s between successive
vernal equinoxes (say) can vary 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.
--
Dear Roger,
It is good of you to remind us of the bronze
ring set in the Square Hall of Alexandria.
You add...
> You can repeat this experiment on any
> correctly aligned equatorial sundial
> or armillary sphere.
You can in fact undertake the essentials
of the experiment using ANY sundial equip
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.
er the years. In 1246 it had left-right
symmetry. (That was a little before my time!)
Best wishes
Frank King
Cambridge, U.K.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
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 & C
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.
--
have to have sundials in museums this is
the kind of thing 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
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
the Dan Brown spoof I
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.
--
American.
Health Warning: this article has kept me up
two nights pondering gear ratios and it is
becoming a serious distraction!
Frank King
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
t;unique artifact". I 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
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
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 vert
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 descriptio
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 li
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 c
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 note
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 friendl
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
ng this of
their own accord?
There is no need to tell lies about the time!
Frank King
Cambridge, U.K.
P.S.
Russell was once challenged at a talk...
OK, suppose you accept the false assumption
that 1+1 = 3, can you prove that you are
the Pope?
Certainly said Russell. You subtract one
o all speedometers. We could
finally 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 da
using "offensive or
defamatory language"!
Ooops! I have just checked and they HAVE
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.
--
c.uk/~fhk1/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.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
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
o
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 numbers
ittle 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
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 = Babylo
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-line
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 line!!
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 accep
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! Yo
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 arc
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. You
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 al
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 sees
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 pro
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 technologi
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
hear who does what!
Frank King
Cambridge, U.K.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
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 rea
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 of
Dear Geoff,
Many thanks for your kind words...
> Congratulations on implementing a novel dialling
> concept in such a beautiful dial.
As you may infer from the citations in my covering
message: you and Gianni Ferrari were the two people
who made me think extra carefully about what I was
doing!
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 Bresci
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 sund
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 Gianni,
You mention:
The time of the Islamic Prayer Zuhr (noon prayer)
The time of the Islamic Prayer Asr (afternoon prayer)
The time of the Islamic Prayer Maghrib (sunset prayer)
The time of the Islamic Prayer Isha (night prayer,
at the end of the astronomical twi
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 wi
incing, the dial is
reasonably 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.
---
https://lists
even 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
-
ou could draw a straight
line through.
These things are usually 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.
---
xford 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
---
https://lists.uni-koeln.de/m
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=6195591101&cont
ent_dir=politicsol
If President Obama is successful, may
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 J
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...
know 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
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
---
https://lists.uni-koeln.de/mai
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!
Dear Andrew (and Fer),
Many thanks for this reference...
http://www.aandc.org/research/nautical_time_and_date.html
That is a splendid article and shows just what pitfalls
one can fall into when attempting to force historical
data to fit the present way of thinking!
I share your thought...
Dear Roger,
As your reference to French Revolutionary Time
says:
The hundredth part of the hour is called
decimal minute; the hundredth part of the
minute is called decimal second.
With 10 hours in the day (one mean Earth rotation
with respect to the sun) this gives:
10x100x100 = 100
Dear Richard,
You refer to a Portuguese communal flag...
> This is the only example I have seen of a
> sundial on a flag (combining two of my
> interests) - are there any others ?
You might look at the Portuguese National
Flag which has an armillary sphere as its
background. See:
http://en.w
Dear Frank,
You say:
I have not come across an altitude dial
resembling an analemmatic dial in that the
gnomon is moved with the seasons and the
time curve is a single ellipse.
One interpretation of what you seek is to
have a dial on a vertical wall where the
gnomon is horizontal (and pe
de sundials,
> even if they are built on a vertical wall.
Nevertheless, I think the sundial that Frank Evans
wants IS an Analemmatic Dial on a Vertical Wall.
He wants an elliptical hour ring and so on.
Perhaps he will tell us all soon!
Frank King
uld like explained is
just what projection is used.
Can James Morrison comment please?
Frank King
Cambridge, UK.
---
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Dear Marcello,
Several members of this list have been discussing
the Brazilian National Flag privately. We would like
to know how accurate it is!
The best article I can find is in:
http://www.zenite.nu/04/0804.php
The key paragraph is:
Adotada em 19 de novembro de 1889, seu
Dear Marcelo,
Many thanks for your reply...
> ...the republic was officially proclaimed
> (signed) at 8:30 am on 15 November 1889
That is very impressive. Most people I
know are hardly awake so early in the
morning.
> Methinks it [sidereal time] is mentioned
> in the legislation to avoid ambig
Dear John,
I really enjoyed your analysis distinguishing the
standpoints of British and U.S. diallists when it
comes to longitude-corrected dials. I need to
send two replies. Here is the first...
In the U.K. most of us are indeed fairly close,
in time, to the Greenwich Meridian. I am about
26
Dear John,
Your inspiring message about longitude correction
prompts more thoughts from me. You say:
> ... most of our [US] Time Zones have wiggly
> irregular boundaries that sometimes span
> distances far greater than 15 degrees.
Everyone necessarily lives within 7.5 degrees of
a multiple of 1
Dear John,
That is a fascinating map...
http://www.travel.com.hk/region/timezone.htm
It bears out many of my prejudices and gripes!!
Alaska seems to be a whole time-zone wrong and
John Pickard's eloquent contribution draws
attention to the curious way that Australia
is carved up.
One particu
Dear John,
I looked into your interesting assertion about
the Equation of Time. You say:
On the average, it is only off [mean time]
by about seven minutes...
It isn't really appropriate to use the term
average here because we are not dealing with
random variables or errors. We are just loo
Dear John,
I sympathise...
> I flunked statistics in college.
I never got the hang of statistics until I
was fingered to give a lecture course on
the subject and I have never looked back!
In dialling, I use statistics for error
analysis and also when trying to do things
which are impossible! R
Dear Brent,
You have started an interesting train of
thought. You, and others who have replied
to you, should dig out the February 2011
issue of Scientific American and read the
article:
How Language Shapes Thought
This is subtitled:
The languages we speak affect our
percept
Dear Jackie,
That is an interesting observation...
> ... I moved from London to Brighton...
> In London it seemed usual to say it's on
> the left of the street, but here on the
> coast, far more people say it's on the
> east side.
Next time I am in Brighton I shall test the
natives.
The natives
Dear Claude,
Those are fascinating pictures especially:
http://www.gallerydiabolus.com/gallery/upload/utisz/my%20sun%20and%20your%20s
un3.jpg
This is almost straight out of M.C. Escher!
You ask:
What's the declination of that wall?
That's a fun question. As with many Escher
drawings the
Dear Willy,
I am not very familiar with the Prague
clock and I am confused by the recent
messages. You say:
... the clock indicates now Central
European Time rather than solar time
as it once was...
This suggests something far more radical
than simply setting the clock for the
wrong longi
Dear Jim,
I am grateful to you, and to Willy and Geoff,
for various points of clarification. The key
point in your comment is:
A hand with a Sun figure rotates once in
a mean solar day...
This at once distances the clock from an
astrolabe where, properly set, you look at
true solar time and
Dear Brent,
You ask a fascinating set of questions.
> Has the leap year problem been solved with
> solar calendars?
At one level, the problem is intractable. You
get defeated by the calendar bequeathed to us
by Pope Gregory XIII...
The problem is that the Gregorian calendar is
hardly an improv
Dear Brent,
Slight goof. In step 7 I meant to say:
7. Keep going until 12 noon on 29 February
next year. You will have drawn EXACTLY
366 little lines. [Note that 29 February
is 365 days AFTER 1 March the previous
year, not 366 days.]
You have 366 lines and 365 normal gap
Dear Andrew,
Thank you for your two messages, sent off-list but my
response may be of trifling interest to others...
It is true that 128 tropical years is very close
to 46751 days but when it comes to a real solar
calendar (one you can look at and say "Oh, I see
that today is 9 March") I regard t
Dear Brent,
Thank you for your follow-up...
> While I am trying to digest all of that I
> have a new question.
>
> Do the ancient solar calendars like the
> Incas still work?
>
> Do their rocks still show where the
> solstices will occur now?
I am not an expert in this area and others
may supply
Dear Brent,
I understand your excitement...
> In my excitement I forgot that solstice
> to solstice is not one year but only one
> half of a year.
But is isn't :-(
The best you can say is that it is ABOUT
half a year. The Earth doesn't have a
circular orbit and the solstices don't
coincide wit
Dear Roser,
Willy Leenders is quite right that...
PERIGEE is the point in the orbit of
the moon or a satellite at which it
is nearest to the earth.
BUT...
Strictly, this is when the centre of the
moon is nearest the centre of the Earth.
YOU are unlikely to be at the centre of
the Eart
Dear Reinhold,
I see you are trying to provoke me...
> Frank King will tell us perhaps a nice
> sounding Latin expression?!
This is the worst day of the year for me,
truly...
Dies irae, dies illa...
The day of wrath, that day... :-)
Or, perhaps, you seek my thoughts on whoever
go to the trouble of making a flint sundial when
you can stand up straight and look at your own shadow?
Frank King
Cambridge.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
Dear John
You write...
> How in the world did your local Education
> Authority reach the absurd conclusion
> that interactive human analemmatics are
> "dangerous for children".
Have you never heard of the expression about
"being afraid of your own shadow?"
This is a well-known phobia which has
Dear John,
That looks to be a monumental achievement
in several senses!
http://www.flickr.com/photos/jlcarmichael
Judging by the photographs, you could have
set this up with any orientation you liked
so some questions:
1. Why did you choose to have it facing
south-west? [Do the loca
Dear John,
Many thanks for the follow-up. I now
have a heap more questions!!
In your drawing you have half-hour dots
and quarter-hour tick-marks. In the
photographs, I can't see the tick-marks.
Is that my poor eyesight or did these
get lost as a budget-saving measure?
Also in the drawing, you
sun is shining. What you see
are Fabio's alignment hours.
Frank King
Cambridge, UK
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
t and the 12h hour line
on the side that faces south and so on.
I have a final piece of advice...
If you really want to drill lots of holes
at awkward angles you are going to need
some kind of jig. I cannot think of a
good way to design this jig but I am sure
there are other list members who can h
Dear Kevin,
I was interested in your comments on EoT.
I agree that the kidney curve is not very
pretty. You would be happier if we could
go back to the year 1246 when the analemma
had mirror symmetry about its long axis.
This would tidy up the kidney a little!
You say...
> ...the master of all
Dear Chris,
As always, you prompt further thought...
> Gears, although limited to an integral number
> of teeth, are essentially analogue devices,
> aren't they?
Er, not sure :-)
In earlier days, I spent many a happy hour
looking at clocks and counting teeth. That
felt like a digital experienc
Dear John,
Yes, I like your candidates...
> The Washington Monument
> Stonehenge
> The Earth!
How about Jupiter and its four principal moons?
You can tell a lot from the various ways they can
go into eclipse.
Oh, and if you want an expensive man-made sundial,
how about the Martian sundial by Bi
Dear Brent,
You note:
> The people who live in the tropics have
> another special event, when the sun is
> directly over their latitude.
This is not quite true unless you go to
an enormous amount of trouble. If you
live in the tropics, what normally happens
is that the sun crosses to the south
Dear Jackie,
You are right...
> I seem to remember hearing about a "sun well"
> ... The sun only shone right down it at midday
> when it was directly overhead.
I once made a hunt-the-sub-solar-point trip to
Hong Kong. I had been invited to give a course
of lectures but I insisted on visiting a
Dear Frank,
I enjoyed your message about determining your
position when the sun is close to overhead.
Your theory is sound and I certainly cannot
compete with your practical experience but
something bothers me...
> You measure the sun's altitude assuming
> it is within a few minutes of arc from
Dear John,
Yes, Eratosthenes was a great man who is
also noted for his sieve for extracting
prime numbers.
This may not be the right list for asking
about the performance of camels but I am
intrigued that it took a camel 50 days to
travel from Aswan to Alexandria.
The straight line distance is a
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