Dear Gianni,
It is always a pleasure to read your messages
to this list. As usual, your reply is full of
scholarly interest and invites more questions!
1. CHANGE FROM TEMPORARY HOURS TO EQUAL HOURS
You say that in classical times The only system of
hours used was that of the temporary
. This was
marked out by Francesco Bianchini in 1703.
The great Italian diallist, Mario Catamo,
calls the device Il Cronometro.
With this, Bianchini could note the moment
of the equinox to within a fraction of an
hour.
Good luck with your observations!
Best wishes
Frank King
Cambridge, U.K
Dear Frank,
Mixed in with the discussion ... was a question
... about when the use of equal hours by the
Romans began.
You are quite right that, in astronomical matters,
equal hours were used in antiquity. As you say:
Little doubt that the refined values quoted by
these ancient fellows
Dear Gianni,
Once again, you give a splendid reply!
Your explanation of the transition from Temporary
Hours to Equal Hours is a very complete answer to
my question.
I can see that the advent of tower clocks simply
forced the pace of change.
In Italy today all dialists to point out the hours
Dear Frans,
You ask a very perceptive question:
No doubt the transition to equal hours (whether
starting at noon, midnight, sunrise or sunset)
was gradual but I feel it long predates mechanical
clocks.
Do you have any evidence supporting your feeling?
No! I had heard (from you and
Dear Frans,
Like Gianni, you produce splendid scholarly
input to this list!
I promised not to challenge your answer so
I will constrain this reply accordingly!
You have made me think about Zinner's
imagination...
If you have a medieval sundial such as you
describe [a vertical dial, assumed
Dear Roger,
Yes, it is easy to get the wrong sundial when
looking at Braunschweig Cathedral!!
The bigger (17th century?) dial has recently been
restored and I have in front of me a newspaper
cutting which explains:
Die Kosten von rund 700,000 Euro werden von
der Dombaustiftung und von
Dear Karlheinz,
I have now read your article more carefully.
It is excellent, one of the most interesting
articles I have read for a long time!
I think now understand your comment...
...you see that the winter circle is not
divided in 12 parts as it should be for
unequal hours.
I
Dear Mario,
Many thanks for your kind explanation...
Censorinus and Gellius citing Varro say that
in Rome the day was intended in two ways: natural
and civil.
I am slowly gaining some understanding of time in
ancient Rome. Gianni Ferrari has pointed us at:
see the concrete
platform. On Google Earth it is at:
52 deg 12' 53.80 N 0 deg 5' 45.57 E
I hope this starts off a more serious discussion
about this curious sundial!!
Best wishes
Frank King
Cambridge, U.K.
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Dear Nicola,
You write...
Yes this is a very curious (and unique) sundial.
Well, we have curious sundials in England too :-)
Take a look at:
http://www.cl.cam.ac.uk/users/fhk1/SSinB.jpg
This photograph was taken by a friend of mine in
Cornwall, in south-west England, and shows a dial
on
Dear Nicola,
I think I have to agree with Chris Lusby Taylor's
analysis of the Villa Cimbrone dial:
http://gnomonices.blogspot.com/
Lord Grimthorpe cannot have seen this sundial.
He always wanted the best (or his idea of the
best!) and I don't think he would have liked
this! It is not a
Dear Gianni,
It is good to have Mario's comment...
Mario Catamo has suggested me that very probably
the term Italic (in Italic hours) comes from
the Latin word Italicus (that means Italian),
that the word Italianus doesn't exist in Latin
and that until the end of the XVIII century almost
Dear Frans, Roger, Karlheinz, Gianni et al,
Braunschweig is fascinating and I have a new
design to offer. See:
http://www.cl.cam.ac.uk/users/fhk1/BraunschweigV.pdf
and I have an associated puzzle for anyone who
enjoys spherical geometry. See below!
First, some history...
THE SIMPLE CASE
Dear Karlheinz
Thank you for sending us this information...
only in 1985 there were placed a polar
gnomon on the dial from 1346...
If the date of 1346 is correct nobody
knows.
I think you said 1346 is the date of the
buttress into which the sundial is cut.
This is clearly a poor basis for
Dear Roger et al,
Many thanks for your delightful message and
for the associated diagram.
Your improvements to the Braunschweig dial
are very interesting.
The procedure I proposed for an Improved
Braunschweig Temporary Hours Dial must surely
be reinventing a well-known wheel?
To respond to
.
Best wishes
Frank King
Cambridge, U.K.
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Dear Geoff,
You get full marks and go to the top of the class!!
Your analysis almost exactly parallels what I
had in mind and your description is delightfully
eloquent!
SOLUTION TO THE PUZZLE
The S-shaped curves in your attachments are
very convincing. It seems not to be well
known that
just
have one lonely sundial which averages all the
features on these two.
Have great fun!
Frank King
Cambridge, U.K.
---
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to be published annually.
Geocentrism for ever.
You will be pleased to hear that I continue to
show Cambridge first-year science classes diagrams
in which the Sun is in orbit round the Earth! The
word ecliptic comes to mind :-)
Happy New Year
Frank King
Cambridge, U.K
!
Frank King
Cambridge, U.K.
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nautical miles you add a third instead
of a half.
For heights which are small compared with the radius
of the Earth, the results are remarkably good. It is
easy to do the arithmetic that verifies this!
Admirers of Napoleon and his metric ideas may not
appreciate these thoughts!!
Frank King
Cambridge
Dear Aimo,
Ha! Yes I like your metric version...
1. Take your height above the ground in
meters and multiply by ten
2. Add a half
3. Take the square-root
4. The result is the distance to the
refraction rised horizon
It is spoilt slightly by the instruction
to multiply
did the Greeks change to midnight
as the moment one date changed to the
next?
6. Is there a paper or a book or a website
with the answers to these and related
questions?
Many thanks for any help with these matters.
Frank King
Cambridge, U.K
is next best since it has a nice
matt finish too.
Marble I think is hopeless, especially in the UK.
Stainless steel is even more hopeless if left in
mirror condition. Everything Tony Moss says about
stainless steel is right but it sounds very hard
work to me!
Best wishes
Frank King
Dear Mario,
A Very Happy Equinox to you!
Thank you very much for your splendid
answers to all my questions. You have
provided me with many useful references
which I shall study later.
When your book is finished please let us
all know!
I was particularly interested in your
comment about early
+I or H = (B+I)/2 so you are right!
Worked examples:
In my latitude, there are two days either side of the
summer solstice when exD = 2 hours when:
H = B + 4
H = I - 4
At sunrise B = 0 and I = 8 so H = 4h.
At sunset B = 16 and I = 24 so H = 20h.
What fun :-)
Best wishes
Frank King
Dear Mario,
Thank you again for all your help.
I now have a better understanding of
how the Roman Army kept time both day
and night.
For ordinary people, the change from
unequal hours to equal hours must have
been very difficult.
This is more difficult than changing
from liras to euros. There
Dear Mario,
I have now read all your messages again. As Jim
Talliman says...
Thanks for some very interesting scholarship!
One important thing you said is:
When in Italy the hour system changed with the
new hours ab occasu solis, nothing changed
for lawyers and notaries, the roman
strikes and you are out!
Best wishes
Frank King
Cambridge, U.K.
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The following link has nothing
whatsover to do with sundials...
My sound card has gone but I watched
carefully while this nice lady very
closely examined a gnomon which, much
of the time, she held at an angle that
seemed just about right for the latitude
of West Lothian. I think the nodus at
such as:
20090807T060504+0321
Maybe you didn't want to know any of this?
Frank King
Cambridge, U.K.
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Dear John,
Your Burger Puzzle was too hard. Try this...
There was an article in the local paper about
the building where I work and I offered to buy
copies for some colleagues. I went to the boy
who sells newspapers in the street...
Me: How much does the paper cost?
Boy: 28 pence.
Me:
Dear Roger,
Thank you for pointing the list at this
YouTube video
http://www.youtube.com/watch?v=cFH1lz0212o
I found that very compelling and, indeed, all
the associated 10-minute clips.
I particularly noted Al-Battani's expression
for the radius of the Earth:
R =
and SS but these are not
quite what I am wanting!
I think the Aztecs used a pair of animals
and the ancient Egyptians used different
gods but I should be pleased to hear about
other symbols; even a circle with :-) or
:-( might have been used by now!!!
Frank King
Cambridge, U.K
Dear Willy,
I like your symbols very much!!!
There is just one problem...
I think my designer friend wants to put
these symbols on the horizon line at the
beginning and end of the winter solstice
curve...
Of course, with a rising sun, the shadow
of the nodus starts downwards
Dear Willy, Gianni, Carl, Larry, et al,
Thank you all for the splendid selection of
symbols which I shall pass on.
The only ancient one, so far, is the Chinese
symbol sent by Carl. This is the kind of
thing my designer friend was looking for.
I rather like the simple signs myself.
The musical
Dear Willy,
This is an interesting point...
For astrologers, the time of sunrise
and sunset is not necessary...
Is this true? What about astrologers
who use domifying circles?
These circles divide the sky above the
horizon into the Regiomontanus Houses
and the sun passes through each of
Dear Fabio,
That is an excellent list of symbols and
at least one of your friends must have
very clean teeth...
- a whole tube toothpaste and the same
empty and coiled
The bathroom provides may other examples.
For example, you could have a clean-shaven
face at sunrise and stubble at
Dear Fer,
You are right, of course!
I wrote houses when I meant circles.
I still believe that the eastern half
of the horizon circle corresponds to
Domifying Circle #1. As soon as the
sun crosses that circle (at sunrise) it
is in House #12 (as you say). It stays
in that house until it crosses
Dear David,
I use a half a sunburst sitting on a
horizontal line, but with no distinction
between them other than the words 'rise'
and 'set' below the line respectively.
I rather like that. Half a sun clearly
suggests that the sun is on the horizon
and the words 'rise' and 'set' resolve
Dear Chris,
Many thanks for your comments leading to...
R+h=2h/phi^2
as the radius of the Earth given the height
of a mountain and dip (phi) to the horizon.
This is indeed the sensible way to proceed
[hence my note: or knowledge of the series
expansion for the cosine function, or
by several minutes
year on year.
By several minutes I mean about 5 to 7 minutes,
definitely not 61 minutes!
You will have many long winter evenings ahead of
you to ponder all this.
Best wishes
Frank King
Cambridge, U.K.
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Dear John,
This is a good riposte...
You point out here that the declinations
lines normally used (which I assume are
conic sections) are not really correct...
They are indeed conic sections but they ARE correct
provided you call them Constant-Declination Lines
or something equivalent.
If
the years. In 1246 it had left-right
symmetry. (That was a little before my time!)
Best wishes
Frank King
Cambridge, U.K.
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Dear Fred,
You tempt me to digress...
Once we have the idea of graphing tabular values...
It seems that the idea of graphs and graphing is not
nearly as ancient as one might expect.
I commend a book:
Cosmic Imagery: Key Images in the History of Science
- John D. Barrow, W.W. Norton
Richard Mallett wrote:
... dials often become completely unreadable
when left outside...
They do indeed but...
...a sundial which isn't out in the sun is no
more useful than a clock without hands :-)
Frank King
Cambridge, U.K.
---
https
that appeals to me!
Sadly, I recognise that some colourings fade
even in artificial light and sundials which
suffer such sensitivity must, alas, remain
in darkness.
Frank King
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wrote some time ago in:
http://www.cl.cam.ac.uk/users/fhk1/Maggiore.pdf
Unfortunately there aren't very many indoor
sundials in the U.K. Maybe I should do
something about that?
Best wishes
Frank King
Cambridge, U.K.
---
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American.
Health Warning: this article has kept me up
two nights pondering gear ratios and it is
becoming a serious distraction!
Frank King
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wondered
what the closest approximation to it might
be? How much use of gear-wheels (no matter
how simple) is known from that time?
Best wishes
Frank King
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Dear Thomas,
I like your design. You ask for ideas
and comments. Here, in order, are the
steps that I use myself for a big wall
sundial:
1. Make a careful survey of the wall.
The wall will NOT be flat. No wall
is ever flat!!! It won't be vertical
either. No wall is ever
Dear Thomas,
I am becoming addicted to your project!
I would love to come and be your assistant
but I would need too many layers of thermal
clothing at this time of year!!
And I could improve the script to handle
non-flat (not plane) walls, if you give
me a (simple) mathematical description
Dear Tony,
You may have stumbled on a new sport...
He is also said to have fired an air pistol
at a *clay* sundial and urged the patient to
do the same.
I am familiar with Clay Pigeon Shooting and I
can well imagine that when the novelty of doing
that wears off and you want something a
Dear Tony,
I can see you are tempted...
Perhaps the 'staff of office' for the BSSCSS
Secretary should be a bespoke gun by Messrs.
Holland Holland...
I'll duly propose you as Secretary; all we need
is a seconder and the job's yours! There will
probably be a bit of a quibble about the cost
Dear John,
Many thanks for your comments...
Have you considered using the ...
connect the dots method.
Well that's what I normally do but I
set out the dots directly on the wall.
I have a collection of strips of bendy
wood which I use for joining the dots!
The problem with transferring a
Dear Reinhold,
Thank you for drawing our attention to this
fascinating story...
http://www.vignaclarablog.it/200904255581/formello-un-piccolo-gioiello-astronom
ico/#comment-10072
The gnomonisti who did this restoration are to
be congratulated.
There is one sentence which troubles me. In
a
Dear Mike,
It is worse than you assert...
The Sun's position coincides with GMT
on four days of the year...
... this is only true if you live on
the standard meridian appropriate to
your time zone.
Given that they are talking about GMT,
it is not sufficient to be close to
your friendly
Dear Thomas,
You ask interesting questions and the
answers depend slightly on just how
precisely you want the model the way
the sun goes round the ecliptic.
QUESTION 1
... do [Gemini and Cancer] share
*exactly* the same region [on a
sundial] or not?
I think it is reasonable to DEFINE
the
pass the Indiana bill that
attempted to set the value of pi to 3.2,
but only during the summer of course.
Oh, how about adding $1bn to all bank
accounts too?
Hey, wait a minute. Didn't they already
try that one?
Enjoy your extra daylight!
Frank King
Cambridge, U.K
published my remarks. Look at:
http://www.bbc.co.uk/radio4/features/farming-today/comments/
Please send in some more!
Don't let Governments fiddle with time!
Frank King
Cambridge, U.K.
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/Selwyn.pdf
It is a shame it is cloudy now. The U.K. is
not a good place for sun :-(
Frank King
Cambridge, U.K.
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Dear Tony,
Many thanks for your kind message. You are
right to draw attention to:
Letters Slate Cut by Kindersley Cardozo
ISBN 0 9501946 7 0 where the tools and
techniques are described in detail.
My role in their dials is confined to the
calculations and the setting out and a share
of
Dear John,
Many thanks. Several people have asked
the same question...
Is that real gold leaf gilding?
Yes, it is real gold leaf. The nodus and
nodus support are made of brass but they
are gilded with gold leaf in the same way
as the sun, and the Babylonian Hour-Lines,
and associated
puzzle for you all to
enjoy...
Why are the two rates not equal and opposite?
Why 6 seconds per hour for Babylonian hours
and just 4 seconds per hour for Italian hours?
I don't know whether I am educating the locals
but I'm certainly educating myself :-)
Frank King
Cambridge, U.K
Dear Frank,
You pose two questions:
1. How do you lay out Babylonian and
Italian hour-lines?
2. Why use dubious definitions of
sunrise and sunset?
I attend to the dubious definitions below
but let's live with them for a moment.
BABYLONIAN AND ITALIAN HOUR-LINES
Let B =
Dear Jack,
You go straight to the heart of the matter...
I was struck by the fact that the Italian and
Babylonian hours coincide (cross each other)
at the equinox line but not at the solstice
lines.
It is, of course, these criss-crosses which
make having the Babylonian+Italian hour-lines
Dear Gianni,
I like your explanation and I like the
extra comments too.
You have:
P1 on the equinoctial line and
P2 on the horizon line
This is good in theory but not so
good in practice. For example, my
line for Bab = 11 does not run
as far as the equinoctial line or
the horizon
Dear Gianni,
I enjoyed your explanation and (I liked
the deliberate mistake which you included
to make sure we were paying attention)...
If we have a horizontal sundial we
cannot use the method that I have
described yesterday.
Of course, we CAN use your yesterday's
method provided we accept
Dear Frank,
This is an interesting thought...
I'm starting to think that for a vertical
dial in Italian hours it would be simplest
to use the old dialist's trick of laying it
out as a horizontal dial at ninety degrees
away.
I think you will find a tiny snag or two in
this approach! You
Dear Gianni,
Your analysis has silenced the Lista Inglese!
I will summarise what you said so that new
readers may start here...
You have:
D = length of day (sunrise to sunset)
Whenever D is an integer number of hours, the
associated constant-declination curve passes
through a hyperbolic
Dear Roger,
You are right...
This gets more interesting with each note.
The business of labelling gnomonic features
elegantly can be a nightmare!
With an ordinary sundial you have a chapter
ring of one kind or another for the labels of
the hour-lines and life is straightforward!
When you try
Dear Gianni and Roger,
Thank you very much for the clarifications.
Gianni's table is especially clear about
the two cycles of 12 for Italic hours as
used in the Muslim world.
Chris Lusby Taylor's comment is true in a
way but, equally, your original remark can
be interpreted as being correct.
Dear Chris,
Your diagram is a masterpiece!
I still find it intriguing that
the simple-to-define concepts of
Babylonian and Italian hours open
the way to a feast of geometric
delights.
With you dreaming up such eloquent
mappings, this feast clearly has
more courses to come!
All the best
Frank
Dear Mac,
I like your H2SS Card.
You say...
My foolish thought was that every
golfer and hiker and outdoors
person would want this information.
Not so foolish! They DO want this
information but maybe you were
marketing it in the wrong place
and to the wrong group...
The big snag with
Dear Karlheinz
Those are very interesting photographs...
http://www.antike-sonnenuhren.de/fotosbyz.htm
but, in most of them, your comment AND Roger's
comment are BOTH right:
YOU are right that the LINES are marked but
these lines seem to run along the middles of
the hours that one
Dear Doug,
I enjoyed your message. You end:
I hope that I have shed some light on the
annual silly debate, and look forward to
some acclaim (I hope) and probably some
protests.
In my experience this debate takes place twice
a year but, that aside, you may have my acclaim
but also my
Dear Doug,
You make a host of interesting points in your
follow-up...
Did the shift [to our semi-nocturnal life style]
begin with the industrial revolution when better
lighting became available with brighter oil lamps,
incandescent gas mantles and then electric lighting?
These technological
Dear Frank
Your local comprehensive school is a
good example of accepting the natural
inclination to getting up later and
later. By shifting from 9-4 to 10-5
they will precisely nullify the effect
of summer time! Tee hee!
I have been rebuked for spelling
dialist ... instead of diallist.
Dear John,
Many thanks for your illuminating comments.
Alas I made a typing error...
Compared with their fellows in the easternmost
15 degrees, the others are effectively living
with single, double and quadruple summer time.
I meant triple rather than quadruple of course.
This is
to hear who does what!
Frank King
Cambridge, U.K.
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Dear Fer,
Thank you for your message. Your procedure
is almost exactly like mine. I also start
with the equatorial plane (I missed that
step out in my message). I then:
1. Rotate by phi (to make the plane vertical)
2. Rotate by Azimuth (to face the plane in the
Dear All,
The beer-glass sundial spotted by Mike Cowham brought
on a panic attack. More strictly, it was his comment
that caused alarm...
The glass acts as the gnomon but the real horror ...
midday was at VI.
Maybe every reader should pour a glass of beer (or
something stronger) before
Dear John,
That is a great dial. I really must look
into this glass-based colouring that you
use. I can testify to its durability.
The six dials on the Gate of Honour at
Gonville and Caius College are made with
this technology and their colours look
almost as good as new after the better
part
Dear Tony,
You say...
I shall be staying near Brescia in Lombardia...
One thing you can do is to visit
http://www.sundialsatlas.eu
You then click on the map button at the top and,
by dragging the map and zooming, home in on Brescia.
Alas, there are no sundials shown in
Dear Reinhold,
Your news is good news...
The Italian sundial catalogue
announces 24 sundials for Brescia!
My news is bad news...
Alas, there are no sundials shown
in Brescia itself...
I think I should have punctuated my
remark differently and added a t:
Atlas: there are no sundials
Dear Fabio,
You mention some reflection sundials...
In the Convento di San Cristo you can find a
reflection sundial...
In Italy there are other four ancient reflection
sundials ... in the provincia ... of Bergamo, beside
the Brescia one.
... another one is in Palazzo Spada in Rome...
Dear John,
I'm asking you guys if you have seen any
relationship between owls and sundials.
I once tried very hard to establish such a
relationship but my best intentions were
not appreciated...
I had a client and I wanted to symbolise
sunrise and sunset on the proposed sundial.
I offered a
Dear John (and Willy, Aleks, Wolfgang, et al),
I have greatly enjoyed the all the answers
to your question about Owls and Sundials...
Willy Leenders tells us that the Dutch word
zonnewijzer really means wiser sun. How
many of us knew that?
Aleks has sent us a nice illustration of a
sundial
convincing, but there is
something horribly wrong with the
gnomon!
Last summer the Hughes Hall May Ball
supported the World Owl Trust and two
owls were present as guests.
Frank King
Cambridge, U.K.
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cast a straight-edge
shadow :-)
I suspect that the writers of this browser are
not NASS members!
As you rightly say:
Why this name was chosen is not clear.
Maybe someone should try using the browser!
Frank King
Cambridge, UK
---
https
a disappointment.
Either, at the critical moment on the
critical day, the sun isn't shining or
on a quite different day the sun happens
to be in the correct direction and spoils
the story.
Frank King
Cambridge, U.K.
---
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College
but this is proving challenging too. There weren't
many women's colleges in those days so I may have
to search each one in turn.
If anyone has any leads please let me know.
Frank King
Cambridge, UK
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Dear Fred,
As usual, your encyclopedic knowledge has
come up with a couple of nuggets!
http://tinyurl.com/2fpvfah
http://rfrost.people.si.umich.edu/courses/MatCult/content/bladerunner.pdf
These are fascinating and most helpful.
Very many thanks indeed.
Frank
Dear All,
Fred Sawyer notes a plea to President Obama
to have a sundial which was originally in
Hawaii, but is now in Maryland, returned to
its rightful place:
http://www.congress.org/congressorg/bio/userletter/?letter_id=6195591101cont
ent_dir=politicsol
If President Obama is successful,
Dear Wolfgang,
You have come up with some most interesting
references to Kathleen Wright (née Higgins).
At last we know her Oxford College, Lady
Margaret Hall.
I enjoyed your calculations that lead to her
being born in 1926...
Died 1 January 1999 aged 72, therefore...
Since she died on 1
Dear Woody,
This is indeed good news...
http://www.gcstudio.com/suncalc.html
is back working.
I too made much use of GC Studio and greatly
missed it while it was down. As Bill Gottesman
suggests, it must have been off-air for a year
or more.
This is the great snag about the Internet...
almost nothing about iPhone camera
technology and cannot give a convincing
explanation of the physics behind this
artifact.
There is also the surrounding elliptical
red background to explain. Could that be
an image of the hot front surface of the
lens?
Any thoughts?
Frank King
Cambridge, U.K
Dear Tony,
Just to lower the tone a bit more...
I have a colleague who comes from Copernicus's
home town of Torun. Whenever he is asked about
his ethnicity he always says I am a North Pole.
All the best
Frank
---
Dear Brent,
You correctly note...
It looks like the date must have changed at noon.
Indeed so. Interestingly, even with GMT (as used by
astronomers and navigators) the date used to change
at noon (which was referred to as 0h GMT). This was
the case until 1 January 1925, so not very long ago!
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