
> on one side.
>

But I am having a problem understanding something.

Are you saying below that ANY two locations MUST have a moment of mutual 
sunrise/sunset?

Or are you saying, for any location there exists a second location at EVERY 
longitude that will have one mutual moment sunrise/sunset?  I can understand 
the second statement, but not the first.  At first glance I rejected the 
second statement, but clearly it must be true if the sun covers half the 
Earth every instant.

For example,  if I calculate the solar declination for the two latitudes of 
42°N and 10°N and 90° difference of longitude  -- I get a declination 
of -47°.  Certainly this is outside the range of -23.5° to +23.5° for our 
current situation on Earth.  This would be two locations that never share a 
sunrise/sunset event.  Yet 42°N and -64.7S and 90° longitude difference 
share a common event on winter solstice.  Location 2 is determined given 
location 1, difference in longitude and solstice solar declination of 23.5° 
.

Warren

> I have a comment on one of Warren's notes:
>
>> two locations with too great of a difference of
>> longitude, would be too far apart to ever have
>> the same moment of sunset.
>
> This is not quite the whole story...
>
>  The great circle which separates light from dark
>  necessarily encompasses EVERY longitude, so there
>  will be points almost 180 degrees apart which
>  have the same moment of sunset.
>
>  Half the points on this circle will correspond to
>  sunset and half to sunrise.  The most northerly
>  and most southerly points will, respectively, be
>  points where sunset is immediately followed by
>  sunrise and sunrise is immediately followed by
>  sunset.
>
> My formula doesn't distinguish between sunrise and
> sunset and the leading minus sign could equally be
> a plus sign:
>
> tan(dec) = [-]sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2)
>

---
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Re: simultaneous sunset

[Warren Thom]

Dear Mr. Evans and Mr. King,

I liked the problem.  I have not worked out the math yet.  I am not very 
good at quadratics in trig.  I was going to work on "iterations" to close in
on the answer.

I tried a few examples with your math.  They seem to calculate reasonable 
and interesting answers:

--lat of 50° and 35.8°  need a difference of longitude of 11° to get 
solar dec at solstice of around 23.5°
--two locations at different lat need a difference of long of zero to 
set on the equinox (solar dec of 0°).
--two locations with too great of a difference of longitude, would be 
too far apart to ever have the same moment of sunset.
-- here are a few situations - all at the winter solstice

Lat1  Lat2   Diff in Long
42°N  33°N6.7°

42°N  10°N  18.6° (one hour)

42°N -20°S  32°  (two hours)

42°N -51°S  56°   (three or four hours)



Upon the first reading of the problem, I thought it was a continuation of 
the "rotating platform on a polar axis with a pointer of EOT correction" 
thread.  IF you had a pointer on a scale, and you didn't use it for 
corrections for EOT or longitude, then it could point to the name of cities 
that have the same sunset time.  It might require a condition given on the 
horizontal "dial" surface that would have to relate to solar declination.  I 
don't know if I have the correct picture in my head for set up -- but I will 
think more about it.  Any other ideas on this?

Warren


- Original Message - 
From: "Frank King" <[EMAIL PROTECTED]>
To: "Frank Evans" <[EMAIL PROTECTED]>
Cc: "Sundial" <[EMAIL PROTECTED]>
Sent: Monday, June 18, 2007 11:20 AM
Subject: Re: simultaneous sunset


> Dear Frank,
>
> I do enjoy your puzzles!!
>
>> ... a question appeared of the form:
>>
>> "Find a day on which the sun sets (altitude 0 deg.) at
>>  the same moment in London and Paris (positions given)."
>
> Conceptually this is trivial.  Mathematically it gets a
> little messy but I think I can get a closed form of the
> solution.
>
> CONCEPT
>
> I assume that at any instant half the Earth is in sunlight
> and half is in darkness.  A great circle separates the two
> halves.  Any place on this great circle is experiencing
> the moment of (mathematical) sunset or sunrise.
>
> The solution to your problem is to draw a great circle
> from London to Paris and extend it until it reaches the
> Equator.  The angle this great circle makes to the plane
> of the Equator is the complement of the solar declination
> (subject to a minus sign).
>
> MATHEMATICS
>
>  Let t1 = tangent of the latitude of place 1
>
>  Let t2 = tangent of the latitude of place 2
>
>  Let d  = their difference in longitude
>
> We then have:
>
>  tan(dec) = -sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2)
>
> Where dec is the required solar declination.
>
> EXAMPLE
>
> You cite London and Paris.  I take the latitudes as being
> 51 deg 30' and 48 deg 52' and the difference in longitude
> as being 2 deg 23'.
>
> This gives the solar declination as -18.7 degrees.
>
>
> I expect I have goofed.  Some bright youngster can now
> tidy up my efforts!!!
>
> Best wishes
>
> Frank King
> Cambridge, U.K.
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 

---
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Are there any Complex number formulas used in sundial calculations?

[Warren Thom]

To all the maths people out there,

My background is not math, and I don't know how to do the math to approach 
this question.


I do know that complex numbers are used in engineering for work with 
alternating current and frequency samples in electrical signals.  Since 
sundials deal with cycles,  are there any sundial relationships that use 
complex numbers?  Any starting point would be appreciated.


Thanks,

Warren Thom 


---
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NASS Conference in 2007

[Warren Thom]

Hello All,

Did I miss it, or was it announced where and when the 2007 NASS will be 
held?



Warren 


---
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Re: Question about lunar phase and the sun's path in the sky

[Warren Thom]

Hello Greg and Chris,

While Chris explains your question well, I have several observations that 
are related to your question.  I am sure you have made the observations 
also.  But they are interesting.  Who says the motions in the sky are 
static?


1.  At northern latitudes, in the summer, a full moon rises in the southeast 
as the sun sets in the northwest.


2.  In the winter a full moon rises in the northeast as the sun sets in the 
southwest. The full moon sets in the northwest around sunrise.  This gives 
us a lot of moon light in the winter when we can use it the most. From our 
point of view, a NE to south to NW path is a long path and would take more 
than 16 hours.


3.  From day to day, moon rise azimuths change a huge amount, while sun rise 
azimuths do not change much.  As we approach the equinox the sun rise 
azimuth is changing the most from day to day.  .


Thanks for your observation,

Warren



However, my somewhat meager knowledge of dialing led me to a new 
hypothesis:
The sun's path (and the moon's) aren't describing a circular, but rather a 
hyperbolic path in the sky. This means that it's possible to have the sun 
and moon be on the meridian and the horizon, respectively, and yet be more 
than 90 degrees apart.




---
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Dialist Prototye Project

[Warren Thom]

Hi Fer and all,
 
I have just read the latest issue of the 
Compendium, and I must agree with John, the Hollander dials are a very 
attractive invention.  The articles are clear and informative.  
Thanks to all involved.
 
John had suggested writing a DeltaCad macro to 
design the mean-time conical dial.  While I like the idea,  may I 
suggest a greater project for dialists to consider.  May I suggest working 
together on a "Dialist Prototype Package" of software.  It should have the 
following criteria:
 
1.  As universal as possible for both natural language and computer use 
(Windows, Mac, and Linux)
2.  Encourage rapid code 
production.  I have looked at DeltaCad macros.  They are not "rapid" 
to me, but I have not written a program for years.
3.  Can apply to CAD
4.  Able to do math testing like apply the 
equations of the Hollander dials.
5.  Have good visualization.
6.  Have reusable code. 
7.  ( more criteria to come -- or add your 
own.)
 
My nomination for the project is the cross platform 
Python computer language.  Before I go into detail, I would like to hear 
other ideas about such a project.
 
Take Care,
 
Warren Thom
 

  - Original Message - 
  From: 
  fer de vries 
  To: sundial 
  Sent: Monday, August 21, 2006 3:20 
  PM
  Subject: "Mean Time Cone Gnomon 
  Dial".
  
  
  John Carmichael wrote to the Sundial 
  List:
   
  -
  Hi Fer and Hendrik:
   
  I know I speak for everyone at the NASS 
  Conference that we were all very impressed with the Mean Time Cone Gnomon Dial 
  that you helped Hendrik Hollander to develop.  Congratulations to 
  Hendrik for winning the Sawyer Dialing Prize this year. What a 
  surprise.  I knew of Hendrik for his previous work with etched glass and 
  acrylic dials, but I don't think anybody else knew of him.   It 
  caused a great deal of interest at the NASS Conference since none of us had 
  ever heard about Hendrik or his new dial before. We loved the 
  fact that it looks like a simple ordinary dial with straight hour lines, 
  yet it tells Mean Time because it has a tilted cone gnomon. Fred kept 
  saying that he wished that he had thought of it.  Now that's a 
  compliment!!!  We are all anxious to read more about it in the next 
  issue of The Compendium.
   
  Afterwards, Roger Bailey and I discussed 
  ..
   
  John Carmichael
  .
   
   
  At first my help with this dial only was for some tests afterwards. 
  The idea is by Hendrik after reading pubilcations about "Compressed 
  Gnomonic Sundials" by Fred Sawyer.
   
  Many of the readers of the list perhaps won't understand what is a "Mean 
  Time Cone Gnomon Dial".
   
  You may read some of it and see an example of the dial at our 
  website.
  Look for News and then use the link to the september article.
  This article is already on the website.
  More will be published in coming bulletins.
   
  Best wishes, Fer.
   
   
   
  Fer J. de Vries
   
  De Zonnewijzerkringmailto:[EMAIL PROTECTED]http://www.de-zonnewijzerkring.nl
   
  Eindhoven, Netherlandslat.  51:30 
  N  long.  5:30 E
  
  

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---
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Apple Mac to PC on "Text Clippings"

[Warren Thom]

Hello,

Can anyone help me recover the text from a
pixcture/text file created on a Mac under a program
called "Text Clipping"?  I can see the pictures, but I
would like to get the information also.  

(I am going away - so I may not be near a computer for
several days. )

Thanks

Warren
---
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Re: Google Wall Declination

[Warren Thom]

Hi John, Roger and all,

I am sorry that I will miss the 2006 meeting - first one I will miss since 
2001.  Glad to hear you are putting on a DeltaCad workshop.  I was unaware 
about version 6, until you posted your message,  John.  In checking it out, 
they are located near the meeting.  I would urge someone to contact them and 
invite them to the NASS conference.   Midnight Software, Inc., P.O. Box 
77352 ,Seattle, WA 98177-0352 , USA  They could do a talk on the scripting 
that is available in DeltaCad.  Ron Anthony was in contact with them ages 
ago about the scripting language.  For your workshop, you might photocopy 
the article I wrote about 10 years ago for the Compendium.  I do think 
DeltaCad is easy to use --- and I spent hours at my school trying to learn 
AutoCad -- and never got very far.  I printed something from DeltaCad after 
my first 15 minutes.  (I have no  interest in DeltaCad.)


Take Care,

Warren Thom


- Original Message - 
From: "John Carmichael"

To: "Roger Bailey"

Hi Roger:

you asked:

I assume that your Delta Cad workshop will cover the transfer of Zon dxf
files to Delta Cad.


Yes, of course!  That will be an important little part of my Delta Cad 
talk: How to import dxf, dwg and jpgs into a DC drawing.


By the way, the new Delta Cad version 6.0 lets you import jpegs now.  The 
older version would only let you import bmps. (which are huge files). 
This makes adding artwork/photos much easier and the files are smaller. 
You should upgrade to 6.0 if you haven't already done it.  It has other 
useful features that 5.0 did not have.


You might try importing a standard jpeg photo of your building wall in DC. 
Then copy and paste a the DC drawing of your sundial on top of it. You 
will see the DC sundial drawing on top of the photo.



- Original Message - 
From: "Roger Bailey" <[EMAIL PROTECTED]>

To: "John Carmichael" <[EMAIL PROTECTED]>
Sent: Thursday, July 20, 2006 9:17 AM
Subject: RE: Google Wall Declination



Hi John,

I assume that your Delta Cad workshop will cover the transfer of Zon dxf
files to Delta Cad. The ability in Delta Cad to "select all" and "copy" 
to

get the lines only as an overlay was a new one on me. Every other way I
tried gave me an opaque white background, useless as an overlay. This 
works

for PowerPoint, not for Photoshop or Word. There you get the white
background.

See you soon,

Roger

-Original Message-
From: John Carmichael [mailto:[EMAIL PROTECTED]
Sent: July 20, 2006 7:07 AM
To: Roger Bailey
Subject: Re: Google Wall Declination


Very Cool Roger!


- Original Message -
From: "Roger Bailey" <[EMAIL PROTECTED]>
To: "Sundial Mail List" 
Sent: Wednesday, July 19, 2006 11:29 AM
Subject: Google Wall Declination



We have had many discussions on this list on how to determine the
declination of a vertical wall. Let me suggest a new technique for not
only
wall declination but also location (latitude and longitude). Use the
satellite images on "Google Earth". An example is posted in three
PowerPoint
slides at:
http://www3.telus.net/public/rtbailey/WalkingShadow/WallDecG.ppt

For my "Timelines" presentation, I was interested in analysing sundials 
on
mosques in Istanbul. When I took pictures of the three sundials on the 
New

Mosque "Yeni Camii", I did not take field measurements to determine the
wall
declination. No problem. Start up Google Earth and fly to Istanbul.
Without
rotating, just using the X/Y controls, zero in on the New Mosque and 
save
the image. You can insert the saved image into a PowerPoint 
presentation,

add the North South vertical axis, draw a line along the wall and
determine
the wall declination, perpendicular to the wall.

Then start up Zon 2000 and enter the latitude and wall declination from
the
Google image into Fer de Vries program. Calculate for the example 
sundial:
local hours, Italian hours and Islamic Prayer times. Clip the Zon 
drawing,
save it as a dxf file and load the dxf file into Delta Cad. There you 
can

trim the lines to recreate the dial on the wall. Select all and copy the
lines as an overlay on the photograph (corrected for perspective) in 
your

presentation.

The Google Earth technique is sufficiently accurate with large buildings
and
high resolution images. I have used it successfully for three mosques in
Istanbul and the Klementinum in Prague. It even works for my home! The
full
story will be shown in Vancouver.

A conclusion from this analysis is the sundials on the mosques in 
Istanbul

show the mid afternoon prayer time "Asr" as in the standard horizontal
shadow length definition. But a different convention was used in 
Istanbul

for "Zuhr", the prayer just after noon. The Zuhr lines are not based on
the
altitude giving the horizontal shadow length as the noon shadow length +
2

Re: Clever stuff!

[Warren Thom]

Hi Tony,

I too, find the CNC carving and 3D models very interesting.  Listed below is 
a two page paper about sources and USA contacts, including the 3D glass 
images.  She has a web page that shows some of her 3D art.  Google "Math art 
3d" for more hits.  I KNOW there are sundial possibilities.


http://www.bathsheba.com/artist/Bathsheba_RP_handout.pdf

Warren


- Original Message - 
From: "tony moss" <[EMAIL PROTECTED]>

To: "Sundial Mail List" 
Sent: Saturday, May 13, 2006 3:32 AM
Subject: Clever stuff!



Fellow Shadow Watchers,
  The Sign and Graphics industries held a huge trade
show in the UK last week where I spent a day drooling of the very latest
in CNC carving, engraving and every aspect of display advertising.

One new (to me) technique based in France which might just have some
dialling possibilities in future is illustrated at:

http://www.vitrics.com/images/SH2full.jpg

This is laser 'engraving' actually INSIDE plate glass with nothing to
show on either surface.  The artwork consist of tiny apertures within the
glass caused (I'm guessing) by the interaction of two or more laser beams.

Encased in solid glass: what could be more weatherproof?

VITRICS homepage is at

http://www.vitrics.com

but you will have to search to find examples which do justice to this
amazing technique.

Tony Moss
---
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---
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Re: How was the Nass Conference?

[Warren Thom]

Hi John,
 
We missed you at the conference.  We all hope 
you are recovering well.  
 
The loop location of De Paul University was nice to 
the Chicago sights but can be expensive at some of the hotels. ( what big city 
isn't?)  The presentations were informative and interesting.  I 
appreciated how several presenters made "history" interesting to me.  Steve 
Luecking was a great host - with one workshop in Grant Park and access to 
computers for a touch of CAD -- and plenty of food.  The NASS workshops 
were a good addition.  It has sparked my interest in 3D CAD.  I do 
feel a little better grasp of spherical geometry also.  As I recall you 
started the workshop concept with your stained glass workshop.  

 
Navy Pier has a free permanent exhibit on stained 
glass.  No dials, but about 60-80 pieces on display.
 
Next year the NASS conference is the same weekend 
at Vancouver Canada.  Vancouver Island or city - I don't know which or 
both. I wonder if there are there any dials in Buchard Gardens.
 
Congratulations to Tony Moss  for the Sawyer 
award.  He has made many contributions to this list and to the fine art of 
dial construction.
 
Take Care,
 
Warren Thom


  I was in the hospital having spinal surgery 
  (for two herniated disks), so unfortunately I missed going to the NASS 
  conference this year.  I know we'll get to read all about it in the next 
  Compendium, but I'm anxious to hear how it went. How were the 
  workshops?And who won the Sawyer Dialing Prize this year?
   
  thanks
   
  John

Re: Is the USA 'Daylight-Saving' period to be extended ?

[Warren Thom]

Hi Tony,

I think you have something there.  I have an aunt and uncle that ran a dairy
farm 600 miles west of us in Kansas.  We were both on Central time.  They
often bemoaned the concept of "daylight" time.  They compared it to the (
fill in the ethnic group) who would cut off one foot ( 30 cm) of their
blanket and sew it onto the other end to make it longer.  Since their cows
failed to notice the time change, my aunt complained about how their
shopping in town needed adjustment twice a year.

I was a teen before I figured out why Kansas was light at 9:30pm in the
summer, when Illinois was dark around 8:30.  When in Belgium and The
Netherlands in 2000,  I was further surprised to see it light out at 11:00pm
in July.  This is one of the reasons I like Italian and Babylonian hours on
sundials .. they don't depend on daylight saving nor even the time zone.

By the way -- The new statewide daylight law in Indiana did not mention if
Indiana is still split between Eastern and Central time zone.  At one time
counties in Indiana near Chicago were Central and rest of the state was
Eastern.  I bet they only passed the law to avoid the loss of federal
funds -- another way the federal government persuades the states.  The
"right thing to do"  -- yeah right.

Warren Thom

From: "tony moss" <[EMAIL PROTECTED]>


> Hi all,
>Ever one for 'raising hares' but re. DST USA is it/was it true
> that some US agricultural areas stick to what became known as 'cow time'?
> Thus making for strange anomolies in short-haul domestic airline flights?
>
> Tony Moss.
> -

-

Kitt Peak under threat from wildfires

[Warren Thom]

Hi All,
 
It was just reported on our news that Kitt Peak is 
in danger from wild fires near Tucson Arizona.  NASS visited there during 
their 2002 meeting. John Carmichael had done a lot of the data plotting on 
the shadow of the Helioscope there.  It has over 20 telescopes on the 
peak.  Plus the Mayall Sundial.  What reports do you get 
John?
 
Warren Thom

RE: A sundial in Mercury

[Warren Thom]

Whoa --- now wait a minute  (-- eh - eh - wait a day.)

If a day is defined as the time from one midnight to the next midnight -
even on Mercury - then there can only be one sunrise per day.  Granted a
dial would be very bizaare.

Warren Thom  (41.6498 N  88.0964 W)


[EMAIL PROTECTED] wrote:

> that would be a bizaare if impractical device (my understanding is the

> sun actually rises twice on Mercury).  

Yes, I think I saw something like that I some science-fiction tale 
(maybe an Asimov's one) but I am not so sure it's like that.
Near the mercurian perihelion the Sun stops and goes back for some time,

but then it follows its East-West path again.

Best regards,

Anselmo Perez Serrada


-

-

RE: Fabio SAVIAN's Calendario 2003

[Warren Thom]

Dear All,

This is one of the most “far out” set of sundial designs I have ever
seen.  May I assume that each is based on actual possible dials?  The
concept of “solar planes” does help one to envision how many of the
dials operate.  Thanks for posting Reinhold.

Warren Thom  (41.6498 N  88.0964 W)

-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of [EMAIL PROTECTED]
Sent: Friday, January 03, 2003 9:41 AM
To: sundial@rrz.uni-koeln.de
Subject: Fabio SAVIAN's Calendario 2003

Dear friends,

the new year has started and it is time to announce the new sundial
calendar of Fabio Savian, Italy:
Calendario 2003
Luci e Ombre
Gli Orologi Solari di Fabio Savian

The calendar is provided in five different editions for five different
languages!

Have a closer look at:
http://www.nonvedolora.it/calendario2003.htm 

If you want to order it, please contact Fabio Savian directly:
[EMAIL PROTECTED]
Happy new year to all of you!
Best regards,
Reinhold Kriegler

* ** ***  * ** ***
Reinhold R. Kriegler
Lat: 53° 06' 53'' N   
Long: 8° 53' 54" E
Bremen / Deutschland


-

RE: Sundial Trade Association & The Sundial Shoppe

[Warren Thom]

Hi John,

Thanks for the Tucson hospitality.  The tour of your shop was a real
treat.

I did want to correct the location of the Sundial Shop.  It is not
located in Paris, but at Carcassone.  Carcassone is a few hours south of
Paris and is a walled city/castle.  

>On a related topic, Warren Thom showed us a slide of a cute little
store in
>Paris called The Sundial Shoppe that only sold sundials  I thought that
was
>great! I think a similar shop of sundials might work in a big city like
New
>York, LA, Miami, London etc.
>
>But many questions remain:
>
>Would it only stock Association or NASS certified sundials or trash
undials
>too?

I would not be so hard on "not for accuracy" dials.  Many have good
artistic design.  I would avoid a certification or endorsement process
for NASS. Our goal is to promote dialing not setting and enforcing
standards of a good dial.

Take care,

Warren Thom  (41.6498 N  88.0964 W)


-

RE: Gnomonic Octolingual Vocabulary

[Warren Thom]

Dear Mainsa,

 

Is there any possibility that you have this book in electronic form and would sell it via a
charge card?  I now have three books on Cadrans Solaires and would find the book useful.   A second idea is a program that would
translate sundial words from a text file from one language to another.

 

Thank you,

 



Warren Thom  (41.6498 N  88.0964 W)



 

-Original Message-
From:
[EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of mainsa
Sent: Friday, September 13, 2002
3:18 AM
To: sundial@rrz.uni-koeln.de
Subject: Gnomonic Octolingual
Vocabulary

 



 





Dear friends,





 





We inform
you the new price of the second edition of the 





 





GNOMONIC
OCTOLINGUAL VOCABULARY, 





 





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Translation of the Universitat Pompeu Fabra of Barcelona, and
President  of the Societat Catalana de Gnomonica de Barcelona.





 





It has 296
pages and 378 gnomonic entries. Its dimensions are 185 x 265 mm.





 





This
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or _expression_ in the other seven languages.





 





In this
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important gnomonic words, in 17 languages:





 





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Portuguese, (PL) Polish,





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sixteen languages.





 





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Mainsa





 

RE: Solar Telescope Sundial

[Warren Thom]

Hi John,

I am looking forward to the NASS conference in Tucson.  Marking lines on
a horizontal surface around the Kitt Peak Solar Telescope is a great
idea.  You may have mentioned the Mayall dial at Kitt Peak -- it is
worth seeing.  The Mayall & Mayall book was one of the first I read on
dials.  I also look forward to seeing the dial on the campus of that
great school -- The University of Arizona.

My wife and I saw a delightful French movie, "Amelie".  A Gnome was in
the movie.  Does anyone know if the word is related to the word gnomon?
We are getting into a French mood because we are taking my youngest son
to Paris July.  I have directions (thanks to this list) to the Denis
Savoie dial that is on the cover of his book.  Does anyone have the
location of 3 or 4 "don't miss" dials around Paris?  I would appreciate
any advice on Paris dials.

Take Care,

Warren Thom  (41.6498 N  88.0964 W)



-

RE: About the circumpolar parabola

[Warren Thom]

Dear Anselmo,

 

You have caught my attention big
time.  (Forgive the pun.)

 

I am aware of the “circumpolar
circle’ – because I did a construction suggested by Fer de Vries of a Hemispherium.  I urge
the construction for better understanding. 
I used a 4” plastic spherical Christmas ornament and a compass.  See  “http://home.iae.nl/users/ferdv/hemisph.htm”

 

I have a few questions though about the
parabola.

 

How do you draw iti
and bab lines on the
parabola that are tangents, how are they located, and labeled?

Why are 16 hour iti
and bab the same line?

All parabolas are similar shape – so
how can a parabola be used for all the different
latitudes?

 

Thank you for your posting – I find
it very interesting,

 

Warren Thom  (42N 
88W )

 

-Original Message-
From:
[EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Anselmo Pérez Serrada
Sent: Saturday, March 16, 2002 4:54 PM
To: Sundial, Mailinglist
Subject: About the circumpolar
parabola

 



Hi dialists,





 





 This is something I learnt
from Prof. Fernando M. Box and hadn't seen as this in any 





of my books on gnomonics.





 





Most of you know about the
'circumpolar circle', which is, for a given latitude, the





celestial circle for which the stars
'above' it are seen all over the year (in that latitude).





This circle is parallel to the
celestial equator and its declination equals the colatitude.





From the observer's place it touches
the horizon circle just in the northern tip of the





meridian line (so as to say).





 





Now it is easy to see that the
gnomonical projection of this circle is a parabola with





the following parameters:





 





   -- Axis: The meridian
line. The curve opens towards the South, of course.





   -- Vertex: At
H*cotg(2*Lat) from the foot of the (vertical) gnomon, where H is its





height over the ground.





   -- Focal distance:
equals (H/2)*tan(Lat)





 





[HINT: Remember that an sphere
always casts a conical-curve shadow whose





focus lies just in the point of
contact with the ground]





 





The most interesting property
of this parabola is that the straight lines tangent to it coincide
with these of





italic and babilonical hours. Why?
Well, because by the definition of these hours, its corresponding 





(great) circles are necessarily
tangent to the circumpolar circle. 





 





This gives an easy way to draw
these two groups of lines (remember that the line for 16-ita is the





same for 16-bab and that the cross
points define the equinoctial straight line).





 





We could as well make a stereographic
projection instead of a gnomonical one to get all the lines





as circular arcs, or define the
circumpolar cone, which has also quite interesting properties,





but I'll leave these things
for later on.  





 





Isn't it beautiful?





 





Greetings,





 





Anselmo Perez Serrada





 

Re: Acadian domestic sundials

[Warren Thom]

Hi Steve,

The answer is yes,  to the question "can shadow plane dial be constructed to
show hours to sunset (Italian hours)?"   You can think of the plane for one
hour before sunset as the horizontal surface  15° to your west (oops - or is
that east??) on the earth and at your latitude.  A terrella would show this
plane nicely.  Two hours is the horizontal surface 30° away.

Maybe Mac Oglesby has caused me to think more in "planes" but the last issue
(December 2001) of the Compendium had some good articles on lines, planes
and surfaces.  Steve Luecking had some very nice graphics showing "planes".
Gianni Ferrani describes the kalieidoscope cube that allows light only in
certain planes to pass through.  Mac showed some student (hour plane) dials.
Fer had  an article on polar bifilar.  It helped me understand Fer when
Claude Hartman reported on the math work of Rafael Soler Gaya.  I am still
digesting page 5 on how to calculate the lines and planes.

Warren Thom ( 88W  42N)

> Edley mentioned hearsay of a window dial, thus:
>
> "[The source] said they carved out deep narrow notches which, when the sun
> fully filled the notch, it was that particular time".
>
> That's sounds very much like a shadow-plane dial, but reversed to use
> illumination rather than shadow as the indicator. But according to the
> report, these dials were used to indicate time left before supper. This
> situation got me thinking - could a shadow plane dial be constructed in
such
> a way as to show time since sunrise / time to sunset? The descriptions
I've
> read, as I remember them, all relate to modern hour markings.
>
> Steve
>
>

Re: Cast Away

[Warren Thom]

Hi Bill and All,

I was also one that could not figure out how he got the figure 8 analemma.  He
did have a watch with Her picture in it -- but was it working?  I had problems
with the following two other scenes.

(1) At the start of the movie, along the country Texas road the fence posts gave
very long shadows -- I leaned to my wife jokingly and said "about 1 hour to
sunset (or from sunrise)"   Then when the FedEx van reaches the house the name
over the entrance gave a very short shadow -- about noon time.  Did it take 5-6
hours drive down that road from the intersection?   I know Texas is big -- but
not that big.

(2) In the cave the shape of the hole went over his face.  But light rays come
into the cave in parallel lines -- so the shadow should be as large as the hole
not as small as his eye/nose.

I am glad I am not the only one who notices such things.

Warren Thom  -- Where we can see the shadow moving back after touching the
winter solstice line. (42N  88W)

[EMAIL PROTECTED] wrote:

> I saw "Cast Away" last week, and had a question about sudials and the movie.
> After Tom Hanks has spent several years on a desolate island, he constructs
> an impressive analemma from a thin beam of light that enters his cave,
> complete with days of the months.  This would not be hard, if he had a
> working watch, but I don't think he did.  So, my question is, is this just
> Hollywood chicanery, or is it really a possible thing to do?  Bill G.  (I
> need to know, in case my plane goes down in the south Pacific some day).

Re: equal hour lines 3 versions

[Warren Thom]

Hi John, Fred and All,

Observation #1 -- We return to the correct hour tonight when we set our clocks
back one hour.

#2  The line for an equal angular dial has been interesting to me since I first
read about it in Fred's  Sciatheric Notes.  After he revisited the concept at
the NASS conference, I wrote an Excel spreadsheet to draw the curve. I would be
happy to send a copy to anyone interested - it is 48K long.

Fred Sawyer noted two variables -- (1) where the center of the equant circle is
placed on the horizontal dial and (2) the ratio of size of the hour in the two
dials.  You (and I) have noted a third variable - the starting lines.  I
picture the dial as a locus of points where a horizontal dial line intersects
an equal angular line (they must have different centers) .  The starting line
on the dial will intersect more than one line on the equal angular set -- so
you have a choice of starting points.  It becomes more interesting as the
increment becomes less.  Forgive my weak explanation -- it is difficult to
describe.

Warren Thom (41.649 N  88.096W)

John Carmichael wrote:

> Hello again:
>
> I played around some more drawing a horizontal sundial that has equally
> spaced hour lines and was able to find three different designs that seem to
> work.  I used the same geometric technique using little circles of equal
> radii that I described in my first mailing on this topic.  Because the
> circles in the early morning and late afternoon interset the adjacent hour
> lines at two points I noticed that different versions were possible.  And
> low and behold, version C looks a lot like the version Fred talked about at
> the conference!  (You were right Fred!)
>
> I used one hour time lines as before to keep the drawings simple, but as
> Fred pointed out, if you use smaller time increments, the drawings become
> even more precise.
>
> I am e-mailing this new drawing which clearly shows all three versions to
> those people who requested drawings.  If anyone else would like me to send
> this to them, please let me know.
>
> John Carmichael

Re: Genk Sundial Park website

[Warren Thom]

Dear Frans,

Thank you for posting the pictures and information on the Genk Sundial
park in Belgium.  I would like to mention that the park is more than just
12 dials.  Each of the 12 designs takes a design "one step further".  For
example, the "Analemmatische zonnewijzer" uses the same gnomon ( a person
standing on the month mark) for two analemmic dials - one of which is
circular like  G.E.Taylor's famous circular sundial.

I do have a question about the #7. "Bifilaire zonnewijzer".  One picture
shows a curved chain and another shows a straight wire between two
posts.  In either case, I did not understand how it was "bifilar" in
nature.

Thanks for posting -

Warren Thom  (41.649 N  88.096 W)

"Frans W. MAES" wrote:

> Hi all,
>
> I guess you have heard about the Sundial Park in Genk (Belgium),
> an ambitious project to install a dozen novel or otherwise special
> sundials in a public park.
>
> This spring the Park was completed and was opened officially.
> Those of you who read Dutch are invited to visit the Unofficial
> Website of the Genk Sundial Park and join the guided tour.
>
> The URL is: http://www.biol.rug.nl/maes/genk/

Re: Meridian Line Question

[Warren Thom]

Hi Allan,

On the equinoxes, you can plot the shadow of any point and it will produce
an East-West line.  A perpendicular would be a N-S line.

Warren

Allan Pratt wrote:

> Hello,
> All dialists know, I'm sure, of the verical-stick, strike and arc,
> bisect the angle method of determining a north-south line.
>
> But is there any other method of doing so which does not require some
> additional data, like date, time, or something similar? Or is this the
> only known way of doing so without external data?
>
> Al Pratt

Re: sundials in Brussels

[Warren Thom]

Hi André,

The Sundial Park in Genk, Belgium  is about two hours east of Brussels.  It
has 12 different dials, each one is nicely done.  There is a page on the web
that describes them and has pictures.

See   <http://www.biol.rug.nl/maes/zonwyzer/en/zwgenk-e.htm>

I thought it was well worth the trip from Brussels.

Warren Thom




"André E. Bouchard" wrote:

> Hi every one,
>
> I plan to go to Brussels for a week
> (Sept 8-15 2000)
>
> I would appreciate very much to know
> where I can see and explore some sundials
> ... it could be a good topic for our Bulletin (Le Gnomoniste)of the Quebec
> Sundial Society
>
> Yours sincerely
>
> Andre E. Bouchard, Ph.D.
> <[EMAIL PROTECTED]>
>
> -
> visitez mon site Web :
> celui de la Commission des cadrans solaires du Quebec
> http://cadrans_solaires.scg.ulaval.ca/

Re: Sundial Glossary - out now

[Warren Thom]

To Anyone attending the NASS meeting in San Francisco,

If you would like a printed copy of The John Davis Sundial Glossary,  I
will work with John to provide a copy for about $10 to anyone that can
let me know before noon Thursday (July 6).  I will personally carry them
back from Britain.

Warren Thom

Re: GPS Accuracy

[Warren Thom]

Hi Allan,

Garmin makes a GPS unit called eMap.  It came out in March 2000.  It sells
for around $200.  Service Merchandise is reducing the line of products they
sell and they have the unit for $150 around here.  These units have the 2.04
version of firmware, but with a PC cable ($30 more) you can upgrade with v
2.5 for "free".  It has a moon and sun "locator" in its 2.5 version of
firmware.  I am not sure what that means - and would appreciate anyone
shedding light on the topic.

Caution:  If you want maps of streets, points of interest, etc. -- you can
only use Garmin Map Source MetroGuide CD ROMs (USA, United Kingdom, France,
Germany, Italy,Sweden and Denmark, or Belgium, Netherlands and Luxembourg  $
124.99 each) with a PC that will load only a portion of the maps onto an
8(`$90) or 16 Meg ($125) cartridge for eMap to use. -- You could connect the
GPS to something like Street Atlas on a laptop (or Palm?) , but that would
defeat the purpose of a hand held mapping device.

I found a lot of interesting things in the last issue of the Compendium.  I
was expecting some discussion on this list about some of the concepts.  It
is a great publication.  I really liked the "interactive" dial of moving
one's hand up a vertical pole - when the hand shadow hit a date line on a
horizontal surface - the hand was on the hour mark.  Any comments - anyone?

Warren Thom
(41.649N  88.096W)

Allan Pratt wrote:

> As most of you know, the US government has relaxed the restrictions on
> the GPS system. Supposedly the accuracy has improved from 10 meters to 1
> meter. My question is, do the actual GPS units in use permit this
> accuracy? At the equator, one degree is 111,308 meters in length.
> One-meter is thus .09 (9 millionths) of a degree. Even as far north
> as Miami FL, a meter is about .1 (1 one-hundred-thousanths) of a
> degree. At my location, a meter is .107 degrees. Do the GPS units
> read out to 5 or 6 decimal digits of accuracy?
>
> Al Pratt
> 33 20 36 N
> 111 54 14

Re: DeltaCad vs. TurboCad

[Warren Thom]

Hi John,

The problem with any CAD program is the time to learn to use it.  They all
have learning curves that are steep. Delta CAD let me see my "first" work
quicker, but all will print a drawing once you figure out the required
steps.   It also depends on what you want to do.  All of the CAD programs I
have seen will import DXF file format, which you can edit/add text/connect
lines.  If you want to use the output from Fer's programs to add text and
clean up, then any CAD should work.  For some reason I thought your question
had something to do with gif files.  Those are something I am still learning
to manipulate.  If I can help in any way, let me know.

Warren Thom

John Carmichael wrote:

> Hello dialists (esp. Mac, Sarah, & Alexei):
>
> Last week after I asked if anybody could supply a Cad printing service, a
> couple of you responded with generous offers in the afirmative.  Others
> offered to help me learn either DeltaCad or TurboCad. Encouraged by your
> support, I just ordered the Delta Cad program and downloaded the free Demo
> version too.
>
> I'm wondering, should I acquire TurboCad also, or is Delta Cad sufficient
> (for printing large copies of Zonwlak and Shadows files)?
>
> Which is better, DeltaCad or TurboCad?  What's the difference?
>
> Thanks,
>
> John Carmichael
> Tucson Arizona

Re: Stone sandblasting

[Warren Thom]

Hi John,

One thing I have wondered about was how do you "plane" a rock surface to a
smooth, flat surface?  Do you use a belt "sander" of some type?  or do you use a
concrete saw blade to make a cut?  - which would be limited to less than the
radius of the blade.  Do you have a stone cutter that you farm this out to 
before
your start?

(I am going to be out your way in Mesa next month to see my new baby grandson.)

Just curious,

Warren Thom

Re: art project

[Warren Thom]

Hi Robert,

I teach at Stagg High School which is west of Morgan Park on 111th street.
Let me know if I can be of any help.  I would like to see if others are from
the Chicago area.  I am surprised you did not mention either the Adler
Planetarium or the Time Museum in Rockford, which were inspirations to me.
Robert Adzema is a member of the North American Sundial Society, and
attended the October meeting in Hartford.  He gave a talk and we visited one
of his art/dials.

Warren Thom

robert langston wrote:

> Hello,
>
> I am an art teacher in Chicago Illinois interested in creating a sundial
> as an art project for the 2000-2001 school year. I came across some old
> xerox's I had made years ago at the School of the Art Institute from a
> book by Robert Adzema. So that's inspiration number one.
>
> The second inspiration comes from my visit a couple of years back to the
> Islamic observatories in Jaipur and Delhi, India.
>
> I am wondering if there are any "sundial artists" or gnomonists based in
> Chicago (or nearby) who would be interested in helping me develop a high
> school curriculum for art and math/science courses. I would appreciate
> any suggestions, contacts or references.
>
> Best Regards,
> Robert
> --
> Robert Langston
> Chair, Visual Arts
> Morgan Park Academy
> 2153 W. 111th Street
> Chicago, IL 60643
> Office (773) 881-6729
> Home(773) 239-2250
> 
> YOU'RE PAYING TOO MUCH FOR THE INTERNET!
> Juno now offers FREE Internet Access!
> Try it today - there's no risk!  For your FREE software, visit:
> http://dl.www.juno.com/get/tagj.

Re: Azimuthal sundials - again

[Warren Thom]

That was a short article but an interesting concept of  " mapping" the lines on
a transparent medium and showing time where their shadow meets a point.  A page
or two later in that Compendium, Fred Sawyer showed how a stained glass window
could apply the concept.  I know Claude Hartman has done several designs that
use light that way.  I respect the creativity of the concept and designs.  They
are really neat!  Thanks.

Warren Thom

"T.& M. Taudin-Chabot" wrote:

> >I can see that in abstract terms that we have dials which are
> >
> >- projection of a point onto a surface (perhaps curved)
> >- projection of a line (perhaps curved) onto a surface (perhaps curved)
> >- projection of two lines (perhaps curved) onto a surface (perhaps curved)
> >- other non-projection types, such as the wonderful CD-diffraction dial.
>
> You forgot (at least) one:
> - projection of many lines onto a point on a surface.
> (see NASS Compendium Vol.1 nr.3 page 6 or BSS bulletin 91.2 page 14)
>
> -
> Thibaud Taudin-Chabot
> 52°18'19.85" North  04°51'09.45" East
> home email: [EMAIL PROTECTED]
> (attachments max. 500kB; for larger attachments contact me first)

Re: sundial taxonomy

[Warren Thom]

Hi John,

Thanks  to Sara, Fer, and Gianni for helping us keep the types of dials clearly
labeled.  I am sorry for being one of those that contributed to the confusion.
I understand now why azimuthal dials must have a vertical style.

The Glossary is nicely done.  I like how you linked key words so a mouse click
gives more information.  I do have a comment about the bifilar definition given
in the glossary.  It reads:

bifilar ~: invented in 1922 by Hugo Michnik in its horizontal form, although
it
can be on any plane. The time is indicated by the intersection on the dial
plate,
of the shadows of two wires stretched above and parallel to it. The wires
often
run E-W and N-S, with their (different) heights above the plane being a
function of the location of the dial. It has equiangular hour markings, and
hence can be delineated to show many kinds of hours.


The ratio of wire heights must be just right for the hour angles to be equal.
Fred Sawyer deals with the special case of equiangular hours in a past issue of
the Compendium and in Sciatheric Notes #1.  While the original Michnik dial was
equiangular, Fer de Vries has shown in an early issue of the BSS Bulletin, that
the hour angles are not required to be equal.  The last sentence of the bifilar
definition could be worded to reflect this expansion.  The last sentence could
read  "It can have equiangular hour markings, and can be delineated to show many
kinds of hours."

Warren Thom (41.649N   88.096W)

John Davis wrote:

> Hi All,
>
> I'll buy this, and put in in the next draft of the Glossary.  I really don't
> want a different term for every possible type of dial!
>
> Regards,
>
> John
> 
> Dr J R Davis
> Flowton, UK
> 52.08N, 1.043E
> email: [EMAIL PROTECTED]
>
> - Original Message -
> From: Patrick Powers <[EMAIL PROTECTED]>
> To: sundial 
> Sent: 27 February 2000 20:28
> Subject: Re: sundial taxonomy
>
> Message text written by "Sara Schechner"
>
> >As an alternative approach we could get round this by specifying
> the angles of universality.  e.g., UNIVERSAL 60°N - 10°S<
>
> I would go with this.  I don't like the idea of something being 'partly
> universal'.  It seems to me things are either universal or they are not.
> [A similar problem also can occur with use of  the word 'unique'].  If one
> states the boundaries within which the device is universal that is far
> better to my way of thinking.  But then maybe I am a pedant.
>
> Patrick

Re: R: azimuthal gnomon length problem

[Warren Thom]

Hi Gianni,

Thank you for plotting the lines.

Do I understand the style to be horizontal with a 30 degree angle to the dial
plane?  This makes it closer to being in the plane of the N-S meridian.

I don't understand why the 11am hour line has a gap in the middle.  Does that
mean the sun is behind the dial plane?  I have observed about that time during
the year when the sun starts to reach that vertical surface.

Sincerely,

Warren Thom

Gianni Ferrari wrote:

> I attach the correct image of the sundial for the  Warren's wall.
> Lat. 44N Long. 88W TZ=6 vertical wall with decl. =64 W
> Style on a horizontal plane,  tilted toward right with an angle of 60
> degrees with the perpendicular.
>
> Best
>
> Gianni Ferrari
>

Re: R: azimuthal gnomon length problem

[Warren Thom]

Hi Fer,

Now I am starting to see the low latitude problem for azimuth dials - which was
the original problem described by John C.  But for him, at 33 degrees latitude,
a vertical south facing dial (equal to one at 57S) would be better than
horizontal - but for me a vertical decliner would be worse.  I will take the
suggestion to use a vertical line for the shadow maker and see what I get.
Ref:June 1996 issue of the BSS on "Azimuth Sundials Horizontal and Vertical" by
G. Fantoni

Thanks,

Warren

"fer j. de vries" wrote:

> Hello Warren,
>
> Lets start again :
>
> Latitude = 42
> Inclination of dial = 90
> Declination of dial = 64
>
> Calculated:
> style height v = -19.01
> substyle at b = -135.05
> longitude correction ts = 71.93
>
> Now we have to deal with a horizontal azimuthal sundial at low latitude :
> 19.01S, that is even between the tropics.
> This will give problems with the hourlines if the sun's declination is near
> or
> lower then -19.01 degrees.
> ( that is about half november untill end january )
> During that period some hourlines will cross each other and you can't get a
> good reading of the time.
> To show this I calculated an example for lat. -19.01.
> This example is for local suntime, just to show the effect.
> ( Only one half of the dial is in the picture. Mirror this side to get the
> full dial )
> So I think that your wall isn't very suitable for such an azimuthal dial,
> with a style perpendicular to the wall.
>
> In stead of using the azimuth of 19.01 degrees South use your own azimuth by
> making a dial with a vertical style parallel to your wall.
> As date lines you could use horizontal parallel lines.
>
> Remark :
> Spin.exe as distributed can't calculate dials between latitude 25N and 25S.
> These restrictions were made because of the shown problems.
>
> Happy dialling, Fer.
>
> Fer J. de Vries
> [EMAIL PROTECTED]
> http://www.iae.nl/users/ferdv/
> Eindhoven, Netherlands
> lat.  51:30 N  long.  5:30 E

Re: R: azimuthal gnomon length problem

[Warren Thom]

Hi Fer,

Thank you for checking my question.  My instincts have told me that a dial on a
vertical surface with a perpendicular style was possible, even if azimuthal
might not be the best name for it.

You were correct - my numbers were wrong.  I should have said the wall was 26
degrees south of west or 64 degrees west of south.  I checked this out with your
program and I get the height of style to be about -19 degrees.  I have checked
the declination of the wall several times and I have gotten between 25 and 26
degrees.  I think 25 might have given a style (or latitude where horizontal) of
around -18 degrees.  It was by observation of the wall that I found the error.
I can look for the North star "through" the wall, and I knew the angle was
around 15- 20 but never as much as 40 degrees to the surface.  Also, about now
4pm is not far from a normal to the surface - but the design you sent - the time
was about 1pm.  Sorry for my error.

I do have a 4 foot by 8 foot piece of nice "sign" board to make this dial.  I
must wait for warm weather to paint because my work area is inside the unheated
garage.  I look forward to the project.  Thank you for the help.

Sincerely - Warren Thom


"fer j. de vries" wrote:

> I read :
> latitude 42N
> vertical dial, that is inclination 90 degrees
> declination of dial 26 degrees from South to West
>
> I calculate :
> The height of style ( for a usual dial ) than is : v = -41.91 degrees.
> This equals to a horizontal dial at latitude 41.91S. ( not 18 as you wrote )
> Where is the error ?
> These values may be calculated with Zonwvlak.

Re: R: azimuthal gnomon length problem

[Warren Thom]

Hi Gianni,

Thank you for posting the azimuthal dial with "double dates".  It is very
helpful to see possible lines.

There is an excellent article in the June 1996 issue of the BSS on "Azimuth
Sundials Horizontal and Vertical" by G. Fantoni.  The vertical dials would be
very visible for time during the day, which was the original problem posed by
John C.  The style for such dials is a vertical "wire" that is parallel to the
plane of the dial and vertical.  The dates are horizontal regions on the dial -
pick the date and read the shadow among the hour lines.

I have a south vertical wall that declines 26 degrees to the west.  I know that
surface is equal to a horizontal plane at 18 South latitude with a few hours
different in longitude.  Does anyone know if I could design an azimuth dial for
18 deg S and shift the hours for difference of longitude and use it on that
wall - with a style that is perpendicular to the surface - pointing to 26 deg
west of south?

Just a thought -- Warren Thom (42N  88W)


Gianni Ferrari wrote:

> Hi John ,
> if in an azimuthal sundial we take the circles as you propose we get for
> every month a point.
> If we connect these points we get some hour lines (Standard or Mean Time )
> that have the shape that you can see in the two figures attached.
> In the pictures the lines are made by segments and are not smoothed but a
> better result is gotten taking a point (a circle) every 15 days.
>
> In the pictures the radii are 20 cm for June, 30 for July, 40 for May, 50
> for August, 60 for April, 70 for Sept, 80 for March, 90 for Oct, 100 for
> Feb, 110 for Nov, 120 for Jan and 130 for December.  The  pole is high 150
> cm
> In the second image I have tilted the pole toward North to form an angle of
> 60 degrees with the horizontal plane.
> The figures have been gotten with my program SUND98P distributed with the
> issue of September 1998 of The Compendium.
>
> The curves are very condensed in summer  : I would have to make some other
> test to get good results aesthetically
>
> Best
>
> Gianni Ferrari
>
> ---
> Ing.Gianni Ferrari
> Via Valdrighi, 135
> 41100 - MODENA (ITALY)
> EMail :  [EMAIL PROTECTED]
> http://members.tripod.com/meridiane/index.htm
> ---

Re: Kukulcan Equinox Phenomenon

[Warren Thom]

Hi Roger,

This is the link to the ruins with the two //

<http://www.piramideinn.com/equinox.htm>

Warren Thom,

Roger Bailey wrote:

> The light and shadow phenomenon of the equinox is world famous. See
> . The corners of the nine platforms

Re: Kukulcan Equinox Phenomenon

[Warren Thom]

Hi Roger,

The Mayan pyramid sounds interesting.  Thanks for posting.  I had a problem
with the link in your message.  I did find the following:

<http://www.mont-acad.pvt.k12.al.us/projects/civ/beau/temp.html>

I am still trying to picture how the "snake" image is produced.  You did give a
good account.

Warren Thom

Roger Bailey wrote:

> A highlight of my recent trip to Mexico was the Mayan ruins at Chichen
> Itza, in particular, El Castillo, the Temple of Kukulcan. This great
> pyramid is designed to mark the yearly cycle of the sun. Each of the four
> faces represents a season. Each of the four stairs has 91 steps, the number
> of days in each of the four seasons. The temple at the top represents the

Re: zonwvlak

[Warren Thom]

Hi Alexei  -- My comments are below.

Alexei Pace wrote:

> I have been using the fantastic Zonwvlak program to design sundials ,, but
> I ahve come over a problem every time -
> that is , when designing a complicated sundial , is there any means by
> which one may know which hour line is for noon, which one for 11am , 10am etc?
> The problem arises when one designs babylonic and italian hour lines as
> well//
>

I agree Zonwvlak is a fantastic program by Fer de Vries.  Here are a few ways I
have "marked" the lines.

1.  When selecting the lines to make, duplicate a few of the key lines.  For
example, calculate the local time from hours 4 to 20 step 1.  Then select local
time again and do hour 12 step 12.  It will be drawn twice, but you will not see
it until you select and delete it with a CAD program.  This is only useful if 
you
use a CAD program to process a DXF file of the dial.  A CAD program will also
allow you to select or deselect layers (each type of hour has its own layer) to
see as you process the dial.

2. If the confusion comes from the different types of lines, use the "Settings"
button to select and deselect which lines to show.  I keep a card above my desk
that lists the purpose of each layer.  For example layer K is for date lines.
With a color printer and a CAD program you can color the layers and lines
different colors.

3.  Make and print two files of the same design.  Make one drawing your complete
with all lines.  Make the second a much simpler version, with only a few key
lines.  Use the simpler one to help you locate lines on the more complex one.

4.  I always draw the declination lines for -23.44, 0, and +23.44.  They help me
locate the time of the year.

Do you use a CAD program with Zonwvlak?  I worked with Zonwvlak for over a year
before I investigated a CAD program.  I would do choice 3 above to help keep the
lines clear.  With a CAD program you can mark the lines directly with text as 
soon
as you know what each represents.  The December 1997 Compendium of NASS has an
article I wrote using Delta Cad with Zonwvlak.  I do  not have any relationship
with Delta Cad.  Walmart had it for $10 USD a year ago, but they had none last
month at the store near me.  I did get a notice that they have a new version out
since November.  It has a script language in the new version.  If you use the
methods provided by Fer de Vries and are comfortable with Visual Basic (I am 
not),
Delta Cad scripts can be very powerful.  It sells for around $40 from their web
site of: <http://www.dcad.com/>  They have a 45 day free demo available.

Take Care & Happy New Year,

Warren Thom ( 41.649N  88.096W)

Java - Horizontal Dial

[Warren Thom]

Hi All,

The web site below is a construction of a horizontal dial. It is based
on geometry from Rene Rohr's book.  A viewer can change the latitude or
difference in longitude by dragging the mouse on one of the red
circles.  Warning - it seems to access a lot of Java code to run.

<http://people.ce.mediaone.net/wthom/H_2.HTM>

Have fun,
Warren Thom (41.649N  88.096W)

Re: More on Metal Sundial Processes

[Warren Thom]

Hi Tony,

I have looked around the web for more information and found a caution of:

"Because of its porosity you do not get a satisfactory anodized finish on cast 
aluminium which has been machined. An as-cast aluminium surface will not have a 
lusterous finish when anodized. (looks poor)"

What might one do if they wanted to anodize the Schmoyer dial?  It is aluminum 
cast, isn't it?  Will it work on a cast surface that has been smoothed?  What 
does it mean to be "machined"?  I would think "machined" means to grind and 
mill the surface smooth.  Have you found surfaces of aluminum (or is that 
aluminium - Al  u  MIN nee  um) that have not worked well?   I have found your 
steps very interesting.  I have always wanted to find a
good link of sun dialing to chemistry.

Thanks

Warren Thom

Tony Moss wrote:

>
> Anodising Aluminium in the Home Workshop
>

Re: SEND QUESTIONS!

[Warren Thom]

Hi,

I would like to know how to pronounce "Fer" as in Fer de Vries.  Is it like
"fur" as in the coat of a mink or "fair" as in a fair young maiden?  I bet you
are watching this Fer.

With all due respect to those minds greater than mine.

Warren Thom (42N  88W)

P.S.  How do you pronounce Weh?

Ryan Weh wrote:

> Here's something else that might be good:
>
> How to pronounce the sundial terms--gnomon (is it like, gnome in, or more
> nahm en?), azimuth, analemma (how IS this pronounced, anyway?)...etc.
>
> Ryan Weh
>

Math in sundials

[Warren Thom]

Hi all,

After rereading my last post, I did not wish to insult anyone by
implying  that C=2(pi)r was complex for them.  But that formula and
Tan HA = Sin L x Tan t,  are complex if we wish to draw school age
children into dialing.  So - how do we explain that math to school
children?  Must we do so?  What can be done in dialling that is
understandable with grade school math?  I liked Mac Oglesby's solar
plane dials because he put a lot of effort into reducing the math - not
an easy task.  Are constructions one way to go?  I think so.

Warren Thom

Re: conference & Compendium topics

[Warren Thom]

Hi All,

To me the question is not more or less math, but how can certain concepts best 
be
shown or learned.  Fer de Vries had a set of steps to construct that helped me
understand the eot.  His hemispherium is also a construction that everyone 
should
do.  The math, like C=2(pi)r,  has reasons behind them.  Some relationships
require the math.  I like the variety of the Compendium - it has something for
everyone.

More notes to follow:

Roger Bailey wrote:

> Hi John,
>
> At 09:15 AM 10/13/99 -0700, John Carmichael wrote:
> >
> >First, someone could write an article or series of articles on basic
> >beginning trigonometry as it applies to dialing.
>
> Don't forget the quote from my old trig teacher, "All knowledge comes up
> through a pencil." The best way to learn sundial trig is to do what you and
> I have done. Work it through. Reading equations or hearing a lecture just
> doesn't do it!
>
> >Secondly, I was surprised by how few professional full-time dial makers
> >attended the conference.  Maybe they weren't there because they don't exist.
> >I saw a lot of dialing hobbiests with paper, plastic or wooden sundials.
>
> Your stone dial weighs over 400 lbs. The sun sculptures of Kate Pond and
> Robert Adzema weigh megatons. Real dials are not that transportable
> although I once finished a presentation by unveiling the Walking Shadow
> dial, a 4' x 8' triangular piece of heavy composition board. It stole the
> show but transporting it over 100 miles inside my VW Golf was a problem.
>
> Good to meet you at the NASS conference. Please continue to ask the
> challenging questions. My challenge to all for today is to simply explain
> the basic formula for horizontal dials: Tan HA = Sin L x Tan t.
>

There was a display of clear plastic triangles, ideal for an overhead,  at the
NASS meeting that did just that.  I think it was Don Petrie that displayed them.
I think he will sell a new set for around $70.

Happy Dialling,

Warren Thom  (Lat=42n  Long=88w)


>
> Roger Bailey
> Walking Shadow Designs
> N 51  W 115

NASS Meeting

[Warren Thom]

Hi,

I have returned home from Hartford and reflect on the ideas and energy that
flowed during the meetings.  I too hope to purchase the Schmoyer sundial.

I appreciate all the work by Fred Sawyer, you, and other presenters for
providing us with many opportunities for learning new perspectives.  The
"solar plane" dials were a delight.  The string and block  models were
great.  I also liked the artistic points of view of Robert Adzema, Kate Pond
and others - today few count on only a dial for time - but we all can admire
the beauty of the designs showing the dynamics of shadows.

Thanks to all for a great NASS meeting,

Warren Thom


Mac Oglesby wrote:

> Hi,
>
> I've just returned home from the NASS conference in Hartford, which
> was a huge success.  Among the items displayed was a set of the 9
> castings and instructions which comprise the Schmoyer sundial kit.  I
> can testify that the parts seem to be of high quality and the
> instructions incredibly detailed.
>
> Yes, it's true this is not a kit where one simply bolts together the
> pieces, but, for whatever it's worth, on the basis of what I saw I
> intend to order a kit right away.
>
> Mac Oglesby
>
> P.S.  I have absolutely no connection with those distributing these kits.

Re: Sunrise dial maps

[Warren Thom]

Chris Lusby-Taylor wrote:

> In reply to Warren Thom's query:

> An elegant and obviously correct solution is a standard terrestrial globe.
> It must, of course, be set up with its location on top and in the correct 
> orientation.

This is what started me on this quest.  It is great to see the North Pole 
always in
sunlight all summer and to see Europe in darkness in the evening.  I coated 
mine with
acrylic, but it only lasted a year in the elements before it became damp inside 
the globe.

Warren

Re: Sunrise dial maps

[Warren Thom]

Hi Chris,

I have not given up on a polar orientation surface yet, but I don't think it 
will work
because it needs a line to cast a shadow and I have not been able to picture 
the correct
effect of a line shadow on a polar plane.  A "planispheric projection" might 
give the
location of where the sun is setting.  I will work on it.

I do feel for sure that a horizontal line - directed to where we want to know 
if the sun
is shining - can tell us something - but other places on the map are not 
correct - only to
where the line is directed.

Thanks   - Warren

Chris Lusby-Taylor wrote:

> In reply to Warren Thom's query:
>
> >on a dial map WHERE the sun is setting by a shadow.  I like the opening 
> >screen of
> >the NASS home page that shows the area of daylight on the planet  -- but 
> >that is
> >the computer screen -- I like "real" maps.   Has this been done on a dial? 
> >Fred
> >Sawyer showed in the Compendium the method Foster used to map TIME around the
> >world.Any ideas on this from anyone?
> >
>
> John Carmichael asks:
> >would this work?  A polar dial with a world map on the face with moveable
> >gnomon mounted to a set of hourlines(maybe etched on clear glass)  that can
> >be shifted according to the date?
>
> >This is rather hard to expain, but we can discuss it in Hartford.
>
> No, I don't think it would work, except at the equinoxes, as the edge of the
> polar dial's shadow would not take declination into account, so would show
> sunrise at 6 o'clock regardless of season.
>
> An elegant and obviously correct solution is a standard terrestrial globe.
> It must, of course, be set up with its location on top and in the correct 
> orientation.
>
> Off hand, I cannot think of any solution with a plane map. If one exists, I 
> imagine
> the map might use the planispheric projection of the astrolabe.
>
> Chris Lusby Taylor
> Newbury
> Berks.
> England.

Re: Formula to calculate sunrise

[Warren Thom]

Hi Roger,

I am looking forward to hearing your presentation and meeting you at the NASS
meeting.  I think Fer has pointed out the need for the negative 1 in your first
equation.  I have not seen before the sunrise angle psi of:

>> Sunrise Path: Cos psi = Sin l / Cos D

I assume l is L for latitude and psi is the angle with the horizon.  
Interesting.

I have been pondering some thoughts this summer about planes and some way to 
show
on a dial map WHERE the sun is setting by a shadow.  I like the opening screen 
of
the NASS home page that shows the area of daylight on the planet  -- but that is
the computer screen -- I like "real" maps.   Has this been done on a dial?  Fred
Sawyer showed in the Compendium the method Foster used to map TIME around the
world.Any ideas on this from anyone?

Happy dialing,

Warren Thom  (Lat=41.649N   Long=88.096W) - Chicago

Re: Satelite info

[Warren Thom]

Hi,

Can you reach  on the web?
It is under "Experimental Communications" at
http://celestrak.com/NORAD/elements/.

Good luck,

Warren

"D. Anton Reynecke" wrote:

>  Greetings! I am searching for satellite orbital elements.
> (Particularly the geocentric PAS7 and PAS4 communication satellites
> for Southern Africa). I am using a program called "HOME PLANET" and it
> requires the current orbital elements in "NORAD two-line orbital
> element format", in order to accurately track satellites. (Apparently
> NASA also uses this format) According to the help file, data sets
> (updated daily) can be obtained by anonymous FTP from
> archive.afit.af.mil (129.92.1.66) in the directory pub/space, as well
> as on newsgroups, but I dont have access to USENET. So far I have been
> unable to access the mentioned site, it keeps returning error msgs. I
> would appreciate help, as I don't know where else to start
> looking. RegardsAnton.

Re: fotocopier errors

[Warren Thom]

Hi John,

You are correct about the percentage enlargement and reduction of copies -- they
are not as accurate nor precise as the percentage selected my lead you to 
believe.
Another question to verify is: is vertical changed the same percentage as
horizontal?  There is no harm in having a ruler going both directions for
verification.  The DXF file output from Fer's program does give a line of 
correct
length for the gnomon.  This can be helpful to check lengths.

Happy dialing,

Warren Thom (42 N, 88 W)


John Carmichael wrote:

>
> This error (99% to 102%) may seem small, but can be very significant for
> work on larger dials.  The best thing to do would be to always check the
> final copy size to make sure it is correct.

Re: Dialist's hell: how big?

[Warren Thom]

Yes, you did understand the problem correctly.  A shadow point is not be that
"interesting" because it would be unique for only one instant of time during the
year.  But I think there are unique observations that can be made about any
plane for a sun "setting" beyond the plane.  For example,  I can say there are Y
hours of sunshine that remain in the day for a location X whenever (any day of
the year) the sun "sets" beyond the roof of my house.  I just need a way to
calculate X and Y for and latitude and direction of plane. But X and Y are the
same  every time the sun "passed" that plane.

Jack Aubert wrote:

> Ah, but the problem specifies "flat" surface.  I took this to rule out
> convex-polygonal or elliptical/circular.
> I believe that every truly flat surface with no other obstructions in the
> way would get some glimmer of sunlight.  If the surface is facing north and
> is predominantly in the shade, it will still be illuminated during morning
> and evening hours of the summer when the sun rises in the northeast and
> sets in the northwest.  Even if the surface is facing down (!) it will
> catch rays at sunrise and sunset, assuming that it is high enough to clear
> any surrounding obstructions including mountains, foliage, etc.
>
>
> At 09:39 AM 7/19/99 -0500, William P Thayer wrote:
> >Big enough of course to fit every dialist that deserved it; but what I mean
> >is this:
> >
> >>1.  Is there any flat surface anywhere that never gets sunshine at some
> >>moment during the year?
> >
> >If you mean direct sunlight, yes, lots of them. Trivially, any point
> >adjacent to, and away from the equator from, a vertical wall,
> >convex-polygonal or elliptical/circular in plan, the ends of which cast
> >shadows on it even at summer sunrise and sunset. Tof produce a minimum
> >single point, the arc traced by such a wall would not have to be great,
> >although it increases with latitude.
> >   Extending that, there must be a zone of perennial shade -- you guys with
> >computers can calculate the general formula for its shape and extent based
> >on the latitude and the height of the wall -- including points not
> >immediately adjacent to the wall.
> >
> >Practically speaking, this is the principle behind the urban layout of many
> >old Mediterranean towns: narrow streets make for constant shade in the
> >summer; if in addition they are not straight, they also temper winter
> >conditions. I noticed this in several towns of central Italy; one of which
> >-- Pitigliano, in Tuscany -- has a sundial in about the only place it can
> >have one near ground level: in a piazza where the streets widen out.
> >
> >Geographically, there must be plenty of deep non-N-S valleys, and surely
> >steep enough mountains act as my walls, above, for places on their
> >"leeward" side so to speak.
> >
> >The question then becomes: "Where is the *largest* such surface on Earth?
> >(Now there's a project...!) A similar question would be "Where is the
> >largest *volume* of air on Earth never to see direct sunlight?"
> >
> >***
> >BTW, did anyone see the special on Noah's Ark last night? in which God's
> >rainbow was shown with the colors backward... A miracle indeed!
> >
> >
> >Bill Thayer
> >   LacusCurtius
> >http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman
> >
> >

Re: a dialist's paradise

[Warren Thom]

Hi John,

On the flip side of your question, one could ask "Is there any location on
this planet that is not a sundial lovers paradise?"  or to go one step
further - "Is there any plane (flat surface) at any location  that is not
interesting?"  This leads me to a few questions.

1.  Is there any flat surface anywhere that never gets sunshine at some
moment during the year?

2.  I know that time changes during the year in which the sun will "set"
over a surface.  It might be close (around 4pm for the sun to "go around"
the one side of my home) but there is still a lot of variation - as much as
40 minutes from 4pm during the year.  In other words - the sun is not always
directly east at 6:00 am.  So must we eliminate clock time and sun time from
the "interesting" relationship to a surface (plane)?  -- keep in mind ANY
surface must have an interesting aspect - not just a plane parallel to the
axis of the earth.

3.  I can't  prove this but I think -- "for each flat surface ( plane ) at
any location -- there is a second location on this planet -- with a set
number of Italian hours (hours from sunset) that is the same number of
Italian hours for anytime during the year."  That is -  when the sun  "goes
around" my house -- then at some location X (which doesn't change) there are
Y number of hours (which doesn't change) until sunset.   You could say that
every surface has a twin location.
This is a little like -- any plane has a location on earth where the plane
is horizontal.  But there is a second part -- the Italian hour is constant
and need not be zero.  I need to find a way to prove this, if it is correct.

4. Are there other "times" that can make any surface interesting?


Still thinking -- Happy dialing,

Warren Thom (Lat  41.649deg N - Long. 88.096deg W)


John Carmichael wrote:

> Is there anywhere on earth where there is no Daylight Saving Time and is
> located on the meridian at the center of a timezone?
>
> John Carmichael

Re: Sundials not needing corrections

[Warren Thom]

Dear All,

May I suggest another dial that needs no corrections.  If one were to use the
"antique" hours -  the ancient hours of unequal length - but divide up the
daylight into fractions (1/4, 1/2, 3/4) or percents (10%, 20%, 30% ...) the
dial would indicate how much of the daylight has passed or to go.  It would be
useful for construction workers, parks open from sunrise to sunset or farmers
to estimate the completion of the "days work".

Just a thought,

Warren Thom

Mac Oglesby wrote:

> Some sundials don't need to have their readings related to clock time, and
> thus have absolutely no need for any corrections for longitude, equation of
> time, or even daylight savings.  I offer two examples.  Perhaps members of
> this List will suggest others.

Re: Sundials in Chicago

[Warren Thom]

Dear Gordon,

How did you learn about the closing of the Time Museum?
The collection is too good to be dispersed by selling off parts.
Would the Adler Planetarium be interested in buying it?
I also was very fond of the collections there.  If I recall correctly, Fred
Sawyer had a bifilar equal angular heliochronometer there.

Thanks for posting.
Warren

Gordon Uber wrote:

> The Time Museum in Rockford has been permanently closed.  The Seth Atwood
> family has sold the motel which housed it, and I understand that the
> collection
> will be sold, too.
>
> It was an exceptional museum, and I fondly remember my visits to it.
>
> Gordon
>
> At 10:31 PM 4/20/99 , Ron Doerfler wrote:
> >The next nearest thing is the Time Museum in Rockford, but
> >that's a 90-minute trip each way, though a worthwhile one.
> >
> >Ron Doerfler
>
> Gordon Uber [EMAIL PROTECTED]
> Reynen & Uber Web Design http://www.ubr.com/rey&ubr/
> Webmaster: Clocks and Time http://www.ubr.com/clocks/

AutoCAD

[Warren Thom]

Hi,  I  have a question about Autocad.  Is it possible to place a
"variable" point or points in a drawing that will have other points,
lines, circles and angles "depend" on the location of the variable
point?  That is, the variable point can be "dragged" to a different
place and have other parts of the drawing shift accordingly.  For
example,  you have a circle with points A,B and C on the radius, with A
being variable.  You print triangle ABC, shift A to different place on
the circle and print the new triangle ABC.  OR  you have have a copy of
triangle ABC called DEF in another part of the drawing .  If you change
angle CAB  then the corresponding angle in triangle DEF is moved the
same amount.

I am not one to spend a lot on software (an agreement with the wife),
and AutoCAD is expensive.  But this could be a very powerful feature in
a CAD program for dialist.  Knowledge on the subject is appreciated.
BTW-- The graphing program Graphica comes close to having that power,
but through programming steps.  WinGeom does it, but is has limited
printing and file features.

Thanks  --Warren (Lat 41.649  Long 88.096 -- the front yard,  Long=
88.095 is the back yard)

Re: Latest NASS Compendium -Ptolemaic coordinates

[Warren Thom]

Dear Fer,

I worked on this today.  I now agree with you.  About question (b) you said:

"To my opinion a correction for EoT by moving the E-W rod isn't possible.
In other types, where you have a series of date lines, it is possible to
correct for the EoT."

On this type, the correction might go up 5 cm for  2pm but would need to go up
14cm to correct 5pm -- for the same EoT and date.  That is, the time scale is
not linear so a 5cm raise would effect the reading time depending on the
time.  The Dr. April Furst solution is the only way to get around this.

The Italian hours come out close to straight lines.  They would need a series
of date lines to see where the shadow of the bar would fall then look for the
nearest Italian line.  That is not very easy to read.  I still like the
article though.

Thanks for the help,

Warren (Lat 41.649  Long 88.096)

"fer j. de vries" wrote:

> Warren Thom wrote:
> >
> > I have been thinking about a dial described by Ing. Gianni Ferrari in
> > the March issue of the NASS Compendium.  The article is based on
> > Ptolemaic coordinates.  A background was laid by Fred Sawyer in the
> > September 1998 issue.  Starting simple with the dial on page 19 and
> > labeled figure 12.  Questions:
> >
> > (a) Can (should) the time line be extended upward to the south to give
> > hours after 6pm during the summer?  (I think so.)
> >
> > (b) With corrections for the equation of time and longitude difference
> > from the standard time zone meridian on the declination scale, by moving
> > the E-W rod up or down (like an analemma or figure 8 fashion) -- can the
> > time show clock time fairly accurately?
> >
> > (c) How might I start,  if I wished to look at Italian hours (hours to
> > sunset) on any of the dials described in the article on Ptolemaic
> > coordinates?  I know Italian hours can be considered as great circles on
> > the globe.
> >
> snip
>
> > Thanks to all  -- Warren Thom (Lat=41.649  Long=88.096)
>
> Hello Warren,
>
> Still I need to study the Ptolemaic coordinate sndials but I will try to
> answer your questions.
>
> (a)
> For the late afternoon hours and early morning hours the time scale may
> be extended upwards.
> In the article is pointed to the Parent dial ( 1701 ), but also Samuel
> Foster has described the principle of this type of dial.
> ( 1654 ) ( Rectilineal or Diametral Horologiography )
>
> (b)
> To correct for longitude easily can be done.
> That correction is a constant value all the year, so add or subtract the
> longitude correction to each hourangle t.
>
> To my opinion a corretion for EoT by moving the E-W rod isn't possible.
>
> In other types, where you have a series of date lines, it is possible to
> correct for the EoT.
>
> (c)
> In the types where you have a series of date lines in principle it is
> possible to draw Italian hour lines. Proceed as follows :
>
> For a certain Italian hour calculate for a given sun's declination the
> hourangle t of the sun and calculate one point for these sun's
> declination and hourangle.
> Proceed with another sun's declination for a second point and so on.
> Connecting all these points with a line give the Italian hourline.
> Many other types of lines can be calculated with such a procedure.
>
> Best wishes and happy dialling, Fer.
>
> --
> Fer J. de Vries
> [EMAIL PROTECTED]
> http://www.iaehv.nl/users/ferdv/
> lat. 51:30 Nlong. 5:30 E

Latest NASS Compendium -Ptolemaic coordinates

[Warren Thom]

I have been thinking about a dial described by Ing. Gianni Ferrari in
the March issue of the NASS Compendium.  The article is based on
Ptolemaic coordinates.  A background was laid by Fred Sawyer in the
September 1998 issue.  Starting simple with the dial on page 19 and
labeled figure 12.  Questions:

(a) Can (should) the time line be extended upward to the south to give
hours after 6pm during the summer?  (I think so.)

(b) With corrections for the equation of time and longitude difference
from the standard time zone meridian on the declination scale, by moving
the E-W rod up or down (like an analemma or figure 8 fashion) -- can the
time show clock time fairly accurately?

(c) How might I start,  if I wished to look at Italian hours (hours to
sunset) on any of the dials described in the article on Ptolemaic
coordinates?  I know Italian hours can be considered as great circles on
the globe.

I find the Compendium fascinating.   I am stumped by the quiz "Emerson's
Quandary" this time -- but I will work on it .  Fer deVries program for
the Pingre dial is amazing and the article on Chapuchin dial is well
done.

Thanks to all  -- Warren Thom (Lat=41.649  Long=88.096)

Oops

[Warren Thom]

To All,

I sent a reply about Capuchin dials and had an attachment that was much
larger than I thought.  Please forgive me for anyone that may have been
inconvenienced by the large size.  I will double check size in the
future.  Sorry.

Sincerely,

Warren Thom (Lat=41.649  Long=88.096)

Re: capuchin dial

[Warren Thom]

For anyone interested, the attached file is for a Capuchin dial that can be seen
with a program called Wingeom (about 400k) from the following site:



To change the latitude, put your cursor on point "F" and drag the point up or 
down
by holding down the mouse button.  I think it avoided the "Error Orontii"  that
Fer deVries describes in the March 1999 issue of the Compendium.

> > >   The 007 Capuchin Dial is a PostScript program written
> > > initially by Eric MacPhereson, University of Manitoba and with a
> > > later revision by Andrew J Irwin, c/o Math 007, University of
> > > Toronto [...]

Content-Type: application/x-unknown-content-type-GE2_auto_file;
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Re: cycloid polar dial

[Warren Thom]

Dear Tex,

I also enjoyed the article on the Cycloid Polar sundial by Fred Sawyer.  The
dial as designed by Thys deVries of Prinsenbeek, Netherlands and published
in Jul 1980 De Zonnewyzerkring, has a linear time scale that can be moved to
correct for the longitude and equation of time.

I used the shareware program from NASS "Graphica" to produce a graph of  the
cycloid that produced a DXF file and I imported it into a CAD program
(DeltaCAD - available at Walmart for $10).  It was the only way I could make
the curve at the time.  The templates that Fred provided should also work
fine.  I understand Graphica is no longer supported and I am unaware of its
status.  I have a copy of the DXF file somewhere if it can be of any help to
you.  Just drop me email.

I have discovered on the web a source of both a plotting program and a
"Geometry" program at:

<http://www.exeter.edu/~rparris>

The author of the programs has made them available free of charge.  I don't
believe that either will produce DXF files but they do seem to be well
written and run under  Windows.  I find the "geometry" program interesting
because one can apply the geometry for making a sundial to creation of a
geometry sketch and with one or two of the critical points being "drag"
points -- make the sketch change for different latitudes or conditions.  I
have only begun to understand the geometry language of the program -- but I
would challenge others to try it -- the dynamics of the visuals could be
very stunning.  I would not try drawing a cycloid yet -- but someday maybe.

Good luck --Happy Dialing,

Warren Thom
(Lat=41.649N and Long=88.096W)


Tex Brashear wrote:

> Hello all.
>
>I found Fred Sawyer's excellent article on the cycloid polar sundial
> in the December issue of Compendium to be a fascinating introduction to
> this rarely seen type of dial.
> The math required to solve the cycloidal gnomon was challenging, but
> reasonable; and the proffered templates simplified the process of making
> a sample pattern.
>My question is this: Does anyone know of a graphical approach to
> generating the necessary cycloid for the gnomon? If so, I would
> appreciate the information. Sincere thanks in advance.
>
>   Tex
> Brashear

Re: Cousins book(s)

[Warren Thom]

Hi Mac,

Last summer I requested an interlibrary loan for the two books by Cousins.  I
got both books.  The covers were the same, the wording on each page was the same
in several cases that I checked.  If there was a difference, it may have been
only a slight difference in the appendix or near the end of the books.  The book
is a classic, but 99.9% duplicated between the two editions (1969 and 1970).

Warren

Mac Oglesby wrote:

> Dear All,
>
> I am fortunate to own a copy of Frank Cousins' book "Sundials - A
> Simplified Approach by Means of the Equatorial Dial."  The original
> copyright is 1969, published by John Baker, London.
>
> >From time to time I run across mention of a book by Cousins entitled
> "Sundials - The Art and Science of Gnomonics."  The date is uncertain -
> perhaps 1970.
>
> Are these two different books by Cousins?  If so, do they contain different
> material?  Does anyone on this list have both books and could clear this up?
>
> Thaks,
>
> Mac Oglesby

Re: Definition of Time?

[Warren Thom]

Dear All,

If I wished to study history and pick a time when nothing happened,
what diates should I pick?  (answer below)


> >Thus the time keeps everything from happening at once.

September 11-24 , 1752
Warren

Re: Projection sundials.

[Warren Thom]

Greetings All,

Does anyone have suggestions for good books that deal with projections
as we may encounter in dialing conditions?  It should have information
about translations and rotations.  Does Dover have any good ones that
you may reccommend? Any web pages?
I have found some web pages that are for programmers that seek to
project an image on the computer screen.

Thank for any help.

Warren Thom

fer j. de vries wrote:
> 
> Hi All,
> 
> The English article by Bruno Ernst ( = J.A.F. de Rijk, Netherlands )  in
> the Journal of the British Astronomical Association, published in 1986,
> about projection sundials, now is scanned and can be found at
> 
> http://www.iaehv.nl/users/ferdv/
> 
> Follow the links "English" and "projection dials".
> 
> Especially I am interested in the "Central Projection Sundials" and what
> more about these dials can be found in literature or on the internet.
> 
> Yvon Masse, France, has written about these dials at his page
> 
> http://www.union-fin.fr/usr/ymasse
> 
> Follow the link "Cadrans de type analemmatique à projection centrale"
> 
> Please send anything you can find to
> 
> Fer de Vries.
> 
> [EMAIL PROTECTED]
> 
> Van Gorkumlann 39
> 5641 WN Eindhoven
> Netherlands.

Re: Determing Time of Year

[Warren Thom]

Hi All,

 This is related but slightly off the topic.  The October issue of
the BSS has an article on page 36 about "An Origami Sun Calendar."  It
is a cut out and try insert.  It is a cone with a gnomon marked with
dates based on declination of the sun.  I have tried to draw the cone
for my latitude and cannot find any acceptable values.  My math gives
the amount to cut out of a circle for a cone to be:

X in degrees = sin(latitude)*((360/sin(latitude))-360)

This is a function of latitude only and would not divide the amount to
cut out so
that it is one piece and no extra. A little more must be cut out of the
cut out to get a gnomon that comes out the center of the cone.  Am I
missing something?  Did anyone else try this?

Thaks,
Warren Thom

Re: Projection sundials.

[Warren Thom]

Hi Fer and All,

Attached is a quick and dirty compiled QB program to see equator
projection dials for a flat surface directed in any direction.  The
gnomon is always perpendicular to the surface :(I can post or send
source code (4k) for anyone that can help make a dial for any projecton,
not just perpendicular.  Also, I would like to see point projections.

If the attached file 38K is inappropriate to post, please let me know
privately.

Happy dialing,
Warren
 
fer j. de vries wrote:
> 
> Hi All,
> 
> The English article by Bruno Ernst ( = J.A.F. de Rijk, Netherlands )  in
> the Journal of the British Astronomical Association, published in 1986,
> about projection sundials, now is scanned and can be found at
> 
> http://www.iaehv.nl/users/ferdv/
> 
> Follow the links "English" and "projection dials".
> 
> Especially I am interested in the "Central Projection Sundials" and what
> more about these dials can be found in literature or on the internet.
> 
> Yvon Masse, France, has written about these dials at his page
> 
> http://www.union-fin.fr/usr/ymasse
> 
> Follow the link "Cadrans de type analemmatique à projection centrale"
> 
> Please send anything you can find to
> 
> Fer de Vries.
> 
> [EMAIL PROTECTED]
> 
> Van Gorkumlann 39
> 5641 WN Eindhoven
> Netherlands.

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Re: Polar Sundial

[Warren Thom]

Dear All,
Thank you for this and the information on Equator Projection
Sundials.  I have been digesting both.  It is an understatement to say
these are amazing.   

> >The English article by Bruno Ernst ( = J.A.F. de Rijk, Netherlands )  in
> >the Journal of the British Astronomical Association, published in 1986,
> >about projection sundials, now is scanned and can be found at
> >
> >http://www.iaehv.nl/users/ferdv/
> 
This is a check to see if I understand.  We have six factors here. 

(1) the equatorial circle 
(2) a polar directed axis perpendicular to the equatorial circle 
(3) a projection surface with analemmatic hour marks. 
(4) a stile on the projection surface 
(5) a date line in which the stile (gnomon) moves during the year and 
(6) the direction of the projection.  

The movable stile scale on the projection surface is a projection of the
polar axis.
(#5 from #2 and #6)
The hour point on the projection surface is determined by a line from
the projection direction through the equatorial circle hour mark to the
projection surface.  
(#3 from #1 and #6)
I am working on how the gnomon angle to the projection surface is found.
The stereographic projection from a point lends itself to using a CAD
program to make a design (very much like Rohr describes in his book).
The Quadruple dial is amazing.

Thank you Fer,
Warren   

fer j. de vries wrote:
> 
> Dear Warren,
> 
> Indeed, Thijs de Vries ( no relative ) has published about a polar
> sundial with equidistant hour lines.
> The article is in the bulletin of "De Zonneijzerkring", 1980.
> 
> I have made a short page about this dial at
> http://www.iaehv.nl/users/ferdv/polar.htm
> 
> This page is temporary and will be removed after some time.
> 
> Happy dialling,
> 
> Fer de Vries.

Re: Foster sundials.

[Warren Thom]

Hi Mac and all,

Mac Oglesby wrote:
> 
> Hi Warren,
> 
> C'mon, you can't leave us hanging like this!  Give a hint, at least, about
> the appearance of the Italian hour lines on a Foster-Lambert sundial.
> Please.
> 

My first thoughts:
If you can make a Foster/Lambert dial with a vertical gnomon, why not
one with a horizontal gnomon?  To picture these we would think of moving
a F/L dial north or south along the meridian to a location where the
gnomon is the angle we want for our latitude. For a horizontal gnomon,
set the zero hour on the horizon, level with the gnomon.  As the gnomon
is moved up or down for different declinations of the sun, the zero hour
on a movable ring would also be turned to be level with the horizon. 
More than 12 hours would show in the summer and fewer than 12 hours in
winter.  Would the back of the ring need to be marked also? The last
question that remains is at what angle is the hour ring with repect to a
horizontal gnomon? With (G=(90+L)/2) or (G=(90-L)/2) do we use L for our
latitude or for a new latitude?  If a new latitude, what is it?

Comments are appreciated.
Happy Dialing,
Warren

Re: Foster-Lambert dials

[Warren Thom]

Hi Mac and all,

Do you also wonder if there is a way to design an analemmatic dial that
will show Italian hours (hours till sunset)?  Is there an angle to set a
plate of equal spaced scale of Italian hours around a gnomon?  Can
anyone gives us a direction on this?
 
We missed you at the NASS meeting.  It was a great meeting. The Adler
Planetarium and the Rockford Time Museum should not be missed by a
dialist that is near Chicago.  Claude Hartman had some nice models of
glass window/sky light dials he made with Fer's program.  William Van
Wyke (I think that is his name) made a spherical wood art piece with the
gnomon "built in".  Fred Sawyer showed two new dials he invented.

Hapy Dialing,
Warren Thom

Mac Oglesby wrote:
> 
> Sundial list members who have an interest in Foster-Lambert dials:
> 
> The second edition of "Sundials" by Mayall & Mayall includes, on p.190-2,
> design information (geometrical and algebraic) for Foster-Lambert dials.
> 
> The webpage "Sundials on the Internet" has links which lead to a picture of
> the Royal Greenwich Observatory Sundial
> (http://www.sundials.co.uk/~cantab.htm).  Comparing this photo with the
> picture from Fer de Vries, it appears that the outer ring containing the
> hour points may be rotated with respect to the central tube along which the
> gnomon slides.
> 
> Rotating the hours ring would permit this dial to be set to tell standard
> time or daylight time.  Does anyone know if this sundial is adjustable in
> this manner?
> 
> Mac Oglesby

Re: Foster - Lambert

[Warren Thom]

Hi Dave,

 I also want to thank Fer for posting the image of the
Foster-Lambert dial.

Dave Bell wrote:
> 
> What defines a Foster-Lambert dial, and how are they designed?
> I don't recall seeing any references to this type on your page!
> 

I understand, to have a vertical gnomon, it would be designed for a new
latitude by thinking of moving along the north-south meridian until the
gnomon is vertical.  
That would be at latitude 90 degrees (the north pole). (see below
G=(90+L)/2) But the dial plate would still be tilted at at angle G with
respect to the gnomon.  To have a horizontal gnomon, it would be thought
of as being at zero degrees latitude (equator) with a tilted dial plate
of G found from G=(90+L)/2 where L is the latitude of dial.  

Is this correct thinking?  Any comments are appreciated.

Warren Thom

Mac Oglesby had written that Mayall described the dial. This is part of
the text:

page 192 SUNDIALS by Mayall and Mayall 2nd edition

The Foster/Lambert Dial

This dial does not use a perpendicular gnomon. However,
it must lie in the plane of the meridian YZ and make an
angle G (fig. b) with the meridian equal to I/2 the sum of
900 and the latitude of the place. The gnomon or style PH
must be constructed so that its angle will remain the same
as it is moved north and south along the meridian.

To use this dial, place it on a level surface with YZ in the
plane of the meridian and the hour point 12 to the north.
When the foot of the gnomon or style P is placed on the
corresponding date, the position of the shadow on the circle
will indicate the time. If you wish to compute the various
elements, the formulae are:
  Let
E = distance OE, the eccentric
C = radius of circle (distance 0-I2)
L = latitude of the place
D = declination of sun
R = distance from O north or south of WX on YZ,
for the daily setting
G = angle gnomon makes with the meridian line YZ

  Then
G=(900 + L)/2

R = E tan D

C = E tan G, or C = E cot (900 - G)
  
If the radius C is known, then:

E = C tan (900 - G) or E = C cot G

Re: Foster sundials.

[Warren Thom]

Thank you Fer, for posting a most informative explanation.

You have helped me understand some of the basics of projections.
I think I am correct that your procedures for Zonwvlak show clear steps
for orthographic projections (x,y).  A recent issue of the Compendium
dealt with sterographic projection. To confuse my mind more, (from which
I learn) Fred Sawyer has mentioned to me about a Dutch dial invented in
the 1970's that has a linear equal spaced hour scale based on a polar
dial with a gnomon shaped in a cycloid.  Can you tell us more?

Thanks again,
Wareen Thom

p.s.  I think I have figured out a Foster Lambert dial for Italian
hours, but I want to study it more.

fer j. de vries wrote:
> 
> To all,
> 
> Last week we had a discussion about the Foster Lambert sundials on this
> list and some question still are open.
> 
> Now I will try to give some basic informations for such dials.
> 
> For figures look at
> http://www.iaehv.nl/users/ferdv/foster.htm
> 
> All we now have to do to make an elliptic, circular or linear sundial is
> :
> project the equatorial dial onto our sundial plane in a direction of
> free choice.
> That's all..

some deleted

> 
> To get a linear sundial we choose a style which lies in the equatorial
> plane. Again we project the equatorial dial into this direction onto the
> horizontal plane as you can see in fig. 4. The equatorial circle
> transforms into a simple line.

Re: declination line

[Warren Thom]

Sérgio Garcia Doret wrote:
> 
> Hello everybody
> Where is the people of that list?
Here is one person.
> Can yon help me?
I will try.
> I plot a horizontal sundial for a place at lat 22º15'S and lon 42º 
> 7'W,
> with longitude correction. I have calculated a declination line for july 15, 
> but
> the curve was strange in relation to the solstice line.

How was it strange?

The declination line for July 15 should not be too far from the summer
solstice on a horizontal dial.  Just about 10% closer to the equinox
line. The longitude of the location will not change the "day line" but
will shift the hour lines marked.  It is kinda like declination effecta
the "Y" plot on a plane and the hours and longitude  effect the "X"
direction.  The two together determine one point made by a gnomon like
the intersection of two lines.   

> I'm asking if that angular dfference must be considered (added) to
> the sun's altitude angles in order to get correct results?

I don't understand the question here.  How did you get "angular
distance"?  Is this what you mean by correcting for longitude?  If so,
then there is more to it than adding to the sun's altitude.  Do you mean
by "correct results", the x,y plot of a point on a flat surface?  
> 
> Thanks in advance
> 
> Sergio
I hope this is a little helpful.  Let me know.
Happy Dialing,
Warren Thom

Wish list for a new home.

[Warren Thom]

This thread poses some interesting possibilities.

If you could design a unique home,  what special locations might
a person consider for windows, floor, halls, and rooms so that sunlight
would show in special ways?  

For example, my home faces southwest, and on Christmas day the sun
sets directly in front.  Our tree can be 6 meters from the window
and get sunlight that afternoon.  In June, the back of my home gets
the direct sunrise light. (except I have a large shade tree blocking
it.)

> fer j. de vries wrote:
>> [EMAIL PROTECTED] wrote:
>> determine the projections for extremal values of Sun's zenith (for 
>>each of 365 days, or some other, fewer interval) -- that would give 
>>the area COVERED by the sunlight -- then the solution is everything 
>>OUT OF IT.  

Some deleted

> A mathematical methode how to calculate a plane sundial is on my
> homepage
> http://www.iaehv.nl/users/ferdv/
> Click English and than the page to compute sundials.

Some deleted

> This makes the problem a little more complicated.
> In the horizontoscoop this is directly visible.
> Fer J. de Vries, Netherlands.

Re: Compute flat sundials.

[Warren Thom]

[EMAIL PROTECTED] wrote:
> 
> At 09:53 PM 1/3/97 +0100, you wrote:
> >Dear all,
> >
> >This date I placed some pages on the internet with the title :
> >A uniform method to compute flat sundials,
> >usable all over the world.
> 
> FANTASTIC!!  WONDERFUL!!  AMAZING!!  MARVELOUS!!  ELEGANT!!  
> STUPENDOUS!!
> INGENIOUS!!  BEAUTIFUL!!  AWESOME!!  ENJOYABLE!!  GREATLY 
> APPRECIATED
> 

I second that feeling.

Two questions:

In the main procedure

(1) If x=x3*g/z3  y=y3*g/z3are replaced by
   x=x3   y=y3*g/z3would this give a trace for a 
   cylinder?  That is, curve the
   paper into a half circle, with
   the gnomon at the center of the
   circle (cylinder).

(2) Would x=x3*g/z3 and y=y3  give a cylinder in the other direction?

Thank you, Fer.

Warren Thom

Re: Equation of Time

[Warren Thom]

Gianni Ferrari wrote:
> 
> Dear friends,
> I've followed with much interest the several
> messages arrived in last days on EoT calculation.

I too, find this discussion interesting.  It also requires us to
ask "What is significant?" in effects on time measurement.

So far we have centered our concerns with astronomical variations.
What about geographical concerns?  The fact that the Earth is
an ellipseoid (not a sphere) should be of some concern, but when?
Don't forget the different definitions we can have for sunset, or
our altitude above sea level.

With the help of the basic programs from Sky & Telescope, I have 
worked on the question of how many full moons will fall on Christmas
in the next 100 years. (3-2015,2072,2091) Someone at church said
we would not have a full moon on Christmas for over 100 years---I 
knew that was not likely.  There are several programs for date, time,
right ascension, and declination. The URL for Sky & Telescope is: 

<http://www.skypub.com/software/software.shtml>

> I've calculated, with great accuracy ,the values in all the days of
> the year for 32 consecutive years (1990-2021) and after I've found
> the average values for each day.
> Later on I've developed AR, D, and EoT in Fourier series with 20
> harmonics.

Excellent problem for computer solution. Nice job.

Are these questions moot for sundial design? (Don't stop the thread 
though.)  Having followed the articles in the Compendium on error
analysis of sundials (and from practical experience) a difference
of one millimeter on a gnomon is a greater problem than most of our
cercerns above. But this is an interesting discussion.

My .02 cents---Warren Thom

Re: Thanks to all who helped me with Lettercutting and Engraving.

[Warren Thom]

Roderick Wall wrote:
> Thanks to all who replied to my request for help with letter cutting
> and engraving the hour lines and hour numbers onto stone and brass 
> sundials.  

This was a good thread.  I know this is not about stone or brass. but
I have found some interesting things in the local craft store.
They have a paint that goes on glass, then is heated in the oven
to make it "dishwasher safe".  Fred Sawyer's Astroid design in the 
Compendium would be a possible design.  The craft store also had 100mm 
diameter clear plastic spheres for Xmas ornaments that I used to 
construct the Hemispherium by Fer de Vries.

Warren Thom

Re: babylonian and italian hours

[Warren Thom]

K. Kotynia wrote:
>
> I look for the description how to draw or construct, compute etc.
> babylonian and italian hours
> on a dial. If somebody could help me or point any sources where I can
> find that topic I would be grateful.
>
> Krzysztof Kotynia

Hi,
Since those lines on a flat dial are straight, you need only find
two points and connect them.  Find the time of sunrise from:

  cos(hour)=tan(lat)*tan(declination)   for dec=-23.45 and +23.45

  (From Sundials by Mayall&Mayall)

add or subtract one hour (15 degrees) and plot the point for those
times.

It is interesting that you ask.  Fer De Vries gave a web page for
construction of a hemispherium.  It had an interesting geometric way
to construct those lines by dividing a circle with center at the pole
and radius of 2*radius*sin(.5*(90-lat)) on the hemisphere into
24 parts then drawing a great circle centered at each point.

The Babylonian line does make an angle with the east-west equinox line
of a flat dial.  I do not know how to calculate the angle.  Can anyone
help us on that calculation?

Warren

Re: lat & long

[Warren Thom]

Hi Clem,
If you live in the USA and have "Street Atlas USA", you can locate
any point by lat & long by making that the point when you close
the program.  Then look at the init file in the windows directory for
the program.  It lists the latitude and longitude.  
Gifts for Christmas sound like a nice idea for Winter Solstice.
Good luck.
Warren

Clem Padin wrote:
> 
> Dear dialists,
> 
>   I decided to make sundials for friends this holiday season.  Anyone know
> of a web site that would have the lat & long of cities around the country?
> Maybe a database one could query?
> 
> thanks,
> Clem

Re: NASS Conference

[Warren Thom]

Hello Dialist,

I have been looking forward to reading comments about the NASS meeting
on this mail list.  I have quoted the announcement to see any reactions.
I enjoyed the weekend very much.  The variety was good.  It included 
interesting history, solutions to design and dial building problems,
and a lot of interesting people.  The rain was disappointing but my 
pictures came out better than expected.   

The shareware computer program "The Dialist Companion" has been a new
toy along with the "any" latitude dial.  I estimated the moment of 
winter to be December 21 at 7:52:16 CST with the computer companion.
I have also produced the Foster Dial with the world map that was in the
last issue of the Compendium (3-3).  It came out pretty neat.  I want
to enlarge it and mount it.

Cheers,  Warren

 
Frederick W. Sawyer III wrote:
> The North American Sundial Society
>2nd Annual Conference   September 27-28, 1996
>  at the
> Institute for the History and Philosophy of Science and Technology
> at Victoria College in the University of Toronto, Toronto, Canada.

> Tentative plans call for visiting dials at Pearson Airport,
> Toronto City Hall, Casa Loma, Victoria College, The School of
> Engineering and Hart House.
> 
> Lectures include Samuel Foster of Gresham College - Fred Sawyer,
> Historic Sundials As Evidence Of Consumer Culture - Sara Schechner
> Genuth, A Mean Time Equatorial Dial With Analemmic Gnomon - E.J.
> Buckler, The Horologium In The Tiberius Manuscript - Robert Kellogg,
> A Portable Astroid Dial - Fred Sawyer, Sundial Design With
> Matrices  - Harold Brandmaier, The Sundial Of Merbaka Church -
> M.E. Mickelson, Sundials On The Internet - Piers Nicholson,
> Designing A Vertical Decliner  - Tom Shepard.

Re: ZONWPLT Ideas (no. 2)

[Warren Thom]

I have one question about ZONWPLT.  I use the program to produce
model sundials on paper. The lines for the gnomon are very helpful
to make the model because the dial and gnomon length are drawn to
the same scale.  But with a bifilar dial with two threads, no lines
are drawn.  Is there a simple way to know the length of each thread
for a scale dial that is drawn?  

I cannot praise Fer J. de Vries enough for such a fine quality tool 
for drawing dials.  

By the way, I hope everyone that attended the 2nd annual NASS meeting
in Toronto enjoyed it as much as I did.  I appreciate all the time and
effort of Fred Sawyer, Harold B., Phyllis, and everyone that 
contributed.  My brain was on overload for three days. We sure had
a diverse group present that made for a very interesting weekend.

Sincerely,  Warren Thom

A few questions.

[Warren Thom]

Hi All,
 I printed out a horizontal dial for my 87 year old father.  I make
it with Zonwvlak (available from NASS).  After reading the directions,
I found the software powerful yet easy to use.  F.J. de Vries did an 
excellent job in writng the software.  I found that Ami Pro 3.0 will 
import a picture in the .plt format under HPGL as the choice format.
The aspect ratio is maintaind and it prints to a full sheet of paper.
I had a minor problem using the draw program (Scrplt) because I could
not always remember the file name that I had created.

Now for a few general questions.  

Babylonian hours.  I take it these are the lines for each hour 
since sunrise.  I also assume they are each 1/24 of a day long.
Are they numbered from sunrise, with sunrise=0, one hour later as 1
two hours since sunrise as 2 etc?

Italian hours.  I understand these to be the hours until sunset.
I would take these to also be 1/24 of a day in length.  Is sunset=0
and one hour before sunset=1, etc?

What exactly is a bifilair sundial?  I take it that it has two planes
perpendicular to each other.  If so why does Zonwvlak only print one 
surface?  No waitreading.does a bifilair dial use the lines on
a transparent surface to be read with one point where the "shadows" hit?
 
Now for a math question.  In analytical geometry the equation of an 
ellipse is: (with the origin at the center and semi-axes a and b)

(X**2/a**2) + (y**2/b**2) = 1  (**2 means squared)

the equation of a hyperbola is:

(X**2/a**2) - (y**2/b**2) = 1

Can we draw a sundial from these equations?  How are a and b related to
latitude, declination of the sun, and hour angle?  This will keep me off
the streets and out of trouble for a while.  

Sincerely,

*****
Warren Thom  [EMAIL PROTECTED] or  [EMAIL PROTECTED]
Hompage  Still working on it.
*

NASS is great!

[Warren Thom]

To All,
I just had a great weekend of being able to read the back issues of the 
Compendium.  The Compendium is the journal of the North American Sundial 
Society.  
Contact treasurer Harold Brandmaier at [EMAIL PROTECTED] or Fredrick W. Sawyer 
at [EMAIL PROTECTED] for membership application and information.  Last weekend 
I 
read the book "Longitude" after reading a book review in the journal.  It is an 
excellent book on a topic that threads together science, art, economics and 
politics.   

I am a science teacher at Stagg High School, located southwest of 
Chicago.  Each 
year I tell a few seniors to leave a sundial gift to the school.  Until now I 
really did 
not have any unique designs in mind.

"A Transparent Window Dial" by Thibaud Taudin-Chabot, vol-1-3 of the 
Compendium 
is an inspiration.  I had never considered this design.  It is idea for a 
location with 
a large window area.  We have such an area in walkways between each of our 
three 
buildings.   Is there any church with this design in stained glass?
 
I can't say enough good about the contributions of Fred Sawyer.  Last 
summer I 
worked several weeks on "Reducing a plane to the horizontal" (Vol 1-4)  I ended 
up 
making my changes based on Waugh's chapter on vertical declining dials.  (Waugh 
finds a 
sub-style distance, style height, difference in logitude, and new angle for 
gnomon.)  I 
had considered a spherical triangle solution, but I did not get the math clear 
in my 
head until I read Fred Sawyer's article on spherical triangles (Vol1-3).  

NASS has distributed the shareware program "Graphica" to draw and print 
designs 
and make analysis.  I would like to see any sundial plot files written for 
Graphica as I 
am not having much luck getting what I want with parametric equations.  Please 
post any 
you may have.  I have only worked with Graphica a few hours.  I do like the 
many print 
options.

What dial information produces straight lines on a flat plane? (other 
than hour 
lines of course.) Fred Sawyer gives  "Universal Horizontal Dialfaces" 
(Compendium Vol 
2-3) which has a face of all straight lines! Amazing.  Does anyone have any 
other ideas 
on this?
 

*****
Warren Thom  [EMAIL PROTECTED] or  [EMAIL PROTECTED]
Hompage--I am working on it.