Founder of Trigonometry

[Roger Bailey]

At the NASS conference we got into a discussion on who invented
trigonometry. I knew that the Greeks were great on geometry but thought
that trig functions and tables were a later development, from the early
Renaissance.

A quick web search on the question "Who invented trigonometry?" turned up
the name of Levi ben Gerson. In 1342 he wrote "On Sines, Chords and Arcs"
which developed the mathematical principles of trigonometry and provided 5
figure sine tables. He is best known for developing the algorithm for
extracting square roots that we all learned in high school and then forgot.
He also invented the forestaff for measuring angular distances essential
for celestial navigation. His trig tables were developed for use with the
forestaff or "Jacob's staff" See
.

Was I right? No! A search at the local library, subsequently confirmed on
the web, takes the invention of trig back to the Greek
astronomer/mathematicians, in particular to Hipparchus. He produced a table
of chords in 140 BC. Menelaus and Ptolemy later extended this work. Hindu
mathematicians about 500 AD produced tables of half cords using the name
now interpreted as Sine.

So Hipparcus is the founder of trigonometry. It goes way back! 
See .

This brought home to me how dark the Dark Ages were in Europe. Our
Eurocentric view often misses the fact that civilization disappeared in
Europe for about 800 years. Today, Nov 11, Remembrance Day, reminded me of
recent events that show we are still at it!

For an interesting spin on this topic see the book by Thomas Cahill "How
the Irish Saved Civilization". His premise is that Irish monks on the
fringes of Europe continued to copy not only the bible but the works of the
earlier civilizations. The Renaissance was based on this collected knowledge.

Roger Bailey
N 51  W 115

Re: SEND ANSWERS!

[Roger Bailey]

Quite a while ago I asked the following question on sundial trigonometry.
>
>> My challenge to all for today is to simply explain
>the basic formula for horizontal dials: Tan HA = Sin L x Tan t.

Mac Oglesby responded with the following answer which is much better than
my proposed proof.

>
>Fred gave a demonstration of why this is true in an early issue of 
>Compendium (1-4, I think).  I find the attached drawing (Tan_A.GIF) 
>easier for me to follow.
>
>Best, Mac

Luke Coletti responded by pointing to the followin graphic that
demonstrates the phenomenon very well.

>   A very nice derivation can be found in "A Choice of Sundials", by
>Winthrop W. Dolan, pg. 20-21. For those seeking a more intuitive
>approach, the graphic, inside the book's dust jacket, of a horizontal
>plane "embedded" within the celestial sphere gives a marvelous
>description of why the hour lines are drawn at the angles they are.
>Simply put, the hour lines of the dial must reach out to intersect the
>projected meridian lines. An example of the graphic (made for lat=36.5d)
>can be viewed at the URL below.

>ftp://ftp.gcstudio.com/pub/misc/gcdial.jpg

Thanks Mac, Fred and Luke for SENDING ANSWERS.

Roger Bailey
Walking Shadow Designs
N 51  W 115
Attachment converted: Macintosh HD:Tan_A.GIF 1 (GIFf/JVWR) (810C)

postscript dial bugs

[john hoy]

I have (with help) uncovered a few bugs in my postscript dial programs;

* I (generally) mark only sunny hours in the northern hemisphere--I
apologize. I'll fix it.

* The capuchin dial was chopping off some of the curves for some lats.
It's fixed.

*The equatorial dial crashes if the mottos are left blank.

If anyone uncovers such problems I wish that they would bring them to my
attention. Thanks.

jh

Re: More on Metal Sundial Processes

[Tony Moss]

John Davis wrote:
>
>Great stuff! Can you give any indication of how much currect is needed (per
>square inch of object?).

Glad you find it interesting and potentially useful.
>
>Also, have you ever tried masking some areas of the film ( hour numbers)
>before the dying process, so that they come out a contrasting (or clear)
>colour?
>
See my recent posting on re-anodising through etched 'holes' which would allow 
red/blue/green etc. lines on a yellow or gold background.  The companies who 
specialise in dyes for anodising produce some wonderful metallics in every 
shade from pale gold to deep copper but they only supply 1kg minimum 
quantities.  Try to make personal contacts in firms which specialise in 
anodising and they may sell smaller quantities.  Does anyone know of suppliers 
of smaller quantities?

If there was sufficient interest I might consider buying 1 kg of e.g. gold dye 
and selling it on in 50 gram lots although I would have to charge appropriately 
to make this worth the fair amount of trouble involved.   Or perhaps the BSS 
might consider buying and re-selling for a fair profit?   Fifteen years ago 
Sandoz charged about £UK25 per kg so it will be a lot more than that now.  
Household dyes work quite well but often lack the depth of colour of the 
commercial product.  

I have a voltage/area/time graph compiled by a casual research student which is 
reliable for small workpieces.  I suspect the flattening out of the curve is 
due in part to our power supplies 'running out of legs' so I hope the 
commercial anodisers out there don't laugh too loud.

GIF on request.

To illustrate the durability of the anodic film I kept small samples in my 
labcoat pocket for years alongside bunches of keys, coins, small drills, broken 
cutters, bits of oilstone slip and half-eaten sandwiches and they remained as 
good as the day they were made. 

SAFETY  While both myself and Mike Shaw quite rightly drew everyone's attention 
to possible hazards this is a safe and easy process if handled with ordinary 
common sense.  Dozens of students in my care produced hundreds of anodised 
examples with not a single cause for concern except for a technician who didn't 
bother to switch on the ventilation over extended sessions and temporarily lost 
his sense of smell.

THEORY for them as wants more!  

Why does the film build up in a honeycomb of micro tubes?  My readings of 20 
years ago (can't recall the source) suggested the following reason:

The aluminium sheet will always have a thin coat of atmospheric oxidation.
When connected to a positive supply and placed in an acid electrolyte small 
holes will be eaten through this oxide film to produce  'pits' of positive 
charge.  This takes place all over the plate and, because all the pits have a 
positive charge, they become equally spaced by mutual repulsion eventually 
settling down into a close packed 'honeycomb' arrangement.
No doubt ideas have advanced since I read that but it did seem to make sense.

Rainbow sundials here we come!

Tony Moss.





==

\  ** **
\\ ** **
 \\** ***
 *\\   **  **
  *\\  ******
  **\\
  ***\\   Tony Moss, Lindisfarne Sundials
 *\\  43, Windsor Gardens, Bedlington,
***\\Northumberland, England, NE22 5SY,
  **\\55°  07'  45" N1° 35' 38" W
 Tel/FAX +1670 823232
 Mobile: 07970 208 540
  Website:  http://www.lindisun.demon.co.uk

==

  The first choice for a Millennium Sundial.
 (every one Y2K compliant)

   Horizontal, Vertical, Declining, Analemmatic, Equatorial, 
Polar and Capuchin Sundials individually made in solid 
 engraving brass. Professional-quality Dialling Scales, 
  'engine-divided' meridian layout instruments with software.  
  Analemmatic dial plots - any size for any latitude.
   Graduation, re-cutting and restoration of scales.
  'Lintique' patination of brass.

===

Re: More on Metal Sundial Processes

[Tony Moss]

Warren Thom wrote:
>
>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? 

In my limited experience of anodising aluminium castings, if you want clear, 
even 'bronze look-alike' I would have to agree.  The few castings I anodised 
were always blotchy, even on dressed surfaces.  I have no evidence to support 
my theory but I always thought it might be due to uneven dispersion of copper 
in the skin of the casting or just its irregular structure due to skin 
chilling.  A partly dressed LM6 sandcasting dyed black took on an interesting 
silvery grey 'forged iron' look which we often used to good effect but other 
than that I would always select drawn or rolled material for anodising. 

>I have found your steps very interesting.  I have always wanted to find a good 
>link of sun >dialing to chemistry.

That is how it started for me.  I was tasked with finding interdisciplinary 
projects which would involve contributions from the teachers of chemistry, 
physics, art and workshop crafts.
What could be better than anodising?  Many sessions, many kids, much anodising 
and not a single incident.

Best Wishes

Tony



==

\  ** **
\\ ** **
 \\** ***
 *\\   **  **
  *\\  ******
  **\\
  ***\\   Tony Moss, Lindisfarne Sundials
 *\\  43, Windsor Gardens, Bedlington,
***\\Northumberland, England, NE22 5SY,
  **\\55°  07'  45" N1° 35' 38" W
 Tel/FAX +1670 823232
 Mobile: 07970 208 540
  Website:  http://www.lindisun.demon.co.uk

==

  The first choice for a Millennium Sundial.
 (every one Y2K compliant)

   Horizontal, Vertical, Declining, Analemmatic, Equatorial, 
Polar and Capuchin Sundials individually made in solid 
 engraving brass. Professional-quality Dialling Scales, 
  'engine-divided' meridian layout instruments with software.  
  Analemmatic dial plots - any size for any latitude.
   Graduation, re-cutting and restoration of scales.
  'Lintique' patination of brass.

===

Re: More on Metal Sundial Processes

[John Davis]

Tony,

Great stuff! Can you give any indication of how much currect is needed (per
square inch of object?).

Also, have you ever tried masking some areas of the film ( hour numbers)
before the dying process, so that they come out a contrasting (or clear)
colour?

Cheers,

John

-
Dr J R Davis
Flowton, UK
52.08N, 1.043E
email: [EMAIL PROTECTED]

Sundial Mail List archive.

[Mac Oglesby]

Hello all,

Recently I tried to access the archive of Sundial Mail List messages, using

http://www.reference.com/cgi-bin/pn/[EMAIL PROTECTED]


I got this notice:

"File Not Found

The requested URL /cgi-bin/pn/listarch.py was not found on this server."


If the messages from this mail list are archived, would someone 
please tell me how to reach them?


Thanks,

Mac Oglesby

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!

[John Carmichael]

Hi Skipjack and Les:

I think that you're both half right!  Les is correct that the FAQ questions
and answers should be basic and simple, and you are right that we should
have extensive coverage of all topics.  At the moment, I am gathering ALL
questions, regardless of merit.  We will decide later on which ones to keep,
discard or reword.  Our biggest challenge will be to do justice to these
questions with good understandable answers.

Best,

John

>I disagree.  While I realize everyone has their own preferences, mine are
>just the opposite.  When I am interested in a topic or searching for
>information I try to find the best single source that covers all the
>issues.  For me, more material and detail is better.
>
>--
>> From: Les Cowley <[EMAIL PROTECTED]>
>> To: sundial@rrz.uni-koeln.de; John Carmichael <[EMAIL PROTECTED]>
>> Subject: Re: SEND QUESTIONS!
>> Date: Wednesday, November 10, 1999 5:28 PM
>> 
>> Just some personal preferences ...
>> 
>> I tend not to use long FAQs very much.   A beginner is probably
>> in a hurry and wants to acquire a just a few basic facts and a little
>> knowledge.   More than a page or more gets intimidating and he/she
>> loses interest.
>> 
>> Keep it very simple.  Additional material might go into a multi-age
>> website which could become a longer term project for a number of
>> contributors.
>> 
>> Isn't it so much easier to give advice rather than take it :).
>> 
>> Les Cowley
>> Mail~  [EMAIL PROTECTED]
>> Halos ~  http://www.lc.dial.pipex.com/halo/halosim.htm
>> 
>> 
>> 
>
>

Re: SEND QUESTIONS!

[John Carmichael]

Hi Les:

I'm getting many good questions now, so many in fact that it would very
difficult to resrict their numbers so that they and their answers fit on
only one page.  Too many good questions would be left out.  But I do agree
with you about keeping it simple.  That is why I think it is very important
to categorize the questions and answers.  That way the beginner can skip the
questions that don't interest him and he can zoom in on those that do.

regards,

John

>Just some personal preferences ...
>
>I tend not to use long FAQs very much.   A beginner is probably
>in a hurry and wants to acquire a just a few basic facts and a little
>knowledge.   More than a page or more gets intimidating and he/she
>loses interest.
>
>Keep it very simple.  Additional material might go into a multi-age
>website which could become a longer term project for a number of
>contributors.
>
>Isn't it so much easier to give advice rather than take it :).
>
>Les Cowley
>Mail~  [EMAIL PROTECTED]
>Halos ~  http://www.lc.dial.pipex.com/halo/halosim.htm
>
>
>
>
>

Re: More on Metal Sundial Processes

[The Shaws]

Can I just add a note of caution to Tony's note that concentrated caustic
soda is really nasty stuff as well
as the sulphuric acid.  If you get a splash of conc caustic soda in your
eye, don't bother to rush to the tap - by the time you get there it will
have already gone !!!

Have fun but BE CAREFUL and wear appropriate protective gloves AND GOGGLES

Mike

[EMAIL PROTECTED]
53.37N  3.02W
Chester, UK

Re: More on Metal Sundial Processes

[Tony Moss]

Roger Baily contributed:
>
>Great, informative note. I always wondered how these coloured oxide films
>were created. Thanks, I will try your techniques.
>
>Have you, or others on the list, had any experience using caustic to
>chemically etch aluminum? We used to make hydrogen to fill party ballons
>and make mini hydrogen bombs by reacting aluminum foil with a caustic
>solution (Draino or lye) in a pop bottle. I often thought that this process
>could be used to etch masked aluminum surfaces to produce the base plate
>for a horizontal dial. I never did reduce the idea to practice as the
>hydrogen ballons and bombs were more fun. Were you more successful?
>

Roger and 'Watchers'

   Etching with caustic soda is an interesting stage in an easy 
form of multi-colour anodising - probably very relevant to dial making!  Bill 
Maddux recently suggested etched aluminium dial plates to me.  Come to think of 
it that is probably what jogged this current memory.  Thanks Bill!

Stages.

1.  Produce the anodic film.
2.  Dye and seal.
3.  Stick on self-adhesive paper shapes.  Numerals?  Lines etc.
4.  Spray with auto paint aerosol.
5.  Just as the paint is almost dry (critical) pick off the gummed shapes.
6.  Place in caustic soda which will etch away the exposed coloured areas.
7.  Re-anodise and re-dye a different colour through the 'hole'  OR
8.  Polish the exposed aluminium on a polishing wheel.  The surrounding anodic 
film is impervious to jewllers' rouge  leaving mirror-bright lines/shapes on a 
coloured background.
9.  I discovered (or re-discovered) this process (and several others) by 
experiment.  Has anyone else trod a similar path?

Tony Moss





==

\  ** **
\\ ** **
 \\** ***
 *\\   **  **
  *\\  ******
  **\\
  ***\\   Tony Moss, Lindisfarne Sundials
 *\\  43, Windsor Gardens, Bedlington,
***\\Northumberland, England, NE22 5SY,
  **\\55°  07'  45" N1° 35' 38" W
 Tel/FAX +1670 823232
 Mobile: 07970 208 540
  Website:  http://www.lindisun.demon.co.uk

==

  The first choice for a Millennium Sundial.
 (every one Y2K compliant)

   Horizontal, Vertical, Declining, Analemmatic, Equatorial, 
Polar and Capuchin Sundials individually made in solid 
 engraving brass. Professional-quality Dialling Scales, 
  'engine-divided' meridian layout instruments with software.  
  Analemmatic dial plots - any size for any latitude.
   Graduation, re-cutting and restoration of scales.
  'Lintique' patination of brass.

===

Re: More on Metal Sundial Processes

[Mac Oglesby]

Hi Tony,

Many thanks for posting your step-by-step instructions for anodizing 
aluminum.  Please continue to share your know-how with us.


Best,

Mac Oglesby
Vermont, USA

P.S. Please include me on your list of persons to whom you send that 
GIF of a voltage/current/time graph derived from experiment.

Re: FAQ categories

[Ant�nio Lopes]

John

don't forget the math section (from basic stuff to the more elaborated one). Of
course this can be part of the category "do it yourself" or something similar.
Some of our fellow dialists possess nice and easy math explanations (webpages
with pictures/simple programs) for the how it works not just for the outcome.

Happy sundialing
Antonio

John Carmichael wrote:

> Hi Jean-Paul:
>
> As I'm receiving FAQ questions I will place them into different categories,
> not only to make my job easier, but as a proposal for categorization to the
> FAQ answer committee.  Of course some categories overlap others so it is
> debatable as to whether the question is properly categorized.  But I have to
> start somewhere.  The committee can change things later on if they need to.
> Most of your questions will fall under the "Time" section, others under the
> "History" section.  Since the different kinds of time are intimately linked
> to history, you can see how I'll have some difficulty in properly
> categorizing the questions.
>
> >John,