Thank you all for the answer(s) to this little problem and for the
bread-crumb trail to try to retrace the derivation.
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 really. Actually ...."
What I had meant about reading the answer directly from the sundial,
assuming that you already know the time of sunrise, is that if you were to
lay the straight edge of a protractor between the root of the gnomon and
the time of sunrise on the dial face, you could read the deviation from
east-west where the six o'clock line intersects the protractor scale. Of
course, if my sunrise time were taken from the daily newspaper, I would
have to adjust for longitude.
At my latitude (38.88 north) the formula tells me that on the solstice,
sunrise/sunset deviates from east-west by 30.74 degrees, which looks like
it agrees with the protractor method (allowing for the fact that I can't
actually lay it on the dial without removing the gnomon).
Jack
At 08:28 AM 12/24/2007, Frank King wrote:
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) the azimuth.
It is slightly less obvious that dec+lat and dec-lat
must be in the range -90 to +90 though.
Also...
> ... its comforting to realise that the sun has been
> rising a little bit closer to the north for the last
> couple of mornings.
There is a delightful paradox in this. What you say
is certainly true but, nevertheless, the (clock) time
of sunrise is still getting later, and the latest
sunrise this year is not for another week. You will
have to survive Christmas before you can start feeling
comfortable!!
By way of compensation, the evenings have been drawing
out for the past 10 days.
Best wishes
Frank
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