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 off 10% of the disc cuts off far less than
10% of the light.
Chris asks:
> One point you make that I don't understand is that
> you expect different results going from dark-to-light
> than light-to-dark. Why should that be?
I have two comments:
1. I used the verb "imagine" rather than "expect"
to suggest that this is something to look out
for as a possibility. Maybe I should have
put it even more neutrally.
2. My reason for suggesting this possibility is
that we are investigating something subjective
and I speculate (no more) that, when estimating
the instant that the right bit of the umbra
falls on some hour-line, some observers will
be consistently slightly late (wanting to be
sure it has got there) and others will be
slightly early (those who are naturally
impatient maybe?).
If your personal bias happens to be slightly
late then you will be too close to the dark
side of the umbra in the afternoon and too
far from it in the mornings.
Going from light to dark is clearly not the same
as going from dark to light so any experiment
should at least investigate this. It is just
possible that experienced observers (those who
have followed this thread) may turn out to be
more prone to bias than those who haven't
thought about the problem.
There is another factor which crops up in real
life rather than theory...
No supposedly plane dial is truly flat and the
larger it is the more that minor undulations
show up. If you have truly straight edges on
your wedge gnomon their shadows can appear as
slightly wavy lines.
Of course the hour-lines will appear wavy
too. Each is in the same plane as the
relevant edge of the gnomon but from some
viewpoints they are decidedly not straight.
When you see a slightly wavy edge approaching
a slightly wavy hour-line it is easy to believe
(incorrectly) that some parts of it reach the
target before others. This is just as true
when looking at the centre-line of the shadow
of a rod gnomon.
Yet another factor is with v-cut hour-lines in
stone. The approaching edge first falls into
the valley and then creeps up the far side.
If the v-cut is symmetrical and if you really
could judge the right part of the umbra with
a wedge gnomon then you would be too late in
the mornings and too early in the afternoons.
Because the bottom of the valley is further
from the gnomon than the main face of the
dial there is a case for shifting the centres
of the v-cuts away from the noon line, simply
because they lie in a plane that is slightly
further away.
In practice, stone-cutters won't go along with
this suggestion so you get another source of
bias.
You can tell that I have spent more time than
is good for me watching shadows creep into
and out of v-cuts!
Best wishes
Frank
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