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 improvement on the Julian calendar.
Indeed, right now, we are barely half way
through a near 200-year run of pure Julian
calendar. The last time a leap year was
omitted from the regular 4-year cycle was
in 1900 and the next time will be 2100.
The Julian drift which prompted calendar
reform in 1582 is very much still a problem
for those of us who build calendars into our
sundials.
OK, end of ranting about Pope Gregory (who
actually had many merits but calendar reform
wasn't one of them).
All that said, you can have a perfectly good
solar calendar which will work just fine for
36 years before Julian drift defeats you. If
it is a painted sundial, you could leave some
documentation as to how it should be repainted
every 36 years and set up for the next 36 years.
Let's start afresh with a minimalist sundial
which is set out on horizontal ground and
consists of a nodus and a noon line and
nothing else.
Proceed as follows, starting at local sun noon
on 1 March 2011. This is a crucial date. Pity
you missed it!
1. From, say, four minutes *before* local sun
noon until spot on sun noon sketch the
path traced by the shadow of the nodus as
it approaches the noon line on 1 March 2011.
2. Repeat on 2 March 2011. The declination
is slightly higher so the path will be
very slightly further south than the
path was the previous day.
3. Keep going until the summer solstice.
The succession of lines will now stop
heading south and begin to head north...
4. Still keep going but, to avoid confusion
in the sketch, trace the path from spot on
sun noon until four minutes *after* noon.
This way, as the sun's declination
decreases and your sketch folds back on
itself, you won't have little lines
messing up the ones you already drew.
5. Keep going until the winter solstice.
6. Still keep going but now go back to
sketching lines *before* noon. The
lines will start heading south again.
7. Keep going until 12 noon on 29 February
next year. You will have drawn EXACTLY
365 little lines. [Note that 29 February
is 365 days AFTER 1 March the previous
year, not 366 days.]
8. In the vicinity of 29 February, the
lines you drew will be approximately
equally spaced except that the space
between the line for 29 February 2012
and the line for 1 March 2011 will be
just under a quarter of the space
between the other adjacent lines in
the vicinity.
9. Still with me? It takes just under 365
and a quarter days for the declination
to get back to what it was on 1 March
the previous year. Hence the anomalous
gap.
10. Now, DON'T STOP. Just keep going for
1 March 2012 and so on. You will find
that the line for 1 March 2012 is about
three-quarters of the way from the
1 March 2011 line to the 2 March 2011
line. You really are closer to the
old 2 March line than the old 1 March
line.
11. I am a hard task-master. I want you
to keep going for 36 years. Well you
did ask what to do after all :-)
12. You will, of course, have 36 lines for
1 March which form a patch. You will
have 36 lines for 2 March which form
another patch and so on BUT you have
only 9 lines for 29 February and they
form a patch which is just under a
quarter of the width of neighbouring
patches.
13. Your solar calendar is almost complete.
You label these patches rather than
the individual lines and it all works.
When the solar declination is increasing
(Winter Solstice to Summer Solstice) the
shadow will cross the 1 March patch only
on 1 March. It will cross the 29 February
patch only on 29 February. In years that
are not leap years it skips that patch.
14. For maximum benefit, it really is best to
start on 1 March the year before a leap
year. That's why I said you should start
on 1 March 2011.
Does it work? Has it been done?
Yes. Yes. Been there, done that, got the T-shirt.
Take a look at:
http://www.cl.cam.ac.uk/users/fhk1/PSQ.jpg
This photograph was taken by David Isaacs.
You can see the little patches which are alternating
red-brown and grey. You can see the patch for
29 February is just under one-quarter the width of
its two neighbours, 28 February and 1 March.
This is on a (nearly) vertical wall instead of
on the ground but the idea is the same.
To make it more interesting, instead of having
patches either side of a vertical noon line I
have them making up an analemma so you get the
extra bonus of knowing when local mean noon.
Actually, there is an analemma within an
analemma (the inner one is found by joining
up the points of the little triangles) and
the inner one indicates GMT.
I look forward to seeing what you come up with!
All the best
Frank H. King
Cambridge, UK
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