Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

I can't find an image on the internet, of a Circumference-Aperture
Cylinder-Equatorial dial, but I'm going to post a drawing of one.

By the way, I use a broad definition of Equatorial Dial. Instead of only
dials with a dial-face parallel to the equator, I include all dials that
directly measure the Sun's apparent movement parallel to the equator.

Well, any dial with a polar style (including the Polar Dial and all the
Polar-Gnomon Flat Dials) measures the Sun's movement about the polar axis
*reasonably* directly. Maybe all such dials almost qualify as Equatorial
then. But I only call a dial Equatorial if it directly measures the Sun's
apparent movement parallel to the equator, on a uniform circular scale that
measures along a line parallel to the equator.  ...even if the dial-face
isn't parallel to the equator.

Michael Ossipoff
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Michael Ossipoff]

Correction:

I'd said:

(Tan dec)(R*2Sin(h) ).

...where h is the number hours from 12 noon.where R is the cylinder's
radius.

Here's the correction:

Instead of "hours from 12 noon",

It should say:

"...where h is 15 degrees times the number of hours from 6 a.m., during the
a.m. hours, or the number of hours from 6 p.m., during the p.m. hours."

...which could also be said as: " 15 degrees times (6 minus the number of
hours from 12 noon)".

...for the hours from 6 a.m. to 6 p.m.

Michael Ossipoff


On Mon, Oct 23, 2017 at 7:31 PM, Michael Ossipoff 
wrote:

>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 noon.where R is the cylinderr's
> radius.
>
> Obviously more neatly written:
>
> (Tan dec)(DSin(h) ).
>
> ...where D is the diameter of the cylinder.
> -
>
> But a cone would be better than a cylinder, because it opens toward the
> north, the direction from which it would be observed--making it readable
> from a wider-range of directions, and making the inside surface more
> readable in generral. The use of a cone just slightly more complicates the
> declination-lines, but that would take this post even more off-topic.
> --
>
> I mentioned that I'd read of a drinking-cup with a hole in it being used
> as a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
> orienting it just by estimation wouldn't give very accurate results. (A
> Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
> dial).
>
> But actually, maybe they were talking about a Cylindrical *Altitude*
> Dial. But, though that avoids the direction-estimation, the drinking-cup
> would need a way of hanging it in the right orientation, and so it wouldn't
> be much like an ordinary drinking-cup. ...and the line-marking would be
> complicated by the non-cylindrical shape of the cup.
>
> Michael Ossipoff
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
> wrote:
>
>> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
>> metal working class.  What little I can find on them says they are
>> inaccurate, without being very clear on the problem.  It appears to me the
>> only issue is it needs to be tilted so that the gnomon aligns with the
>> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
>> south, but the end of the gnomon that attaches to the bowl points north.
>> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
>> to cast the shadow on the bowl, and at least month lines for the solar
>> elevation.  The bowl will also have a rod and bracket on the bottom to
>> allow it to be rotated for daylight-savings time and for local longitude
>> corrections.
>>
>>
>>
>> Thanks in advance -- Brad
>>
>> ---
>> https://lists.uni-koeln.de/mailman/listinfo/sundial
>>
>>
>>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Another typo:

When I said:

"And in north declination, the circumference-aperture would be used."

I mean that in *south* declination the circumference-aperature would be
used.

Michael Ossipoff

On Tue, Oct 24, 2017 at 4:33 AM, <wsgalin...@gmail.com> wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff <email9648...@gmail.com>
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer <wissenschaft...@verizon.net>
> *Cc: *sundial list <sundial@uni-koeln.de>
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
>
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 noon.where R is the cylinderr's
> radius.
>
> Obviously more neatly written:
>
>
> (Tan dec)(DSin(h) ).
>
> ...where D is the diameter of the cylinder.
>
> -
>
>
>
> But a cone would be better than a cylinder, because it opens toward the
> north, the direction from which it would be observed--making it readable
> from a wider-range of directions, and making the inside surface more
> readable in generral. The use of a cone just slightly more complicates the
> declination-lines, but that would take this post even more off-topic.
>
> --
>
> I mentioned that I'd read of a drinking-cup with a hole in it being used
> as a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
> orienting it just by estimation wouldn't give very accurate results. (A
> Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
> dial).
>
> But actually, maybe they were talking about a Cylindrical *Altitude*
> Dial. But, though that avoids the direction-estimation, the drinking-cup
> would need a way of hanging it in the right orientation, and so it wouldn't
> be much like an ordinary drinking-cup. ...and the line-marking would be
> complicated by the non-cylindrical shape of the cup.
>
>
>
> Michael Ossipoff
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net>
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Typo:

When I said:

"So, in north declination, the south-notch would be used."

...I meant "*north*-notch".

Michael Ossipoff


On Tue, Oct 24, 2017 at 4:33 AM, <wsgalin...@gmail.com> wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff <email9648...@gmail.com>
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer <wissenschaft...@verizon.net>
> *Cc: *sundial list <sundial@uni-koeln.de>
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
>
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 noon.where R is the cylinderr's
> radius.
>
> Obviously more neatly written:
>
>
> (Tan dec)(DSin(h) ).
>
> ...where D is the diameter of the cylinder.
>
> -
>
>
>
> But a cone would be better than a cylinder, because it opens toward the
> north, the direction from which it would be observed--making it readable
> from a wider-range of directions, and making the inside surface more
> readable in generral. The use of a cone just slightly more complicates the
> declination-lines, but that would take this post even more off-topic.
>
> --
>
> I mentioned that I'd read of a drinking-cup with a hole in it being used
> as a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
> orienting it just by estimation wouldn't give very accurate results. (A
> Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
> dial).
>
> But actually, maybe they were talking about a Cylindrical *Altitude*
> Dial. But, though that avoids the direction-estimation, the drinking-cup
> would need a way of hanging it in the right orientation, and so it wouldn't
> be much like an ordinary drinking-cup. ...and the line-marking would be
> complicated by the non-cylindrical shape of the cup.
>
>
>
> Michael Ossipoff
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net>
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Hi--

I'll look for some images of Circumference-Aperture
Cylinder-Equatorials.and Cone-Equatorials.

It can be shown that the light-spot projected by the circumference-aperture
moves around the inside of the cylinder at a uniform rate that's twice the
rate at which an axial-gnomon's shadow would move.

So, during the 12 hours from 6:00 a.m. to 6:00 p.m, the light-spot moves
all the way around the inside of the cylinder, while the shadow of an axial
gnomon would only move halfway around the cylinder.

(But, as I was saying, if the south-window isn't facing due-south, and so
the early sunrise or late sunset illuminates the dial, then an additional
circumference aperture could be added at the 6:00 p.m. line, on the east
side of the cylinder, or at the 6:00 a.m. line, on the west side of the
cylinder. In that way, the dial would have more than 12-hour coverage.)

So, with the hour-lines twice as far apart, the dial is that much easier to
read accurately. The spacing between hour-lines is .2618 times the diameter
of the cylinder.
-
Of course, with a Cylinder-Equatorial dial, with the circumference-aperture
at the middle of the cylinder, with the declination-line-area having an
axial dimension of 0.867*D, the mid-summer position of the light-spot will
be far down the cylinder, where it could be more difficult to read. That
could be a reason to prefer a Cone-Equatorial.

But, with a Cylinder-Equatorial, the situation could be remedied by adding
another circumference-aperture barely south of the top of the north edge of
the cylinder.  ...or a notch in the north edge of the cylinder. So, in
north declination, the south-notch would be used. And in north declination,
the circumference-aperture would be used.

But then you'd need two separate sets of declination-lines, one for north
declination, and another for south declination. Maybe one set of lines
could be dotted.

Or maybe one set of declination-lines, labeled on the east side of the
cylinder could be solid lines on that side, and dotted on the other side.
And likewise for the other set of declination-lines, labeled on the west
side, solid on that side and dotted on the other side.
--
Of course, instead of a circumference-aperture and an edge-notch, one could
instead use two edge-notches, one north and one south.  But then the
cylinder would best be cut to an axial-dimension of 0.867*D. That would
increase the work of making the dial, and the force involved in sawing or
cutting could deform the cylinder.. The appeal of the combination of a
circumference-aperature in the top- middle, and an edge-notch at the top of
the north-edge  (or just using the aperture and no notch), is that the
cylinder wouldn't have to be sawed or cut.

With the cylinder or cone supported at its north end by a support with a
semicircular hole in which the north end of the cylinder rests, and with
the south-end of the cylinder resting on the window-sill, of course the
cylinder's inclination above the horizontal is easily adjusted by sliding
the cylinder (or cone) northward or southward   ...to incline the cylinder
or cone with its axis parallel to the Earth's axis.

Michael Ossipoff







On Tue, Oct 24, 2017 at 4:33 AM, <wsgalin...@gmail.com> wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff <email9648...@gmail.com>
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer <wissenschaft...@verizon.net>
> *Cc: *sundial list <sundial@uni-koeln.de>
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the

RE: Hemicyclium correction - a figure might be needed

[wsgalinski]

Thank you for your nice considerations. 
I think that some kind of visualization would make them more clear to a general 
public. Could you please support your ideas with a figure or a link to an 
external one (if exists)?

Best regards,

Wojtek

From: Michael Ossipoff
Sent: Tuesday, October 24, 2017 1:32 AM
To: Brad Thayer
Cc: sundial list
Subject: Re: Hemicyclium correction


In the Hemicyclium discussion, the OP mentioned having 6-inch copper tubing. 
So, though it was a bit off-topic, I suggested that the tubing could be used 
for an additional, quicker, project, to make a south windowsill sundial--a 
Circumference-Aprerture Cylindrical Equatorial Dial.
But, when I said that the axial dimension of the cylinder has to be at least 
0.4335 times the diameter, I neglected the fact that there are south 
declinations as well as north declinations. (...funny, because we're in south 
declination now) So, with the circumference aperture in the middle of the 
cylinder, the cylinder's axial dimension has to be at least twice 0.4335, which 
is about 0.867 times the diameter.
But my suggestion for marking points of the declination-lines for each hour was 
correct:
At any hour-line, the axial displacement of a declination-line from the 
equinox-line is equal to the tangent of the declination times the direct 
distance between the circumference aperture and the intersection of that 
hour-line with the equinox-line
That amounts to:

(Tan dec)(R*2Sin(h) ). 
...where h is the number hours from 12 noon.where R is the cylinderr's radius.
Obviously more neatly written:

(Tan dec)(DSin(h) ).
...where D is the diameter of the cylinder.
-

But a cone would be better than a cylinder, because it opens toward the north, 
the direction from which it would be observed--making it readable from a 
wider-range of directions, and making the inside surface more readable in 
generral. The use of a cone just slightly more complicates the 
declination-lines, but that would take this post even more off-topic.
--
I mentioned that I'd read of a drinking-cup with a hole in it being used as a 
cylindrical sundial. Of course if it were a Cylindrical Equatorial, orienting 
it just by estimation wouldn't give very accurate results. (A Cylindrical 
Equatorial is supposed to be a mounted dial, not a portable dial). 

But actually, maybe they were talking about a Cylindrical Altitude Dial. But, 
though that avoids the direction-estimation, the drinking-cup would need a way 
of hanging it in the right orientation, and so it wouldn't be much like an 
ordinary drinking-cup. ...and the line-marking would be complicated by the 
non-cylindrical shape of the cup.

Michael Ossipoff

On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net> 
wrote:
I am looking to make a hemicyclium-type sundial (half-hemisphere) in a metal 
working class.  What little I can find on them says they are inaccurate, 
without being very clear on the problem.  It appears to me the only issue is it 
needs to be tilted so that the gnomon aligns with the Earth’s rotation axis; 
thus the half-bowl faces south and the gnomon points south, but the end of the 
gnomon that attaches to the bowl points north.  Am I missing anything?  I am 
also looking to use an analemma-shaped gnomon to cast the shadow on the bowl, 
and at least month lines for the solar elevation.  The bowl will also have a 
rod and bracket on the bottom to allow it to be rotated for daylight-savings 
time and for local longitude corrections.
 
Thanks in advance -- Brad

---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Michael Ossipoff]

In the Hemicyclium discussion, the OP mentioned having 6-inch copper
tubing. So, though it was a bit off-topic, I suggested that the tubing
could be used for an additional, quicker, project, to make a south
windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.

But, when I said that the axial dimension of the cylinder has to be at
least 0.4335 times the diameter, I neglected the fact that there are south
declinations as well as north declinations. (...funny, because we're in
south declination now) So, with the circumference aperture in the middle of
the cylinder, the cylinder's axial dimension has to be at least twice
0.4335, which is about 0.867 times the diameter.

But my suggestion for marking points of the declination-lines for each hour
was correct:

At any hour-line, the axial displacement of a declination-line from the
equinox-line is equal to the tangent of the declination times the direct
distance between the circumference aperture and the intersection of that
hour-line with the equinox-line

That amounts to:

(Tan dec)(R*2Sin(h) ).

...where h is the number hours from 12 noon.where R is the cylinderr's
radius.

Obviously more neatly written:

(Tan dec)(DSin(h) ).

...where D is the diameter of the cylinder.
-

But a cone would be better than a cylinder, because it opens toward the
north, the direction from which it would be observed--making it readable
from a wider-range of directions, and making the inside surface more
readable in generral. The use of a cone just slightly more complicates the
declination-lines, but that would take this post even more off-topic.
--

I mentioned that I'd read of a drinking-cup with a hole in it being used as
a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
orienting it just by estimation wouldn't give very accurate results. (A
Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
dial).

But actually, maybe they were talking about a Cylindrical *Altitude* Dial.
But, though that avoids the direction-estimation, the drinking-cup would
need a way of hanging it in the right orientation, and so it wouldn't be
much like an ordinary drinking-cup. ...and the line-marking would be
complicated by the non-cylindrical shape of the cup.

Michael Ossipoff

On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
wrote:

> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Dan-George Uza]

I find the video below extremely instructive!

https://youtu.be/0hs6QqwJIhs

The sundial is marked in old temporary (or seasonal) hours. Changing them
to modern hours does not make much sense to me.

For it to become a hemicyclium I guess you just have to leave out the
unused part of the half-sphere.

Dan Uza


On Sun, Oct 22, 2017 at 2:40 PM, Patrick Powers <
patrick_pow...@compuserve.com> wrote:

> Hi Brad
>
> Further to your interest in an hemicyclium you might like to know of this
> link to the former webpages of the late Frans Maes who set out his
> instructions for *“Construction of Hemispherium”* some time ago and which
> is based on several earlier documents – all referenced.  You might find it
> useful – or at least interesting!
>
> http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm
>
> Good luck
>
> Patrick
>
>
>
> *From:* Brad Thayer <wissenschaft...@verizon.net>
> *Sent:* Monday, October 16, 2017 1:48 PM
> *To:* sundial@uni-koeln.de
> *Subject:* Hemicyclium correction
>
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
> --
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Maes, F.W.]

Hi Patrick,

Thanks for pointing this out. Fortunately, I am still alive and sometimes
kicking a bit ...

I put the link to Fer de Vries' article temporarily on my own website as it
was the quickest and easiest way to answer a query by someone on this list.
By now, the (same) article is also available on the website of the Dutch
Sundial Society.

Best regards,
Frans Maes

<http://www.avg.com/email-signature?utm_medium=email_source=link_campaign=sig-email_content=webmail>
Virusvrij.
www.avg.com
<http://www.avg.com/email-signature?utm_medium=email_source=link_campaign=sig-email_content=webmail>
<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

On Sun, Oct 22, 2017 at 7:36 PM, Patrick Powers <
patrick_pow...@compuserve.com> wrote:

> Hi Brad,
>
> My message re your interest in hemicyclia should have made it clear that
> it was Fer De Vries’s original work on the construction of a Hemispherium
> that he placed on his website and which was republished after his death by
> Frans Maes and then placed on his own website for us to read today. My
> sincere apologies to Frans!
>
> Patrick
>
> *From:* Patrick Powers <patrick_pow...@compuserve.com>
> *Sent:* Sunday, October 22, 2017 12:40 PM
> *To:* Brad Thayer <wissenschaft...@verizon.net> ; sundial@uni-koeln.de
> *Subject:* Re: Hemicyclium correction
>
> Hi Brad
>
> Further to your interest in an hemicyclium you might like to know of this
> link to the former webpages of the late Frans Maes who set out his
> instructions for *“Construction of Hemispherium”* some time ago and which
> is based on several earlier documents – all referenced.  You might find it
> useful – or at least interesting!
>
> http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm
>
> Good luck
>
> Patrick
>
>
>
> *From:* Brad Thayer <wissenschaft...@verizon.net>
> *Sent:* Monday, October 16, 2017 1:48 PM
> *To:* sundial@uni-koeln.de
> *Subject:* Hemicyclium correction
>
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
> --
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Patrick Powers]

Hi Brad, 

My message re your interest in hemicyclia should have made it clear that it was 
Fer De Vries’s original work on the construction of a Hemispherium that he 
placed on his website and which was republished after his death by Frans Maes 
and then placed on his own website for us to read today. My sincere apologies 
to Frans!

Patrick

From: Patrick Powers 
Sent: Sunday, October 22, 2017 12:40 PM
To: Brad Thayer ; sundial@uni-koeln.de 
Subject: Re: Hemicyclium correction

Hi Brad

Further to your interest in an hemicyclium you might like to know of this link 
to the former webpages of the late Frans Maes who set out his instructions for 
“Construction of Hemispherium” some time ago and which is based on several 
earlier documents – all referenced.  You might find it useful – or at least 
interesting!

http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm

Good luck

Patrick



From: Brad Thayer 
Sent: Monday, October 16, 2017 1:48 PM
To: sundial@uni-koeln.de 
Subject: Hemicyclium correction

I am looking to make a hemicyclium-type sundial (half-hemisphere) in a metal 
working class.  What little I can find on them says they are inaccurate, 
without being very clear on the problem.  It appears to me the only issue is it 
needs to be tilted so that the gnomon aligns with the Earth’s rotation axis; 
thus the half-bowl faces south and the gnomon points south, but the end of the 
gnomon that attaches to the bowl points north.  Am I missing anything?  I am 
also looking to use an analemma-shaped gnomon to cast the shadow on the bowl, 
and at least month lines for the solar elevation.  The bowl will also have a 
rod and bracket on the bottom to allow it to be rotated for daylight-savings 
time and for local longitude corrections.

 

Thanks in advance -- Brad




---
https://lists.uni-koeln.de/mailman/listinfo/sundial

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Patrick Powers]

Hi Brad

Further to your interest in an hemicyclium you might like to know of this link 
to the former webpages of the late Frans Maes who set out his instructions for 
“Construction of Hemispherium” some time ago and which is based on several 
earlier documents – all referenced.  You might find it useful – or at least 
interesting!

http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm

Good luck

Patrick



From: Brad Thayer 
Sent: Monday, October 16, 2017 1:48 PM
To: sundial@uni-koeln.de 
Subject: Hemicyclium correction

I am looking to make a hemicyclium-type sundial (half-hemisphere) in a metal 
working class.  What little I can find on them says they are inaccurate, 
without being very clear on the problem.  It appears to me the only issue is it 
needs to be tilted so that the gnomon aligns with the Earth’s rotation axis; 
thus the half-bowl faces south and the gnomon points south, but the end of the 
gnomon that attaches to the bowl points north.  Am I missing anything?  I am 
also looking to use an analemma-shaped gnomon to cast the shadow on the bowl, 
and at least month lines for the solar elevation.  The bowl will also have a 
rod and bracket on the bottom to allow it to be rotated for daylight-savings 
time and for local longitude corrections.

 

Thanks in advance -- Brad




---
https://lists.uni-koeln.de/mailman/listinfo/sundial

---
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Re: Hemicyclium correction

[Michael Ossipoff]

Correction:

I said that the declination lines would be circles around the cylinder's
inside circumference.

Actually, because the distance of the light-spot from the
circumference-aperature varies, around the dial, the declination lines
wouldn't be that simple.

The drawing of the declination lines would just be a bit trickier. At a
certain hour-line, the axial displacement of the declination-line from the
equinox line would be equal to the tangent of the declination, times the
straight-line distance between the circumference aperature and the place
where the hour-line intersects the equinox line.

If a cone (such as a drinking-cup)  is used instead of a cylinder, that
complicates the declination-lines a bit more, but it's still do-able.

I've read that, in ancient times, drinking-cups, perforated with a
circumference-aperature nodus, were sometimes used as portable sundials.
Presumably, for some particular property-area, a person might know what
tree, building or mountain landmark was due north. S/he could point the cup
in that direction, with the circumference aperature on top, pointing the
cup upward so that its axis points above the horizontal by an amount
approximately equal to the local latitude.  ...and read the time from the
hour-lines marked inside the cup.

Obviously the circumference-aperature would limit how high you could fill
the cup, when using it for drinking.

Michael Ossipoff

On Thu, Oct 19, 2017 at 2:31 PM, Michael Ossipoff <email9648...@gmail.com>
wrote:

> Of course, for the Cylinder Equatorial with circumference aperature, you
> could have declination-ilnes, which would be circles around the cylinder's
> circumference.
>
> Michael Ossipoff
>
> On Wed, Oct 18, 2017 at 10:23 PM, Brad Thayer <wissenschaft...@verizon.net
> > wrote:
>
>> Michael,
>>
>>
>>
>> Thank you for the lengthy response.
>>
>>
>>
>> This will actually be the fifth sundial I have completed (and the 6th
>> that I have started).  I’ve already made a band-equatorial (using “Mayan
>> digits”), two analemmatic horizonatal sundials, a south-facing vertical
>> sundial, and started a cylindrical sundial (aka, shepherds staff).  With
>> each one, I try something new and challenging.  I also use it as a way to
>> improve my metal working skills.  As I am currently taking a copper
>> raising/sinking and chasing metal forming class, I was interested in making
>> a bowl with chased lines (aka, repousse) for practice, hence the idea for
>> the hemicyclium.
>>
>>
>>
>> I lucked into some used 14 gauge copper tubing about 6 inches in
>> diameter, which I annealed, cut open and pounded flat as a starting point.
>> So I have the basic starting materials.
>>
>>
>>
>> If the inside surface is marked with the lines analogous to lines of
>>  longitude on a globe spaced 15 degrees apart, radiating from the “pole” of
>> the hemicyclium, and the entire device is tilted to align with the earth’s
>> axis, would it then read out in Local True Solar Time?  That is my primary
>> sticking point.  I’d prefer that than the ancient Temporary hours.  It
>> would seem it would be mathematically similar to a section of an armillary
>> sphere.
>>
>>
>>
>> With a proper adjustable mount, I can adjust for the longitude correction
>> (I am currently about 4 degrees away from my nearest meridian) and DST
>> twice a year as well.
>>
>>
>>
>> *From:* Michael Ossipoff [mailto:email9648...@gmail.com]
>> *Sent:* Tuesday, October 17, 2017 8:44 PM
>> *To:* Brad Thayer <wissenschaft...@verizon.net>
>> *Cc:* sundial list <sundial@uni-koeln.de>
>> *Subject:* Re: Hemicyclium correction
>>
>>
>>
>>
>>
>>
>>
>> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net>
>> wrote:
>>
>> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
>> metal working class.  What little I can find on them says they are
>> inaccurate, without being very clear on the problem.
>>
>>
>>
>> But the way, I've seen it spelled "Hemicycleum" as well. I don't know
>> which is correct, but "Hemicycleum" looks better, it seems to me. But I'll
>> use your spelling. It's probably better-accpeted.
>>
>>
>>
>> Whoever said that was mistaken. Hemicyclia are as in principle as
>> accurate as any sundial can be.
>>
>>
>>
>> In ancient times, Hemicyclia were devised, instead of our modern
>> polar-gnomon garden sundial, or our equatorial sundials, because in those
>> days, they weren't using our Equal-Hours for civil time (Astronomers used

Re: Hemicyclium correction

[Michael Ossipoff]

Of course, for the Cylinder Equatorial with circumference aperature, you
could have declination-ilnes, which would be circles around the cylinder's
circumference.

Michael Ossipoff

On Wed, Oct 18, 2017 at 10:23 PM, Brad Thayer <wissenschaft...@verizon.net>
wrote:

> Michael,
>
>
>
> Thank you for the lengthy response.
>
>
>
> This will actually be the fifth sundial I have completed (and the 6th
> that I have started).  I’ve already made a band-equatorial (using “Mayan
> digits”), two analemmatic horizonatal sundials, a south-facing vertical
> sundial, and started a cylindrical sundial (aka, shepherds staff).  With
> each one, I try something new and challenging.  I also use it as a way to
> improve my metal working skills.  As I am currently taking a copper
> raising/sinking and chasing metal forming class, I was interested in making
> a bowl with chased lines (aka, repousse) for practice, hence the idea for
> the hemicyclium.
>
>
>
> I lucked into some used 14 gauge copper tubing about 6 inches in diameter,
> which I annealed, cut open and pounded flat as a starting point.  So I have
> the basic starting materials.
>
>
>
> If the inside surface is marked with the lines analogous to lines of
>  longitude on a globe spaced 15 degrees apart, radiating from the “pole” of
> the hemicyclium, and the entire device is tilted to align with the earth’s
> axis, would it then read out in Local True Solar Time?  That is my primary
> sticking point.  I’d prefer that than the ancient Temporary hours.  It
> would seem it would be mathematically similar to a section of an armillary
> sphere.
>
>
>
> With a proper adjustable mount, I can adjust for the longitude correction
> (I am currently about 4 degrees away from my nearest meridian) and DST
> twice a year as well.
>
>
>
> *From:* Michael Ossipoff [mailto:email9648...@gmail.com]
> *Sent:* Tuesday, October 17, 2017 8:44 PM
> *To:* Brad Thayer <wissenschaft...@verizon.net>
> *Cc:* sundial list <sundial@uni-koeln.de>
> *Subject:* Re: Hemicyclium correction
>
>
>
>
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net>
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.
>
>
>
> But the way, I've seen it spelled "Hemicycleum" as well. I don't know
> which is correct, but "Hemicycleum" looks better, it seems to me. But I'll
> use your spelling. It's probably better-accpeted.
>
>
>
> Whoever said that was mistaken. Hemicyclia are as in principle as accurate
> as any sundial can be.
>
>
>
> In ancient times, Hemicyclia were devised, instead of our modern
> polar-gnomon garden sundial, or our equatorial sundials, because in those
> days, they weren't using our Equal-Hours for civil time (Astronomers used
> it though). They were using "Temporary Hours), that divided each day into
> 12 equal hours, for their civil time.
>
>
>
> To achieve that, they used a stick-tip nodus or bead-nodus. to cast a
> point-shadow on the hemicyclium surface. As the Sun's declination changes
> seasonally, of course the tip-nodus's path on the hemicyclium changes too.
> So the hour-lines were curves, drawn so that, for any particular solar
> declination, those marks divide the day (sunrise to sunset) into 12 equal
> parts.
>
>
>
> As you can imagine, that makes the dial more complicated than modern ones.
> "Early" doesn't always mean "simpler".
>
>
>
> ...and so there was much opportunity for error in the calclulations and
> drafting,for those curved hour-lines.
>
>
>
> So maybe some hemicyclia *were* inaccurately drafted. For one thing, of
> course the exact time of day wasn't as crucial in those days, and of course
> the more precisely made, and prestigiously made, a sundial was, the more it
> was likely to cost.
>
>
>
> But there's no reason why your hemicyclium should be made for Temporary
> Hours. Make it for our modern Equal-Hours, also referred to as Local True
> Solar Time (LTST).
>
>
>
>
>
> It appears to me the only issue is it needs to be tilted so that the
> gnomon aligns with the Earth’s rotation axis;
>
>
>
> The equinox circle on the Hemicyclium, the line that the tip-nodus follows
> on the day of the equinox, should be a circle parallel to the celestial
> equator.
>
>
>
> And yes, if you're going to use a polar gnomon instead of a tip-nodus,
> then that polar gnomon should be parallel to the Earth's axis, pointed at
> the north celestial pole. ...and sho

Re: Hemicyclium correction

[Michael Ossipoff]

Just one safety quibble:

If you mount the spike sticking up, then it will be an eye-hazard, even
with the ball on its end.

That's a good reason to mount the spike horizontally, at the rim of the
bowl. It could be mounted in a north-south groove at the south side of the
bowl. Mounting the spike at the south side of the bowl is likewise probably
best for eye-safety, because people will more likely be reading the dial
from its south side.   ...because the dial-lines are mostly toward the
north side.  That's probably traditional too.

Anyway, that's traditional, it seems to me, and so it's better of ancient
realism.

Besides, with the spike horizontal, its tip-nodus will still have a shadow
that the spike itself doesn't get in the way of at equinox noon.

Michael Ossipoff
f
.



On Thu, Oct 19, 2017 at 11:13 AM, Frank King  wrote:

> Dear Brad,
>
> I'm delighted that you enjoyued
> my "tutorial"...
>
> > However, its your step 19 I am
> > interested in.
>
> Ah yes.  That's where I mention
> marking out equal hours.  I thought
> you would be most interested in
> that step :-)
>
> You add...
>
> > And if I do tilt the hemispherium
> > so that the horizon line is now
> > instead parallel to the earth's
> > axis, does that solve any of the
> > issues?
>
> This is like taking an aircraft as
> your inspiration for designing a
> car and not appreciating what the
> wings are for.
>
> The absolutely key feature of the
> hemicyclium design is that, at its
> top, there is a FLAT HORIZONTAL
> surface.
>
> It isn't like that just so the
> Greek user could put his Retsina
> glass on it.  It is like that in
> order to be parallel to the plane
> of the horizon and...
>
> That is important because it
> echos the position of the sun at
> sunrise and sunset and...
>
> That is important because the
> principal purpose of this dial
> was to divide the day into
> equal intervals of time starting
> at sunrise and ending at sunset.
>
> These unequal hours may not be
> to your taste but this is the
> scheme that was in widespread
> use for thousands of years!
> Why not educate your friends?
> Why not educate yourself?
>
> OK, I'll get round to what you
> really want shortly but, meantime,
> I am going to stick to the original
> purpose...
>
> In my previous message I was
> simplifying matters by saying
> that you should cut the sphere
> (the orange) into quarters.
>
> The problem with using a quarter
> of a sphere (and this also applies
> if you insist on equal hours) is
> that you can't represent sunrise
> and sunset in the summer months.
>
> A real hemicyclium was rather more
> than a quarter of a sphere.  Take
> a look at:
>
>   http://www.sundials.co.uk/leicester/fig04.jpg
>
> You can see the horizontal surface
> easily enough and you can also see
> a forward-sloping face at the front.
>
> The slope, relative to the vertical,
> matches the local latitude.  This is
> about 37 degrees off the vertical
> in Greece but 50+ in the U.K.
>
> By leaning forward this allows the
> horizontal surface to grow so that
> its inside rim is no longer a
> semi-circle.  It is now much more
> of a circle.  The tip of the spike
> serves as the nodus and this is at
> the centre of the rim circle.  The
> two "wings" are way beyond this
> tip.
>
> If you look at the markings you can see
> the three main constant-declination
> arcs.  The middle one is a great circle
> and the tip of the spike is the centre
> of this circle too.
>
> The upper arc is for the winter
> solstice and the lower is for the
> summer solstice.  These are small
> circles.  If you hold one end of
> a piece of string on the tip of
> the spike and run the other end
> round either of these circles
> you would see the string sweeps
> out a cone, not a disc.
>
> OK, once you have this elegant
> hollow shape you can make cardboard
> templates which exactly fit these
> three circular arcs.  The template
> for the equinoctial arc will be an
> exact semi-circle.  The other two
> have a slightly smaller radius
> than the equinoctial circle.
>
> Clearly, the template for the
> summer solstice is more than a
> semi-circle and that for the
> winter solstice is less than
> a semi-circle.  If you fit the
> two together you should get a
> perfect circle.  Can you see
> why?
>
> Now all you have to do is to
> divide the rims of each of these
> three circles into 12 equal parts.
> This gives you the unequal hours
> of the day exactly as in fig 4.
>
> Of course, what you really want
> are new-fangled equal hours...
>
> Well, you make the same three
> templates as before and then,
> on each, mark the centre point
> on the rim.  This is the noon
> point.  You then mark off at
> 15-degree intervals either
> side of this point.
>
> This is easy for the equinoctial
> template.  For the other two I
> suggest you butt them together
> so you can see the centre of
> the common circle.
>
> It is then a case of joining
> the dots to get the equal hour
> lines.
>
> You will find that several

Re: Hemicyclium correction

[Frank King]

Dear Brad,

I'm delighted that you enjoyued
my "tutorial"...

> However, its your step 19 I am
> interested in.

Ah yes.  That's where I mention
marking out equal hours.  I thought
you would be most interested in
that step :-)

You add...

> And if I do tilt the hemispherium
> so that the horizon line is now
> instead parallel to the earth's
> axis, does that solve any of the
> issues?

This is like taking an aircraft as
your inspiration for designing a
car and not appreciating what the
wings are for.

The absolutely key feature of the
hemicyclium design is that, at its
top, there is a FLAT HORIZONTAL
surface.

It isn't like that just so the
Greek user could put his Retsina
glass on it.  It is like that in
order to be parallel to the plane
of the horizon and...

That is important because it
echos the position of the sun at
sunrise and sunset and...

That is important because the
principal purpose of this dial
was to divide the day into
equal intervals of time starting
at sunrise and ending at sunset.

These unequal hours may not be
to your taste but this is the
scheme that was in widespread
use for thousands of years!
Why not educate your friends?
Why not educate yourself?

OK, I'll get round to what you
really want shortly but, meantime,
I am going to stick to the original
purpose...

In my previous message I was
simplifying matters by saying
that you should cut the sphere
(the orange) into quarters.

The problem with using a quarter
of a sphere (and this also applies
if you insist on equal hours) is
that you can't represent sunrise
and sunset in the summer months.

A real hemicyclium was rather more
than a quarter of a sphere.  Take
a look at:

  http://www.sundials.co.uk/leicester/fig04.jpg

You can see the horizontal surface
easily enough and you can also see
a forward-sloping face at the front.

The slope, relative to the vertical,
matches the local latitude.  This is
about 37 degrees off the vertical
in Greece but 50+ in the U.K.

By leaning forward this allows the
horizontal surface to grow so that
its inside rim is no longer a
semi-circle.  It is now much more
of a circle.  The tip of the spike
serves as the nodus and this is at
the centre of the rim circle.  The
two "wings" are way beyond this
tip.

If you look at the markings you can see
the three main constant-declination
arcs.  The middle one is a great circle
and the tip of the spike is the centre
of this circle too.

The upper arc is for the winter
solstice and the lower is for the
summer solstice.  These are small
circles.  If you hold one end of
a piece of string on the tip of
the spike and run the other end
round either of these circles
you would see the string sweeps
out a cone, not a disc.

OK, once you have this elegant
hollow shape you can make cardboard
templates which exactly fit these
three circular arcs.  The template
for the equinoctial arc will be an
exact semi-circle.  The other two
have a slightly smaller radius
than the equinoctial circle.

Clearly, the template for the
summer solstice is more than a
semi-circle and that for the
winter solstice is less than
a semi-circle.  If you fit the
two together you should get a
perfect circle.  Can you see
why?

Now all you have to do is to
divide the rims of each of these
three circles into 12 equal parts.
This gives you the unequal hours
of the day exactly as in fig 4.

Of course, what you really want
are new-fangled equal hours...

Well, you make the same three
templates as before and then,
on each, mark the centre point
on the rim.  This is the noon
point.  You then mark off at
15-degree intervals either
side of this point.

This is easy for the equinoctial
template.  For the other two I
suggest you butt them together
so you can see the centre of
the common circle.

It is then a case of joining
the dots to get the equal hour
lines.

You will find that several
hour lines run up to the rim
and abruptly stop.  With the
unequal hours ALL the lines
run from the winter solstice
arc to the summer solstice
arc as in fig 4.

As a refinement, I don't care
for the way the Greeks mounted
their spikes!  I would allow
you to improve on that...

I suggest you drill a hole at
the point where the noon line
and equinoctial arc intersect.

You now need a rod whose exposed
length matches the radius of
your sphere.  Fix the hidden
part in the hole and fix a 
small ball at the outer end
to serve as the nodus.  Make
sure it is at the centre of
the main horizontal rim.

This means that at noon on
the day of an equinox, the
shadow of the nodus falls at
the foot of the support rod.

If you REALLY want a polar-oriented
gnomon then you drill a hole through
the nodus that is at right-angles
to the support rod and insert the
gnomon into this new hole.  Make
sure it is oriented towards the
north celestial pole.  I regard
this as serious uglification.

Best of luck with your efforts.

Frank


---
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Re: Hemicyclium correction

[Michael Ossipoff]

Brad--


>
> If the inside surface is marked with the lines analogous to lines of
>  longitude on a globe spaced 15 degrees apart, radiating from the “pole” of
> the hemicyclium, and the entire device is tilted to align with the earth’s
> axis, would it then read out in Local True Solar Time?
>

Yes, the hour-lines would be exactly like the 15-degree meridian
longitude-lines of a globe. (plus whatever intermediate fractional-hour
lines).

It seems to me that, in the photos and drawings I've seen, both the
Hemicyclia and the Hemispheria had a horizontal flat top edge-surface. With
that bowl-edge horizontal, and with the stick-tip nodus at the same level
as that bowl-edge, the dial wIould tell time whenever the Sun is above the
horizon. (So do the Horizontal Dial, the Band-Equatorial, and lots of
others)

It also seems to me that, in the photos and drawings that I've seen, the
stick for the stick-end nodus was horizontal, sticking out so that its tip,
the nodus, is at the center of the bowl.

If you're sure you want the bigger task of a Hemicyclium instead of a
Band-Equatorial, then I'd use the traditional horizontal stick, with its
end (nodus) at the bowl's center.   ...instead of using a polar-parallel
gnomon.  Easier, for one thing, and more realistic, for a Hemicyclium or
Hemispherium.

Though the system of hour-lines should have its poles at the ends of an
imaginary line parallel with the Earth's axis (north-south, tipped up at
the north-end by an amount equal to your north-latitude), I'd just leave
the top-cut, bowl-edge horizontal, like the pictures that i've seen.
Anyway, if the surface that includes the bowl edge were tipped from the
horizontal, wouldn't that interfere with ensuring that the dial will tell
time whenever the Sun is above the horizon? I'd leave the bowl-top edge
horizontal. I think that's how Hemicyclia and Hemispheria always were.

I'd have declination-lines in the bowl, in addition to the hour-lines. Of
course the declination-lines would be exactly like the parallels on a globe.

People often mark declination-lines with the date. I'd have the lines
marked with declination-degrees as well.

In older centuries, they marked declination-lines with zodiac signs instead
of month-names. That made sense really, because the zodiac signs coincide
with exact solar ecliptic longitudes, corresponding to exact declinations
(if you disregard the small change-rate of the obliquity). But of course
nowadays the months are much more famiiar. But I'd mark the
declination-lines in degrees too.


That is my primary sticking point.  I’d prefer that than the ancient
Temporary hours.  It would seem it would be mathematically similar to a
section of an armillary sphere.

Yes, just maybe a more challenging construction than an Armillary
Band-Equatorial. The globe-meridian-like hour-lines would be more work than
the straight hour lines on a Band-Equatorial. But, with your metal-working
experience, you probably *want* something more challenging.

>
>
> With a proper adjustable mount, I can adjust for the longitude correction
> (I am currently about 4 degrees away from my nearest meridian) and DST
> twice a year as well.
>

Ok, but that seems unnecessary extra work, since the longitude-correction
could be added to EoT in your conversion-table plaque displayed near the
dial. Anyway, it seems more aesthetic for a dial to give Local True Solar
Time.

Interesting project. I once considered proposing a project of a brass
band-equatorial mounted in a concrete structure resembling a Hemicyclium.

The copper bowl will have a cool ancient look when it weathers.

Michael Ossipoff


>
> *From:* Michael Ossipoff [mailto:email9648...@gmail.com]
> *Sent:* Tuesday, October 17, 2017 8:44 PM
> *To:* Brad Thayer <wissenschaft...@verizon.net>
> *Cc:* sundial list <sundial@uni-koeln.de>
> *Subject:* Re: Hemicyclium correction
>
>
>
>
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net>
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.
>
>
>
> But the way, I've seen it spelled "Hemicycleum" as well. I don't know
> which is correct, but "Hemicycleum" looks better, it seems to me. But I'll
> use your spelling. It's probably better-accpeted.
>
>
>
> Whoever said that was mistaken. Hemicyclia are as in principle as accurate
> as any sundial can be.
>
>
>
> In ancient times, Hemicyclia were devised, instead of our modern
> polar-gnomon garden sundial, or our equatorial sundials, because in those
> days, they weren't using our Equal-Hours for civil time (Astronomers used
> it though). They were using "Temporary Hours), that divided each day into
> 12 equal ho

RE: Hemicyclium correction

[Brad Thayer]

Michael,

 

Thank you for the lengthy response.

 

This will actually be the fifth sundial I have completed (and the 6th that I 
have started).  I’ve already made a band-equatorial (using “Mayan digits”), two 
analemmatic horizonatal sundials, a south-facing vertical sundial, and started 
a cylindrical sundial (aka, shepherds staff).  With each one, I try something 
new and challenging.  I also use it as a way to improve my metal working 
skills.  As I am currently taking a copper raising/sinking and chasing metal 
forming class, I was interested in making a bowl with chased lines (aka, 
repousse) for practice, hence the idea for the hemicyclium.

 

I lucked into some used 14 gauge copper tubing about 6 inches in diameter, 
which I annealed, cut open and pounded flat as a starting point.  So I have the 
basic starting materials.

 

If the inside surface is marked with the lines analogous to lines of  longitude 
on a globe spaced 15 degrees apart, radiating from the “pole” of the 
hemicyclium, and the entire device is tilted to align with the earth’s axis, 
would it then read out in Local True Solar Time?  That is my primary sticking 
point.  I’d prefer that than the ancient Temporary hours.  It would seem it 
would be mathematically similar to a section of an armillary sphere.

 

With a proper adjustable mount, I can adjust for the longitude correction (I am 
currently about 4 degrees away from my nearest meridian) and DST twice a year 
as well.

 

From: Michael Ossipoff [mailto:email9648...@gmail.com] 
Sent: Tuesday, October 17, 2017 8:44 PM
To: Brad Thayer <wissenschaft...@verizon.net>
Cc: sundial list <sundial@uni-koeln.de>
Subject: Re: Hemicyclium correction

 

 

 

On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer <wissenschaft...@verizon.net 
<mailto:wissenschaft...@verizon.net> > wrote:

I am looking to make a hemicyclium-type sundial (half-hemisphere) in a metal 
working class.  What little I can find on them says they are inaccurate, 
without being very clear on the problem.  

 

But the way, I've seen it spelled "Hemicycleum" as well. I don't know which is 
correct, but "Hemicycleum" looks better, it seems to me. But I'll use your 
spelling. It's probably better-accpeted.

 

Whoever said that was mistaken. Hemicyclia are as in principle as accurate as 
any sundial can be.

 

In ancient times, Hemicyclia were devised, instead of our modern polar-gnomon 
garden sundial, or our equatorial sundials, because in those days, they weren't 
using our Equal-Hours for civil time (Astronomers used it though). They were 
using "Temporary Hours), that divided each day into 12 equal hours, for their 
civil time.

 

To achieve that, they used a stick-tip nodus or bead-nodus. to cast a 
point-shadow on the hemicyclium surface. As the Sun's declination changes 
seasonally, of course the tip-nodus's path on the hemicyclium changes too. So 
the hour-lines were curves, drawn so that, for any particular solar 
declination, those marks divide the day (sunrise to sunset) into 12 equal parts.

 

As you can imagine, that makes the dial more complicated than modern ones. 
"Early" doesn't always mean "simpler".

 

...and so there was much opportunity for error in the calclulations and 
drafting,for those curved hour-lines.

 

So maybe some hemicyclia were inaccurately drafted. For one thing, of course 
the exact time of day wasn't as crucial in those days, and of course the more 
precisely made, and prestigiously made, a sundial was, the more it was likely 
to cost.

 

But there's no reason why your hemicyclium should be made for Temporary Hours. 
Make it for our modern Equal-Hours, also referred to as Local True Solar Time 
(LTST).

 

 

It appears to me the only issue is it needs to be tilted so that the gnomon 
aligns with the Earth’s rotation axis; 

 

The equinox circle on the Hemicyclium, the line that the tip-nodus follows on 
the day of the equinox, should be a circle parallel to the celestial equator.

 

And yes, if you're going to use a polar gnomon instead of a tip-nodus, then 
that polar gnomon should be parallel to the Earth's axis, pointed at the north 
celestial pole. ...and should go through the center of the sphere from which 
the Hemicyclium is cut. 

 

But, if you're going to do that, then why make it a Hemicyclium? Why not just a 
Band-Equatorial dial? You could mount a cylindrical brass band, parallel to the 
equator, with a polar-parallel rod-gnomon mounted to go through the central 
axis of that band.

 

You could mount that brass Band-Equatorial on a mount of whatever kind. For 
extra durability, you could mount it inside a concrete structure resembling a 
Hemicyclium. The durability of a Hemicyclium, with the simplicity and modernity 
of a Band-Equatorial.

 

So then the hour-lines would just be polar-parallel lines equidistantly drawn 
along the inside of the band, dividing the lower half of the band into 12 

RE: Hemicyclium correction

[Brad Thayer]

Frank,

Thank you for the tutorial.  I believe I followed all the logic and steps.
However, its your step 19 I am interested in.  Any suggestions as to how to
mark the inner surface with equal duration hours throughout the year?

And if I do tilt the hemispherium so that the horizon line is now instead
parallel to the earth's axis, does that solve any of the issues?

-Original Message-
From: Frank King [mailto:f...@cl.cam.ac.uk]
Sent: Monday, October 16, 2017 11:12 AM
To: Brad Thayer <wissenschaft...@verizon.net>
Cc: sundial@uni-koeln.de; Frank King <f...@cl.cam.ac.uk>
Subject: Re: Hemicyclium correction

Dear Brad,

You say:

> I am looking to make a
> hemicyclium-type sundial
> (half-hemisphere) in a
> metal working class.



> Am I missing anything?

Er, yes.  Rather a lot alas...

Before you start bashing metal
it may be worth spending rather
less effort on a prototype.

> ...they are inaccurate...

I am not sure where you got that
from.  There is no reason why they
shouldn't be accurate provided you
know what you can expect of one.

> ...without being very clear
> on the problem.

I suspect the writer of your
quote either didn't know what a
hemicyclium was or had looked
at one and noted that it didn't
indicate the same time as his
watch so it must be wrong.

> It appears to me the only
> issue is it needs to be
> tilted so that the gnomon
> aligns with the Earth's
> rotation axis...

Er, no.  The polar-oriented
gnomon wasn't invented for
nearly 1500 years after the
hemicyclium was in common
use.

What looks like a gnomon and
may well be CALLED a gnomon
is not what you think of as
a gnomon.  It is actually
a "nodus support".  Only
the shadow of the tip is
of interest.

> I am also looking to use
> an analemma-shaped gnomon
> to cast the shadow on the
> bowl...

First, build a prototype.
You can think about fancy
upgrades later.

Imagine the following...

 1. Take an orange.

 2. Cut it in half.  Throw
one half away.  [OK,
maybe eat it first.]

 3. Then cut the half
in half and throw
one of these quarters
away.

 4. What you are left with
is your half hemisphere.

 5. This has one curved
surface and two plane
surfaces.

 6. Arrange for one of the
planes to be horizontal
and the other to be
vertical and facing
due south (assuming you
are in the northern
hemisphere).

 7. Now place a bead in the
middle of the edge that
is common to the two flat
faces.  THIS is the nodus.

 8. Now imagine that all the
space between the bead
and the skin is replaced
by a transparent medium.

 9. You now have an embryonic
hemicyclium.  Let's think
about some of its
properties

10. At sunrise (and sunset)
the sun is in the plane
of the horizontal flat
surface, and the shadow of
the bead (in the winter
half of the year) will
fall on the inside rim
of the horizontal element
of skin.  This rim is the
"horizon line".

11. At an equinox the shadow
of the bead during the
course of a day will
follow a great (half)
circle on the inside
surface of the skin.

12. At the winter solstice
it will follow a small
(less than half) circle
on the inside surface
and this will be above
the equinoctial circle.

13. At the summer solstice
you hit a minor snag.
At sunrise the sun is
north of due east and
the shadow of the bead
will not fall on the
rim.  Don't worry about
this yet.  [The Greeks
DID cope with this but
that's for later.]

14. Instead, pick up the
path of the shadow
starting from when the
sun is due east and,
by then, some way
above the horizon.

15. You will again get a
small (less than half)
circle.

16. Now add lots of
intermediate small
circles for other
times of year.

17. At this point you have
a choice as to how you
chop up each circle into
hours...

18. The ancients chopped each
part circle in the winter
half into 12 parts, thus
dividing the daylight
period into unequal hours.
You could label the spaces
1 to 12 if you like.  The
Greeks didn't have digits
or even Roman Numerals and
labelled the hours alpha,
beta, gamma etc.

19. That's the way I would do
it but if you insist on
using iconoclastic new
fangled equal hours then
you can.  You will find
it rather harder!

20. That completes your
prototype.  Now have a
long think about what
you really want to do.

Very best wishes

Frank

Frank H. King
Cambridge, U.K.



---
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Re: Hemicyclium correction

[Michael Ossipoff]

When I have a clock and not a sundial, clock time has to be converted into
sundial time (Local True Solar Time) to make it day-relevant.

So, if you make a sundial, shouldn't it just show sundial time? Isn't that
really what a sundial for--showing Local True Solar Time?

You could make a correction-table to convert sundial-time to
clock-time--consisting of the EoT, with the longitude-correction added to
it for converting from sundial time to clock time.   ...and display it
beside the sundial.

By the way, when I said that a Disk Equatorial is incomparably easier to
make than a Band or Cylinder Equatorial, of course should have added
"...unless you already have a cylinder or a band, and a means to make a
hole in it, to make a circumference hole-nodus.

Of course such a dial can only show 12 hours of time, but that can be
remedied by having more than one circumference-hole nodus.

I don't know the right terminology for what I call a Band-Equatorial or a
Cylinder-Equatorial.

If the band is wide enough for a circumference hole-nodus to cast it
light-spot on the band all year, so that the band has a width equal to
D*2tan(obliquity), giving it a width nearly equal to half its diameter,
maybe that's the practical-difference-point at which a Band-Equatorial
becomes a Cyllinder-Equatorial.

As I understand it, "Equatorial Dial" usually refers to a Disk-Equatorial.
I call it the Cylinder and Band versions Equatorials because they measure
time in the same direct way that a Disk-Equatorial does.   ...but their
dial-surface is parallel to the Earth's polar-axis so someone could argue
that they should be called Polar Band or Cylinder dials.

So what are they correctly called?

Michael Ossipoff

..

On Wed, Oct 18, 2017 at 3:29 AM, Nathaniel Shippen 
wrote:

> Well, my first attempt at a sundial is about the simplest you could
> imagine. However, I did follow Albert Waugh's suggestion in "Sundials:
> Their Theory And Construction" and offset the time marks to Hawaii Standard
> Time, so I only have to keep the daily Equation of Time value in mind. Note
> that the 12:30 mark is almost vertically below the gnomon. At my location
> near Honolulu mean solar time is 32 minutes behind HST (GMT - 10). In fact
> until after World War 2 clocks in Hawaii were set to GMT - 10:30, much
> closer to mean solar time throughout the state. In 1947 Hawaii was
> shoehorned into the GMT - 10 timezone also used in the Aleutian Islands.
>
> https://en.wikipedia.org/wiki/Hawaii%E2%80%93Aleutian_Time_Zone
>
> Nathaniel Shippen
>
> On Wed, Oct 18, 2017 at 3:53 AM, Michael Ossipoff 
> wrote:
>
>> But, if you're willing to give up the Horizontal-Dial's advantages, then
>> an Equatorial-Dial has the following advantages:
>>
>> 1. Its equally-spaced hour-lines allow perfectly accurate linear
>> interpolation of the time, when the shadow is between hour-lines.
>>
>> (But, when usiing pocket horizontal tablet-dials, linear interpolation
>> gave results accurate with 3 minutes, when only the hours and half-hours
>> were marked. So interpolation with unequally-spaced hour-lines doesn't seem
>> a problem.)
>>
>> 2. Its principle is obvious. The Horizontal-Dial's construction-principle
>> isn't difficult to explain, but the Equatorial's construction-principle is
>> obvious at a glance.  It would make perfect sense to anyone, without any
>> explanation.
>>
>> (By the way, it's true that a Bifilar Dial shares the advantage of
>> equally-spaced hour-lines. But it only tells time for part of the day,
>> because, when the Sun is low, the shadow of interest won't be on the
>> dial-plate.)
>>
>> Of course a two-sided Disk-Equatorial is incomparably easier to construct
>> than a Band-Equatorial or Cylinder-Equatorial.   ...if you don't mind the
>> fact that a Disk-Equatorial can only be read from the north in the summer,
>> and from the south in the winter.
>>
>> Michael Ossipoff
>>
>>
>>
>>
>> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer > > wrote:
>>
>>> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
>>> metal working class.  What little I can find on them says they are
>>> inaccurate, without being very clear on the problem.  It appears to me the
>>> only issue is it needs to be tilted so that the gnomon aligns with the
>>> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
>>> south, but the end of the gnomon that attaches to the bowl points north.
>>> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
>>> to cast the shadow on the bowl, and at least month lines for the solar
>>> elevation.  The bowl will also have a rod and bracket on the bottom to
>>> allow it to be rotated for daylight-savings time and for local longitude
>>> corrections.
>>>
>>>
>>>
>>> Thanks in advance -- Brad
>>>
>>> ---
>>> https://lists.uni-koeln.de/mailman/listinfo/sundial
>>>
>>>
>>>
>>

Re: Hemicyclium correction

[Michael Ossipoff]

But, if you're willing to give up the Horizontal-Dial's advantages, then an
Equatorial-Dial has the following advantages:

1. Its equally-spaced hour-lines allow perfectly accurate linear
interpolation of the time, when the shadow is between hour-lines.

(But, when usiing pocket horizontal tablet-dials, linear interpolation gave
results accurate with 3 minutes, when only the hours and half-hours were
marked. So interpolation with unequally-spaced hour-lines doesn't seem a
problem.)

2. Its principle is obvious. The Horizontal-Dial's construction-principle
isn't difficult to explain, but the Equatorial's construction-principle is
obvious at a glance.  It would make perfect sense to anyone, without any
explanation.

(By the way, it's true that a Bifilar Dial shares the advantage of
equally-spaced hour-lines. But it only tells time for part of the day,
because, when the Sun is low, the shadow of interest won't be on the
dial-plate.)

Of course a two-sided Disk-Equatorial is incomparably easier to construct
than a Band-Equatorial or Cylinder-Equatorial.   ...if you don't mind the
fact that a Disk-Equatorial can only be read from the north in the summer,
and from the south in the winter.

Michael Ossipoff




On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
wrote:

> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction

[Michael Ossipoff]

On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
wrote:

> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.
>

But the way, I've seen it spelled "Hemicycleum" as well. I don't know which
is correct, but "Hemicycleum" looks better, it seems to me. But I'll use
your spelling. It's probably better-accpeted.

Whoever said that was mistaken. Hemicyclia are as in principle as accurate
as any sundial can be.

In ancient times, Hemicyclia were devised, instead of our modern
polar-gnomon garden sundial, or our equatorial sundials, because in those
days, they weren't using our Equal-Hours for civil time (Astronomers used
it though). They were using "Temporary Hours), that divided each day into
12 equal hours, for their civil time.

To achieve that, they used a stick-tip nodus or bead-nodus. to cast a
point-shadow on the hemicyclium surface. As the Sun's declination changes
seasonally, of course the tip-nodus's path on the hemicyclium changes too.
So the hour-lines were curves, drawn so that, for any particular solar
declination, those marks divide the day (sunrise to sunset) into 12 equal
parts.

As you can imagine, that makes the dial more complicated than modern ones.
"Early" doesn't always mean "simpler".

...and so there was much opportunity for error in the calclulations and
drafting,for those curved hour-lines.

So maybe some hemicyclia *were* inaccurately drafted. For one thing, of
course the exact time of day wasn't as crucial in those days, and of course
the more precisely made, and prestigiously made, a sundial was, the more it
was likely to cost.

But there's no reason why your hemicyclium should be made for Temporary
Hours. Make it for our modern Equal-Hours, also referred to as Local True
Solar Time (LTST).



> It appears to me the only issue is it needs to be tilted so that the
> gnomon aligns with the Earth’s rotation axis;
>

The equinox circle on the Hemicyclium, the line that the tip-nodus follows
on the day of the equinox, should be a circle parallel to the celestial
equator.

And yes, if you're going to use a polar gnomon instead of a tip-nodus, then
that polar gnomon should be parallel to the Earth's axis, pointed at the
north celestial pole. ...and should go through the center of the sphere
from which the Hemicyclium is cut.

But, if you're going to do that, then why make it a Hemicyclium? Why not
just a Band-Equatorial dial? You could mount a cylindrical brass band,
parallel to the equator, with a polar-parallel rod-gnomon mounted to go
through the central axis of that band.

You could mount that brass Band-Equatorial on a mount of whatever kind. For
extra durability, you could mount it inside a concrete structure resembling
a Hemicyclium. The durability of a Hemicyclium, with the simplicity and
modernity of a Band-Equatorial.

So then the hour-lines would just be polar-parallel lines equidistantly
drawn along the inside of the band, dividing the lower half of the band
into 12 equal parts. Of course you'd want half-hour lines too. Maybe, if
you want it to be fancier and more accurate, you could divide each hour,
instead, into 3, 4, or even 6 parts.   ...depending on how much precision
and work you want.

But that's a lot of work.

There's a good reason why the garden-style Horizontal-Dial is the most
popular design for a stationary dial--

1. It's easy to construct.

2. It tells the time whenever the sun is up (a Hemicyclium can do that too).

3. Unlike a Hemicyclium, a Horizontal-Dial is readable from all directions,
provided that you're close enough to look at it from above.

I'd say, forget about the analemic-edge gnomon. For one thing, that of
course hugely complicates the design and construction. For another thing,
if someone wants clock time, they can look at a clock or watch. A sundial
should give sundial time, Local True Solar Time.

You can have a nearby plaque-chart that tells the corrections, what to add
to the sundial's time, to give the Standard-Time for your time-zone at
various times of year.. ...and a reminder to add an hour for
DaylightSavingTime, between the specified dates.

I'd make the sundial for Local True Solar Time, equal-hours, instead of for
Temporary Hours, because, not only is that easier, but it's also the basis
Standard-Time (when adjusted for Equation-of-Time and for your longitude).

I'd suggest changing your project to a garden-style Horizontal-Dial.

Michael Ossipoff

>
>
>
---
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Re: Hemicyclium correction

[Frank King]

Dear Brad,

You say:

> I am looking to make a
> hemicyclium-type sundial
> (half-hemisphere) in a
> metal working class.



> Am I missing anything?

Er, yes.  Rather a lot alas...

Before you start bashing metal
it may be worth spending rather
less effort on a prototype.

> ...they are inaccurate...

I am not sure where you got that
from.  There is no reason why they
shouldn't be accurate provided you
know what you can expect of one.

> ...without being very clear
> on the problem.

I suspect the writer of your
quote either didn't know what a
hemicyclium was or had looked
at one and noted that it didn't
indicate the same time as his
watch so it must be wrong.

> It appears to me the only
> issue is it needs to be
> tilted so that the gnomon
> aligns with the Earth's
> rotation axis...

Er, no.  The polar-oriented
gnomon wasn't invented for
nearly 1500 years after the
hemicyclium was in common
use.

What looks like a gnomon and
may well be CALLED a gnomon
is not what you think of as
a gnomon.  It is actually
a "nodus support".  Only
the shadow of the tip is
of interest.

> I am also looking to use
> an analemma-shaped gnomon
> to cast the shadow on the
> bowl...

First, build a prototype.
You can think about fancy
upgrades later.

Imagine the following...

 1. Take an orange.

 2. Cut it in half.  Throw
one half away.  [OK,
maybe eat it first.]

 3. Then cut the half
in half and throw
one of these quarters
away.

 4. What you are left with
is your half hemisphere.

 5. This has one curved
surface and two plane
surfaces.

 6. Arrange for one of the
planes to be horizontal
and the other to be
vertical and facing
due south (assuming you
are in the northern
hemisphere).

 7. Now place a bead in the
middle of the edge that
is common to the two flat
faces.  THIS is the nodus.

 8. Now imagine that all the
space between the bead
and the skin is replaced
by a transparent medium.

 9. You now have an embryonic
hemicyclium.  Let's think
about some of its
properties

10. At sunrise (and sunset)
the sun is in the plane
of the horizontal flat
surface, and the shadow of
the bead (in the winter
half of the year) will
fall on the inside rim
of the horizontal element
of skin.  This rim is the
"horizon line".

11. At an equinox the shadow
of the bead during the
course of a day will
follow a great (half)
circle on the inside
surface of the skin.

12. At the winter solstice
it will follow a small
(less than half) circle
on the inside surface
and this will be above
the equinoctial circle.

13. At the summer solstice
you hit a minor snag.
At sunrise the sun is
north of due east and
the shadow of the bead
will not fall on the
rim.  Don't worry about
this yet.  [The Greeks
DID cope with this but
that's for later.]

14. Instead, pick up the
path of the shadow
starting from when the
sun is due east and,
by then, some way
above the horizon.

15. You will again get a
small (less than half)
circle.

16. Now add lots of
intermediate small
circles for other
times of year.

17. At this point you have
a choice as to how you
chop up each circle into
hours...

18. The ancients chopped each
part circle in the winter
half into 12 parts, thus
dividing the daylight
period into unequal hours.
You could label the spaces
1 to 12 if you like.  The
Greeks didn't have digits
or even Roman Numerals and
labelled the hours alpha,
beta, gamma etc.

19. That's the way I would do
it but if you insist on
using iconoclastic new
fangled equal hours then
you can.  You will find
it rather harder!

20. That completes your
prototype.  Now have a
long think about what
you really want to do.

Very best wishes

Frank

Frank H. King
Cambridge, U.K.


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