Greetings, fellow dialists,
Following Tony Moss's query about dials on declining walls I am
tormented with some fairly pointless thoughts and a question on vertical
sundials.
A south facing vertical sundial is fairly easily comprehended with its
symmetrical hour lines showing the time from six to six and its vertical
gnomon inclined to the wall at an angle of ninety degrees minus the
latitude so that a dial at the equator would have its gnomon horizontal
and one at the pole vertical. But there is a little subtlety in a south
facing dial and even more in a declining one.
First, the six o'clock hour lines show sunrise and sunset only at the
equinoxes, when the sun rises and sets east-west. In the summer the
rising and setting points are behind the wall since the sun rises and
sets north of east-west and in the winter the sun rises later and sets
earlier than six. So in the winter, if those hour lines were not there
we would hardly miss them except for interpolation with the hours of 7
am and 5 pm.
With the south facing dial the time lines are, as noted, symmetrically
grouped around twelve noon. But more fundamentally, they are also
symmetrically grouped around the gnomon. Fundamentally, because time
lines (not necessarily hour lines) are always grouped symmetrically
around the gnomon, whether the dial faces south or not.
In a dial which does not face south the style or shadow edge of the
gnomon points (almost) to the pole star. The angle between the style and
the ground, if the style was long enough to reach the ground, is the
latitude. This angle is converted, or resolved, by dialists into two
angles known in the hermetic jargon of the fraternity as style height
and substyle distance. Presumably these terms descend to us from the
days when dialling brethren worked in chords, or lines drawn across a
circle, instead of using protractors and pocket calculators or computers
as we do today. The substyle distance is the angular deflection of the
gnomon from the vertical as would be seen in a full-face photograph.
Around it the time lines cluster symmetrically. But what of the style
height? It is an angle sticking out of the wall at right angles to the
plane of the dial plate but inclined away from the dial plate by the
amount of the substyle distance. The combination of style height and
substyle distance defines the style and reflects the direction of the
earth's axis. Now it has been said that a dial may tell the correct time
anywhere in the world where the sun shines so long as the dial plate and
gnomon are in the same relation as in the place for which they were
made. Perhaps you remember the photograph that Mike Cowham once
displayed of the English dial on the wall of the parish church in
Stellenbosch in South Africa. People laughed at the ignorance of the
vicar who was given the dial from his parish church on the English south
coast and set it up there. Of course, the sun goes round anticlockwise
in the southern hemisphere so the hour lines read absurdly. But if the
dial were to be turned approximately horizontally to be in the plane of
southern England it would tell the time well enough.
What then of the style height. We have said that the gnomon of a south
facing dial sticks out of the wall at an angle of ninety degrees minus
the latitude. With a non-south facing dial it is at different angle. For
instance, in my latitude, 55 deg. north the style height is 35 deg with
a south wall but with a wall declining 30 deg from south it is about 17
deg. Note that the longitude where I live is close to 0 deg. Let us now
convey our 30 deg declining dial to latitude 73 deg north and make the
gnomon vertical (substyle distance = 0deg) Now the time lines are
clustered symmetrically around the gnomon as in a south-facing dial but
they are telling the wrong time. The error is the substyle distance, 31
deg, in hours and minutes. Can we correct this? Simple. Just move the
dial to 31 deg west and it’s telling the right solar time, corrected for
longitude. My question, Chairman, is, are there intermediate points
between 55 deg north 0 deg and 73 deg north, 31 deg west where the dial
can also be made to tell the right time, and do these points lie on a
great circle. Please hasten with your replies as I am not sleeping at
all well because of it all.
Frank 55N 1W
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