Inferior polar dial
What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units. David Brown Somerton, Somerset, UK
Inferior Polar Dial
What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units. Thank you for the various replies sent in (4). I clarified the term 'inferior' later on that day thus: "Inferior"..Think first of a 'normal' polar dial, parallel to the polar axis, aligned E-W but face open to the south i.e. that part of the celestial equator above the horizon. Now consider the underneath of this polar dial, face open to the north, facing that part of the celestial equator which is (mostly) below the northern horizon. You've now got an 'inferior' polar dial. The term is used in a document I came across recently (on the internet). I suppose that an equivalent description would be 'a polar dial facing north' or a direct north dial inclining at an angle to the horizon equal to the latitude of the place (52 deg in this case). Yes - it will be latitude independent, but I included that detail so that it would pin down the discussion a bit. The BSS Glossary also defines 'inferior' as "refers to an event on the celestial sphere below the horizon. Opposite of superior." Let me now tell you the reason for my enquiry: I was looking at the website of the Museum of the History of Science, Oxford (epact.mhs.ox.ac.uk/catalogue), and brought up the details of Nicolaus Kratzer's portable polyhedral dial (1525) made of gilt brass which he presented to Cardinal Wolsey (Inventory No. 54054). It appears to have been made for latitude 52 deg. N There are dials on nine faces. One is described as an 'inferior polar dial, with lines marked 4,6,8. This puzzled me - what is the sense of only hours 4,6,8 on any dial? The illustration given on the museum's web page is not clear enough to get any detail other than to see that the north face is not visible. However, a postcard I bought at the museum some years ago does show the north face and knowing the overall height of the dial (100mm) I estimate that the height of the gnomon on the inferior polar dial is 13 mm. It seems that the lines for 4 am ( to the west and 8 pm to the east) are wrongly positioned - they should be about 22.5 mm away from the centre of the dial, and are nowhere near this distance. A further puzzle - why did Kratzer mark the line on which the gnomon lies with a 6? It should be 12 (midnight!) if it's going to be anything - or was it because 6 comes exactly between 8 and 4? A blunder, perhaps? More measurement pending.. David Brown Somerton, Somerset, UK
Re: Inferior polar dial
Pardon my ignorance David, but what's an "inferior" polar dial, please? Surely the latitude is irrelevant, as a polar dial is merely inclined. If I'[m right in thinking the dial is shaped like an inverted letter "T", it seems to me that the shadow of the gnomon will fall on the dial for 3hours 40 minutes either side of noon, so I suppose the answer to your question is that it should show 8:30am to 3:30pm in GMT, and 9:30 to 4:30 BST, assuming it's for the UK. Regards Chris Lusby Taylor 51.4N 1.3W - Original Message - From: [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Sunday, January 25, 2004 7:40 PM Subject: Inferior polar dial I think I know the answer to this one, and I'll say more in due course, but just to see what all you gurus say..What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units. David BrownSomerton, Somerset, UK
Re: Inferior Polar Dial
Ah, so that's what the enquiry was about! The correct URL is http://www.mhs.ox.ac.uk/epact In the picture in the catalogue, which is the only one I've seen of this dial, this inferior polar dial isn't visible. But I have to agree that 4,6,8 sounds unlikely. How much do we know about Kratzer's ability to make accurate dials? The direct west-facing dial visible in the picture seems to be for 45 degrees, not 52 degrees latitude. And what do you make of the gnomon of the reclining south-facing dial? When studying the Kratzer-like polyhedral dial in Holbein's Ambassadors I found a surprisingly simple equation that allows you to convert angles and dimensions in a photograph or perspective painting into the original object's dimensions. I'll email it to anyone interested. It allowed me to calculate, for instance, that the apparently square dial on the end of the dial is actually very inaccurate. Which could have been Holbein's error in painting it, not Kratzer's. Anyway, we'll be in Oxford in a couple of months so I'm looking forward to the chance to see this dial for myself. Best wishes Chris Lusby Taylor 51.4N, 1.3W (so only about 25 miles from Oxford. Lucky me) - Original Message - From: [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Friday, January 30, 2004 8:56 AM Subject: Inferior Polar Dial On 25th Jan I posted the following query:What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units.Thank you for the various replies sent in (4).I clarified the term 'inferior' later on that day thus:"Inferior"..Think first of a 'normal' polar dial, parallel to the polar axis, aligned E-W but face open to the south i.e. that part of the celestial equator above the horizon. Now consider the underneath of this polar dial, face open to the north, facing that part of the celestial equator which is (mostly) below the northern horizon. You've now got an 'inferior' polar dial. The term is used in a document I came across recently (on the internet). I suppose that an equivalent description would be 'a polar dial facing north' or a direct north dial inclining at an angle to the horizon equal to the latitude of the place (52 deg in this case). Yes - it will be latitude independent, but I included that detail so that it would pin down the discussion a bit.The BSS Glossary also defines 'inferior' as "refers to an event on the celestial sphere below the horizon. Opposite of superior."Let me now tell you the reason for my enquiry:I was looking at the website of the Museum of the History of Science, Oxford (epact.mhs.ox.ac.uk/catalogue), and brought up the details of Nicolaus Kratzer's portable polyhedral dial (1525) made of gilt brass which he presented to Cardinal Wolsey (Inventory No. 54054). It appears to have been made for latitude 52 deg. NThere are dials on nine faces. One is described as an 'inferior polar dial, with lines marked 4,6,8. This puzzled me - what is the sense of only hours 4,6,8 on any dial?The illustration given on the museum's web page is not clear enough to get any detail other than to see that the north face is not visible. However, a postcard I bought at the museum some years ago does show the north face and knowing the overall height of the dial (100mm) I estimate that the height of the gnomon on the inferior polar dial is 13 mm. It seems that the lines for 4 am ( to the west and 8 pm to the east) are wrongly positioned - they should be about 22.5 mm away from the centre of the dial, and are nowhere near this distance.A further puzzle - why did Kratzer mark the line on which the gnomon lies with a 6? It should be 12 (midnight!) if it's going to be anything - or was it because 6 comes exactly between 8 and 4? A blunder, perhaps?More measurement pending..David BrownSomerton, Somerset, UK
Re: Inferior polar dial
On Sun, 25 Jan 2004 [EMAIL PROTECTED] wrote: > I think I know the answer to this one, and I'll say more in due course, but > just to see what all you gurus say.. > What hour lines should be inscribed, and in what places, on an inferior polar > dial for latitude 52N? The centrally-placed gnomon is 13 units high, the > overall plate width (east-west) is 37 units and the north-south plate height > is 26 > units. > David Brown > Somerton, Somerset, UK With a style height of 13 and half-width of 18.5, I make the angle out at 35.1 degrees. Therefore, only lines more than two hours before 0600 and after 1800 will be meaningful. At high latitudes, there should be a short time in the Summer, when both sun and style shadow hit the face... Dave 37.277N 121.966W -
RE: Inferior Polar Dial
On Fri, 30 Jan 2004, Roger Bailey wrote: > The epact link didn't work for me. I was "not authorized to view this page". > The main link did work. http://www.mhs.ox.ac.uk I then went to the > collections database link and searched for 54054. There are six pictures of > the Kratzer dial available. Pictures 1 and 2 are from the south west and > show the top horizontal, superior polar, south vertical, inferior equatorial > and west vertical dials. Pictures 3, 5, and 6 are from the north east > showing the top horizontal, superior equatorial, north vertical, inferior > polar and east vertical. > > Picture 5 shows the details of the north facing inferior polar dial from the > north west. The engraved lines are not too clear and no numbers are visible. > I could see only three lines, one for midnight and one one each side, > perhaps showing sunrise and sunset as discussed in my earlier note. Strange, the different results and accessibility! Both links work for me, but while the epact site seems to be structured axactly like the database link Roger used, it only has the single photo. Too bad, because epact also allows clicking in to a much higher resolution than the other! Dave 37.277N 121.966W -
Re: Inferior polar dial
Thanks for your interest, Chris David Brown Somerton, Somerset, UK
Re: Inferior polar dial
Hi David, if I have not made great mistakes in my calculations - done quickly :-) - you cannot inscribe any hour lines on your polar sundial facing north. At Lat. 52N on summer solstice, the Sun rises at 3h 47m (civil time) or at 3h 45m apparent Solar time. At 4h apparent time, the sun has (year 2004) : Azimuth= -127.3508d and Altitude=1.7789d. With these values and with a gnomon 13 units high, the shadow point falls at 22.5 units from the dial center westward and at 11.3 units downward : for this reason out your dial. In the next hours, and in different days, the things become worse and the shadow point moves away. For example at 4h30m (apparent time) the shadow falls at 31.4 units from the center westward, etc. At 6h the Sun passes in front of the dial. Obviously the things are symmetrical in the evening hours. Best Gianni Ferrari 44° 39' N 10° 55' EMailto : [EMAIL PROTECTED]
Re: Inferior Polar Dial
The Wolsey/Kratzer dial is discussed in Peter Drinkwater's booklet "The Sundials of Nicholas Kratzer". Although he doesn't analyse the hourlines, it is clear that Drinkwater is no admirer of Kratzer's dialling abilities - he accuses him of all sorts of muddles and mistakes. The "6" marking on the sub-style line sounds like an attempt at using Italian hours, measured from sunset. But that couldn't be correct. Can you tell from the picture whether the dial is read from the shadow of the tip of the gnomon (as was common on Kratzer's dials) or from its whole length? Obviously there is a need to look at the dial closely in April! Regards, John --[EMAIL PROTECTED] wrote: On 25th Jan I posted the following query:What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units.Thank you for the various replies sent in (4).I clarified the term 'inferior' later on that day thus:"Inferior"..Think first of a 'normal' polar dial, parallel to the polar axis, aligned E-W but face open to the south i.e. that part of the celestial equator above the horizon. Now consider the underneath of this polar dial, face open to the north, facing that part of the celestial equator which is (mostly) below the northern horizon. You've now got an 'inferior' polar dial. Th! e term is used in a document I came across recently (on the internet). I suppose that an equivalent description would be 'a polar dial facing north' or a direct north dial inclining at an angle to the horizon equal to the latitude of the place (52 deg in this case). Yes - it will be latitude independent, but I included that detail so that it would pin down the discussion a bit.The BSS Glossary also defines 'inferior' as "refers to an event on the celestial sphere below the horizon. Opposite of superior."Let me now tell you the reason for my enquiry:I was looking at the website of the Museum of the History of Science, Oxford (epact.mhs.ox.ac.uk/catalogue), and brought up the details of Nicolaus Kratzer's portable polyhedral dial (1525) made of gilt brass which he presented to Cardinal Wolsey (Inventory No. 54054). It appears to have been made for latitude 52 deg. NThere are dials on nine faces. One is described as an 'inferior polar dial, with lines marked 4,6,! 8. This puzzled me - what is the sense of only hours 4,6,8 on any dial?The illustration given on the museum's web page is not clear enough to get any detail other than to see that the north face is not visible. However, a postcard I bought at the museum some years ago does show the north face and knowing the overall height of the dial (100mm) I estimate that the height of the gnomon on the inferior polar dial is 13 mm. It seems that the lines for 4 am ( to the west and 8 pm to the east) are wrongly positioned - they should be about 22.5 mm away from the centre of the dial, and are nowhere near this distance.A further puzzle - why did Kratzer mark the line on which the gnomon lies with a 6? It should be 12 (midnight!) if it's going to be anything - or was it because 6 comes exactly between 8 and 4? A blunder, perhaps?More measurement pending..David BrownSomerton, Somerset, UK Dr J R Davis! Flowton DialsN52d 08m: E1d 05m)
RE: Inferior polar dial
Hello David, Thanks for the good question. Although there are no hour lines possible for the inverted polar dial of these dimensions at your latitude of 52 degrees, the crack of sunrise and sunset may just show on the edge of the dial. The height of the gnomon (13) and width of the dial plate (37/2) works for a time angle maximum* of +/- 55 degrees or +/- 3 hours 40 minutes from midnight. At other times the shadows would either be too long or on the south side of the plate. The dial would work well during the summer in polar latitudes when the sun rise and set is less that 3:40 from midnight. This would limit your dial to latitudes** to above 52.9 degrees even for the summer solstice. This is based on the theoretical altitude of the center of the sun being zero. For the observed first and last crack of sunset, you have to adjust for semidiameter and refraction (dip). Allowing for semidiameter (16") and refraction (32"), the*** crack of sunrise/set on the summer solstice are at ~3:38:18. This time angle of 54.57 degrees would be just on your dial. * Time angle maximum: Tan t = 37/2/13 so t = 55 degrees. **Sunrise/set time without dip and semidiameter corrections: Cos t = - Tan L * Tan D. For t = 55 and D =23.44, L = 52.9. **Sine Altitude = Sin L x Sin D + Cos L x Cos D x Cos t. For Altitude = -48" or 0.8 degrees, L = 52 and D =23.44, t solves to 54.573 degrees. Roger Bailey Walking Shadow Designs N 48.6 W 123.4 For more fun like this, please refer to my presentation on Sunset Phenomenon on the NASS Repository or I can provide copies on request. -Original Message-From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of [EMAIL PROTECTED]Sent: January 25, 2004 11:40 AMTo: sundial@rrz.uni-koeln.deSubject: Inferior polar dial I think I know the answer to this one, and I'll say more in due course, but just to see what all you gurus say..What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units. David BrownSomerton, Somerset, UK
RE: Inferior Polar Dial
The
epact link didn't work for me. I was "not authorized to view this page". The
main link did work. http://www.mhs.ox.ac.uk I then went to the collections
database link and searched for 54054. There are six pictures of the Kratzer dial
available. Pictures 1 and 2 are from the south west and show the top
horizontal, superior polar, south vertical, inferior equatorial and west
vertical dials. Pictures 3, 5, and 6 are from the north east showing the top
horizontal, superior equatorial, north vertical, inferior polar and east
vertical.
Picture 5 shows the details of the north facing inferior polar dial from
the north west. The engraved lines are not too clear and no numbers are visible.
I could see only three lines, one for midnight and one one each side, perhaps
showing sunrise and sunset as discussed in my earlier note.
Thanks
for the question David. It got me to this website and the wonderful collection
of antique dials. As search of their data base for " sundial" brings up 83
listings.
Cheers,
Roger
Bailey
N
48.6 W 123.4
-Original Message-From:
[EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On
Behalf Of Chris Lusby TaylorSent: January 30, 2004 1:49
AMTo: sundial@rrz.uni-koeln.deSubject: Re: Inferior
Polar Dial
Ah, so that's what the enquiry was about!
The correct URL is http://www.mhs.ox.ac.uk/epact
In the picture in the catalogue, which is the only one
I've seen of this dial, this inferior polar dial isn't visible.
But I have to agree that 4,6,8 sounds
unlikely.
How much do we know about Kratzer's ability to make
accurate dials? The direct west-facing dial visible in the picture seems to be
for 45 degrees, not 52 degrees latitude. And what do you make of
the gnomon of the reclining south-facing dial?
When studying the Kratzer-like polyhedral dial in
Holbein's Ambassadors I found a surprisingly simple equation that allows you
to convert angles and dimensions in a photograph or perspective painting
into the original object's dimensions. I'll email it to anyone interested. It
allowed me to calculate, for instance, that the apparently square dial on the
end of the dial is actually very inaccurate. Which could have been Holbein's
error in painting it, not Kratzer's.
Anyway, we'll be in Oxford in a couple of months so I'm
looking forward to the chance to see this dial for myself.
Best wishes
Chris Lusby Taylor
51.4N, 1.3W (so only about 25 miles from Oxford. Lucky
me)
- Original Message -
From:
[EMAIL PROTECTED]
To: sundial@rrz.uni-koeln.de
Sent: Friday, January 30, 2004 8:56
AM
Subject: Inferior Polar Dial
On 25th Jan I posted the following
query:What hour lines should be inscribed, and in what places, on an
inferior polar dial for latitude 52N? The centrally-placed gnomon is
13 units high, the overall plate width (east-west) is 37 units and the
north-south plate height is 26 units.Thank you for the various replies
sent in (4).I clarified the term 'inferior' later on that day
thus:"Inferior"..Think first of a 'normal' polar dial, parallel
to the polar axis, aligned E-W but face open to the south i.e. that part of
the celestial equator above the horizon. Now consider the underneath
of this polar dial, face open to the north, facing that part of the
celestial equator which is (mostly) below the northern horizon. You've now
got an 'inferior' polar dial. The term is used in a document I came across
recently (on the internet). I suppose that an equivalent description would
be 'a polar dial facing north' or a direct north dial inclining at an angle
to the horizon equal to the latitude of the place (52 deg in this case). Yes
- it will be latitude independent, but I included that detail so that it
would pin down the discussion a bit.The BSS Glossary also defines
'inferior' as "refers to an event on the celestial sphere below the horizon.
Opposite of superior."Let me now tell you the reason for my
enquiry:I was looking at the website of the Museum of the History of
Science, Oxford (epact.mhs.ox.ac.uk/catalogue), and brought up the details
of Nicolaus Kratzer's portable polyhedral dial (1525) made of gilt brass
which he presented to Cardinal Wolsey (Inventory No. 54054). It appears to
have been made for latitude 52 deg. NThere are dials on nine faces. One
is described as an 'inferior polar dial, with lines marked 4,6,8. This
puzzled me - what is the sense of only hours 4,6,8 on any dial?The
illustration given on the museum's web page is not clear enough to get any
detail other than to see that the north face is not visible. However, a
