critical moments.
2. The compass rose is of 24 points. I am more
used to 8, 16 or 32 points. How common
are 24-point compass roses? They are
suggestive of hours of course but only
very loosely.
3. Any chance that 29 February features? :-)
Frank King
Camb
Dear Gianni,
Mea culpa! You are of course right. The
summer solstice arc indeed curves upwards
on a cylindrical surface.
I was assuming that the surface was made of
flat segments (as in the external photograph)
but this is not so.
> - The higher line (at ¾ of the height of the
> doors) (alumin
me banter
Tempora mutantur
Nos atque mutamur in illis.
This Latin is certainly seen on sundials!
Frank King
Cambridge, U.K.
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Yes indeed. Can someone supply a photograph taken at
a much less convincing time just so we can all be sure
we are not suffering from a double bluff!
Maybe even the gnomon and its shadow are painted too!!!
Frank King
Cambridge, U.K.
---
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ncommon but, unless they are made from
a matt material, you can get blinding reflections from
them when you try to read the time near noon!!
Frank King
Cambridge, U.K.
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Dear John
CAMBRIDGE POLYHEDRAL DIAL
I have just received the June BSS Bulletin...
You are to be congratulated on the cover photograph.
Somehow, you have contrived to make what I regard as
one of the most unprepossessing dials in Britain seem
almost elegant!
For over 40 years my no
Dear John et al,
You are giving me some second thoughts...
> I think you are a little harsh on the Downing Site
> polyhedral dial ... which shows so well that the
> gnomons of dials on any plane are all parallel.
Yes, that is certainly something I point out when I
show it to people. You can see
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.
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Dear Frank et al,
An intriguing side issue to your puzzle is that
it relates to the discussion about the Hawkeshead
dial and the notion of a Plane's Longitude and,
implicitly, the notion of a Plane's Latitude.
Once you have taken on board these notions, the
simplest way of expressing the solution
Dear Frank et al,
After a second night sleeping on your nice puzzle I
realised that I DID make a small goof in one of my
assertions and no one has picked me up on it!!
In the formula:
tan(dec) = [-]sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2)
I asserted (correctly) that the argument of the square
Dear John,
Thank you for your suggestions about repairing or
restoring the Downing Site sundial...
> ... a possible solution might be to make a set of
> brass dialplates, each a little smaller than the
> polyhedron's faces, and apply them to the existing
> stone around the gnomons. These would a
Dear Warren,
Happy Summer Solstice!
You ask an astute question:
> Are you saying below that ANY two locations MUST
> have a moment of mutual sunrise/sunset?
Well, I am ALMOST saying that and the mathematics
IS saying that...
The declination of the sun is, of course, constrained
to be between -
as times.
I frequently do this in lectures when I use a
300W lamp and I can wander around simulating a
winter day or a summer day and so on.
A 300W lamp is a bit dangerous for children but,
on a small scale, a suitable torch would do.
Enough!
Frank King
Cambridge, U.K.
--
Dear Roger,
I enjoyed your response to my playground thoughts
and I enjoyed your puzzle even more...
> Calculate the time for the sun to be at azimuth
> of 45º for the summer and winter solstices for
> a given latitude, say 50º.
Alas, I can add nothing to Fred Sawyer's reply.
It is easy to expr
Dear Roger and Mashallah,
Many thanks to you both for a most interesting dialogue.
May I suggest three sundialling heroes who, you will see,
are very relevant your discussion:
1. Frank Evans - The Inspirer
2. Gianni Ferrari - who pointed us at...
3. John Good - who can laugh at us all
Dear Roger,
No one seems to have responded to your interesting letter to
the Editor of the BSS Bulletin.
May I join in?
SEASONAL MARKERS
You write about Seasonal Markers on analemmatic sundials.
Seasonal Markers are two special points on the major axis
of the ellipse (of hour marks). If you s
ho doesn't
know that the time of sunrise at an equinox is 6 o'clock
probably won't be very interested in the Lambert circles!]
Perhaps you should go out with spray paint one night and
mark in some Lambert circles on an analemmatic sundial
near you!!!
Best wishes
Frank King
Cam
you don't
know the length of the day you cannot say by what
fraction of a day the year exceeds 365 days!
What we can be sure of is that for the period 500 years
either side of where we are now, this fraction averages
a lot closer to 8/33 days (the Omar Khayyam value) than
it does to 97/400 days
Dear Doug,
Hong Kong is one of my favourite places but
I do not recall any sundials alas.
That said, there is one place which is just
asking to have a sundial of a rather special
kind and you simply must visit it...
This is the extraordinary HSBC Headquarters
Building which, in plan, is a hollow
Dear Tony,
Sundialling is undoubtedly a very dubious activity
whose practitioners should be treated with the
greatest suspicion.
Try going round a London Square with an architect's
drawing full of arrows all pointing at the Stock
Exchange and labelled "clear view 11:30 to 2" or
"in shadow after 3
additional
assumptions you have to make.
Hey, I feel an examination question coming on!
Frank King
Cambridge, U.K.
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I am not sure about
dialling.
Like many Cambridge Colleges, Newnham has a couple of
sundials: a late 19th century horizontal dial and an
early 20th century pillar dial with four dial faces).
The College has limited parking alas.
Frank King
Cambridge
s formula is rather like using someone else's
toothbrush.
Best wishes
Frank King
Cambridge, U.K.
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I hope you aren't wishing you had never asked
the question!!!
Best wishes
Frank King
Cambridge, U.K.
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the time so again there is no sunrise and
therefore no meaningful azumuth.
You get analogous problems in the antarctic when
phi < -67 degrees.
Best wishes
Frank King
Cambridge, U.K.
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Dear Warren,
Many thanks for supplying Bill Gottesman's comments
which I very much take to heart.
Getting good sightings at sunrise and sunset in real
life is seriously challenging and even when you are
in luck, the shadows are weak and the effect of
refraction is at its greatest and you have to
Dear Geoff,
Yes, you are absolutely right. Silly me for not spotting
a trivial simplification! It is, indeed, much neater to
write:
> cos(az)=sin(dec)/cos(lat)
This also readily shows that reversing the sign of the
declination results in 180 degrees being added to (or
subtracted from)
fter 12 noon but, on thinking about it, I can see several ways
to arrange for shadows to begin lengthening at exactly 3 o'clock.
Would anyone else like to make some suggestions?
As it happens, with just over an hour to go, it is 100% overcast
here so this puzzle is rather academic!
Ha
Dear Geoff,
Yes, I agree with your hasty calculation (having
taken far longer than you to do it!)...
> A hasty ... calculation suggests that a vertical
> dial declining about 38 degs west of south in the
> latitude of Cambridge might experience its shortest
> shadow around 1500hrs.
This was one
Dear Jack,
I enjoyed your the motivation...
> My original question was sparked by wondering about
> the maximum deviation from east-west at the solstice(s)
> so I could display my erudition and bore people with
> comments like: "The sun rises in the East and sets in
> the West, right? Well, not r
Dear Roger,
You chide us :-)
> ... few have been doing their homework, proving that
> Cos Phi = Sin Lat / Cos Dec
The truth is that Geoff Thurston supplied the answer
(well almost the answer) on Christmas Eve so I thought
we could all have a rest!
Geoff and you have both referred to the same cr
han done too! How
bright are the lights of the buildings in the
vicinity?
What worries me is that this splendid device will
be rather wasted in a location with so much light
pollution.
Maybe the light problem is not as bad as I am
guessing?
Best o
f) and, indeed, is still used with this meaning in
certain parts of Scotland. You will need to search in a
very big dictionary to find out more!
Best wishes
Frank King
Cambridge, U.K.
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Dear Willy,
> Following your suggestion I was searching in a
> very big dictionary to find out more...
Alas, your dictionary was not quite big enough!
The full Oxford English Dictionary will give you
details of the meaning of "quaint" as understood
by Shakespeare and Chaucer. Interestingly it i
this kind of sundial!
Best wishes
Frank King
Cambridge, U.K.
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Dear John,
Your question intrigues me...
> The sundial will be located at local meridian
> (longitude) -77.0769 degrees. If it had a
> normal time zone, the Standard Meridian would
> be -75 degrees (UT+ 5 hrs.).
True.
> But since its Time Zone is UT +5:30, then
> wouldn't its Standard Meridian
Dear John,
Many thanks for the clarification...
> Oh but it does matter...
Ah, I now understand...
> The reason is that this dial needs to be corrected
> for longitude shift (called Standard Time in ZW 2000).
OK. All understood so far.
> If I'm not mistaken, you are correct for those dials
>
Dear Chris,
I am a bit behind with my reading and I have only
just read your comments, and corrected comments,
on the umbra discussion.
Subject to your corrections, I concur with almost
all you say but I feel a little amplification of
one of your follow-up remarks is needed. You
say...
> If the
Dear Chris, John [Davis], et al
Thank you for your replies. I do remember the Allen
Mills article and will dig it out. Amongst other
things I think he noted that the solar disc isn't
as bright at the edges as in the centre (astronomers
call this limb-darkening) and the obvious point that
cutting
signature. Meanwhile...
Happy Palm Sunday
Frank King
Cambridge, U.K.
Here is the distribution of possible dates for Easter
over the 5,700,000-year Easter Cycle given the current
algorithm for determining the date and given the
Gregorian Calendar:
Dates Counts
22 March
Dear Mac,
Many thanks for your message...
> If you can find the time, this mailing list member ...
> would much appreciate details about how you derived the
> list of dates.
I am glad you asked this question and equally glad
that Patrick Powers has supplied the algorithm!
I had it in my head th
ht UTC!!
One might suppose the longitude of Rome was
used, or perhaps Jerusalem, or somewhere else?
Even when you settle on the longitude, you still
have to decide whether your two consecutive
instants of inferior solar transit relate to the
true sun or to the mean sun.
Anyone know?
Happy Eas
have
coincided and your client would be a happy lady!
Sadly, you cannot rely on this but it is nice to
be lucky once in a while.
Happy dialling
Frank King
Cambridge, U.K.
---
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he Latin "horologium solarium"
that I can happily live with it.
Intriguingly, non-dialling Italians normally use
the word "meridiana" to mean "sundial" even if
noon doesn't feature on the instrument at all!
OK, b
one with the other but they are parallel to the
horizon line.
Can you show that the vertical separation of this
12-12 line from the horizon line is n.tan(2.phi)
where n is the nodus height and phi is the latitude?
Maybe you could test your client with this?
Happy dialling
Frank King
Dear Tony,
I was about to get in touch when your own
message to the mailing list arrived in my
inbox.
By chance, I met Louise Rigozzi on Saturday
when Mike and Val Cowham and I took three
groups of people on Sundial walks round
Cambridge.
Louise was in my group and introduced herself
as coming f
meridan that puts the
180 degree meridian between Russia and Alaska
then Hamburg would have been a good choice for
the prime meridian.
Certainly Mecca would be a poor choice!
As one who lives close to the Greenwich Meridian
I am content to leave the prime meridian where
it is :-)
Frank King
Ca
Dear Jim and Chris,
I have been enjoying your correspondence
and I have a shocking confession...
When I studied the numerous delights of
astrolabes.org/anaphoric.htm
I looked at the drawings of Leo and I
didn't notice that it was the 'wrong'
way round!!
If I show you a decent drawing of
Dear Doug,
I am so riddled with prejudices about type-setting
equations, and mathematics in general, that it is
hard for me to give a temperate reply to your
enquiry...
> Material often comes ... in Word, and it seems
> that equations do not transfer reliably.
In my view, the Microsoft Equation
Dear Doug et al,
I may have missed a crucial message but the
most obvious starting point for solving the
problem of getting from A to B is to use...
Dijkstra's Algorithm
This was devised by the great Dutch Computer
Scientist E.W. Dijkstra in 1959 for finding
the shortest distance betw
would be for
such a facililty?
For completeness: the photograph was taken
in Piazza Dante in Naples.
Frank King
Cambridge, U.K.
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changes to the Equation
of Time too.
Frank King
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us how he fixed his dial
in Longyearbyen. That was a pretty cold
fixing occasion!
Best wishes
Frank King
Cambridge, U.K.
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Dear Roger,
This is a more public expression of enthusiasm
for your Ottoman Sundial. I very much enjoyed
looking at your PowerPoint via...
http://www.walkingshadow.info/Ottoman.html
The dial looks splendid and I don't think the
re-orientation is a distraction.
I have some comments on the wr
Dear Rheinhold,
Thank you for the pointers. I especially enjoyed:
http://www.ta-dip.de/42c37914dacf0f667e8c985684d07416_Nr_111_Goethe_Uhr.pdf
I knew about Goethe's enthusiasm for
Italian hours but I didn't know that
he wrote about them to his lady friend
back home. I am not sure this is the
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 o
dei Martiri in Rome. 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
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 fello
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 yo
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 dire
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 priv
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 misinte
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:
http://penelope.uchicago.edu/
moved from
Cambridge but you can still 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.
---
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 seri
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 centu
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 basi
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
able to answer other questions
that occur to you.
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 tempo
ving.
Of course, if you want to be boring, you can 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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about sundials. [Do Times readers have no interest in these
instruments?]
Equally unfortunately, the published version leaves out the
important comment that those who want an unchanging timescale
can use GPS time. Moreover, GPS time is provided free!
Best wishes
Frank King
Cambridg
for
navigators continue 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 :-)
H
could be a rewarding challenge!
Frank King
Cambridge, U.K.
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want 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
Camb
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 b
use?
5. When 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
limestone 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
F
Dear Mario,
Thank you very much for your splendid
reply. The quotations from Censorinus
are exactly what I was looking for!
I like the title: De die natali liber!
You say that the intere nychthemeron
was divided into 24 equal hours from
midnight till the next midnight.
Were these equal hours co
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 c
= B+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
Fr
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 ci
ted three or more times.
Two 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 a
time 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,
You have indeed had some excellent advice,
especially from Edley and Kenneth.
I don't make sundials and I have no knowledge
of the U.S. market but I work for a number of
workshops that make sundials as well as plaques
and memorials and such like.
Some things are indeed recession proof
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: M
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 = h.cos(phi)/(1-cos(
and I
have also seen SR 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
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 r
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 c
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 suns
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, o
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