equation of time

[Patrick Powers]

Message text written by Frank Evans

>    but for navigators EoT has always been mean time minus apparent
time.  My
British Admiralty Manual of Navigation, Volume 2, 1938 states simply:
The equation of time is defined as the excess of mean time over apparent
time.<


 I have just looked up a few sources immediately available to me to try and
demonstrate the different thinking on this topic and to see whether I was
right to allege that it was a difference in thinking between navigators and
astronomers.

1.   Mayall & Mayall agree with you saying EoT = Mean Time - Apparent Time;
 and in their book 'Sundials' they quote  from an American Ephemeris.  They
show the EoT running at +14 mins in February.

2.  Waugh on the other hand tries to avoid allocating a + or -  sign and
treats the EoT as a number  which is added or subtracted according to
whether the dial is fast or slow.  However arithmetically he adds the EoT
to Mean time  to get Apparent Time and thus shows EoT running at -14 mins
in February.

3.  My copy of Whitaker's Almanack in their Astronomy section observes that
the Apparent Solar Day is shorter than average at the Equionoxes and larger
than average at the solstices).  It follows this convention to show EoT
running at -14 mins in February.

4.  As another check, the NASS Software Dialist's Companion shows EoT as
running at -14 mins in February.

5.  Then there is the web page of this man Powers
(http://ourworld.compuserve.com/homepages/patrick_powers/homepage.htm) who
also shows EoT at -14 mins in February - but you shouldn't believe him -
he's biassed!

Where does all that leave us I wonder?  :-)  It does look to me a bit as
though it is a difference between navigators and astronomers.

Patrick

Equation of Time

[Tony Moss]

Fellow Shadow Watchers

Current discussions Re.the Equation of Time bring to mind Tad Dunne's 
contribution to the Great Sundial Motto Festival of 1998 - or World War 
III depending on how you remember it  :-)

Hope you don't mind me re-printing you Tad!

"On September One, you can trust the sun
Come Halloween, subtract sixteen.
On Christmas day, the dial's OK
For your Valentine true, add a dozen and two.

Add no more, the mid of month four.
The mid of May, take four away.
On June fourteen, don't add a bean.
When August begins, add seven little mins.

The rest is easy:  For any date
All you do is interpolate."



Tony Moss

Equation of Time

[tony_kitto]

Whitaker's Almanack says "The direction in which the equation of time 
has to be applied in different problems is a frequent source of confusion and 
error." I think the confusion has little to do with any difference between 
navigators and astronomers. I think it had more to do with the increased 
ownership of clocks and the changeover from apparent to mean time. In the 
17th or 18th century no-one would have considered 
labelling a sundial as slow or fast.
Originally an alternative name for the equation of time was the equation of 
natural days. The amount each day differs from 24 hours is accumulated to give 
an equation. Christian Huygens first published an equation of time in 1665. It 
went from zero in February to a maximum in early November. He used it to check 
his watches, noting the regular difference between clock time and sundial time. 

John Flamsteed published his equation of natural days in 1673. He calculated 
his times to add or subtract from apparent solar time to give mean solar time 
for astronomical purposes. Flamsteed fixed mean solar time by the times of the 
aphelion and spring equinox.
Thomas Tompion sold equation tables to go with his clocks from 1683. The 
equation values were provided by Flamsteed. Tompion’s table. It shows 
"How much a good Pendulum Watch ought to be faster or slower then a true 
Sun-Dial, every day of the Year". The values were nor assigned + or -, 
instead starting in January the Watch is too fast. After April 4th 
the Watch is too slow, in June watch too fast again etc. . Both the clock tables 
and the sundial at Bath Pump Room followed the instructions "Set the watch 
so much faster or slower than the time by the sun, according to the Table for 
the Day of the Month, when you set it; and if the Watch go true, the difference 
of it from the Sun any day afterwards will be the same with the Table".
I hope this shows the two different applications of the equation of time in 
the 17th century. You can find out more about Flamsteed’s 
equation of natural days by visiting the web-site promoting an exhibition of the 
founding of Greenwich Observatory at http://www.burnley.gov.uk/towneley/ttt/index.htm 
.
Tony Kitto
 [EMAIL PROTECTED]

equation of time

[Willy Leenders]

The equation of time has two causes. The first is that the orbit of the earth 
around the sun is an
ellipse and not a circle. The second is that the plane of the earth's equator 
is inclined tot the
plane of the earth's orbit.
Please can anyone explain me the second cause so that I can conceive it. I am 
not a astronomer!

You can do it in Dutch (for preference), in French, in German or in English.

Willy Leenders
Hasselt
Belgium

Equation of time

[Yvon Mass]

Dear all,

I would like to know how the equation of time (EoT) is defined according to
country.
For example in France, traditionally: EoT = real time - mean time
while in USA: Eot = mean time - real time.
Could you tell me how you define the Eot in your country ?

Many thanks

Yvon

Yvon MASSE  7, rue des Tilleuls  95300 PONTOISE  FRANCE
Mél:  [EMAIL PROTECTED]

Equation of time

[Yvon Mass]

Hello all,

Ooops!... Of course, I make a mistake:

>For example in France, traditionally: EoT = real time - mean time
>while in USA: Eot = mean time - real time.

Please read:
For example in France, traditionally: EoT = local mean time - solar time
while in USA: Eot = solar time - local mean time.

Yvon

equation of time

[Frank Evans]

Greetings fellow dialists

In his recent article on the equation of time in BSS Bulletin 17 (iii), 
Chris Daniel writes that the earliest appearance of the analemma in a UK 
publication is perhaps the illustration in the second edition of Mrs. 
Gatty's sundial book, dated 1889. Here the figure and construction 
details are the work of Wigham Richardson, a Tyneside shipbuilder. In 
his diagram the familiar "figure of eight" is superimposed on the noon 
line. Of necessity such a construction demands a nodus on the gnomon and 
we may describe the arrangement as a graphic indicator of the equation 
of time through the year.


Earlier, in 1881 Wigham Richardson made a sundial which he placed at the 
entrance to his shipyard. This dial bore a curve stretched over a 
straight line, which was also clearly an expression of the equation of 
time. Unfortunately neither the old photograph of the dial in situ nor 
the more recently repainted dial shows any indication of the months to 
which the parts of the curve are related. But they must originally have 
been present.


Such a snake-like curve is not an indicator of the equation of time but 
a graphic illustration of its changes through the year.


My question is: Was this, like Richardson's appendix in Mrs. Gatty's 
book, a first appearance of an equation of time line? Can anyone supply 
earlier earlier examples of such a line on dials either in the UK or 
elsewhere?


Frank 55N 1W



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equation of time

[Frank Evans]

Greetings fellow dialists

Re the earliest analemma on a dial in the UK nothing has turned up 
before the 1889 example cited by Chris Daniel but thanks to Franz Maes, 
Dave G. and Tony Moss for helping the problem along. Early equation of 
time corrections engraved around the edge of horizontal dials are common 
enought. It would also seem that in the UK tables of the equation of 
time were preferred to analemmas. There are several examples, e.g. the 
1876 vertical dial by John Smith in Albert Park, Middlesbrough.


At the risk of repetition I offer the following from a book on Scottish 
lighthouses: "Scotland's Edge" by Keith Allardyce and Evelyn M. Hood. It 
reads:


Since a general order of 29 January 1852, it has been the practice to 
have clocks set at local time calculated from sundial readings. The 
order is precise: "The Lighthouse Timepiece is to be kept right, by 
observing, if possible, once a week, the indication of the Sun-dial, in 
the following manner:- The Principal Keeper shall go to the dial, when 
the sun is shining, and shall watch until the shadow of the style 
touches any hour, half hour or other time agreed upon before hand, with 
the Assistant, who shall stand on the balcony, waitng a signal from the 
Principal. The Principal shall then make the signal, on seeing which the 
Assistant shall immediately set the Timepiece to the time already agreed 
upon. The Principal shall then take a note from the Table of the 
Equation of Time engraved on the sundial, of the number of minutes by 
which the clock should differ from the time given by the dial, and shall 
afterwards proceed at once to the Lightroom where he shall put the 
timepiece back or forward according as the Clock shall be slower or 
faster than the sun at the time."


Frank 55N 1W



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equation of time

[Frank Evans]

Greetings John Davis and other fellow sundialists,
Well, yes, this whole thing started, of course, with my question of 12 
October arising from Chris Daniel's excellent article in the September 
BSS Bulletin, which I cited.

Frank 55N 1W



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equation of time

[Cornec Jean-paul cnet-lab-smr-tcm (Tel 96051274)]

I have recently discovered the newsgroup about sundials. Here is a text 
in complement of the last message of C. Lusby-Taylor about the equation of 
time. Hoping it will contribute to the debate.  
As for myself I am of course interested in sundials from all points of 
view.  I belong to the french Commission des Cadrans Solaires of the Societe 
Astronomique de France. My main interests are in the recording and filing of 
ancient sundials and more specially in Brittany; and also in the computation of 
any kind of sundials. 

Yours sincerely


J.P. CORNEC



Here is the text :

I have just dicovered the debate about Equation of Time and Analemma. 
In complement to the last message of C. Lusby-Taylor, may I mention that tables 
of Equation of Time were published pretty early, as soon as the 16 th century, 
in relation with the first planetary tables. An example from 1528 is given in 
the june 1995 issue of "L'Astronomie", bulletin of the french Socie'te' 
Astronomique de France, in an article by J. Meeus et D. Savoie. That paper was 
dealing with the history, the meaning , the computation of the Equation of Time 
, and, especially, its changes through the centuries. It is true that, as long 
there was no precise and stable clocks, i.e. not before late 17th or early 18th 
century, there was no point to bother about the difference between solar and 
mean time in the everyday life, where, anyway, these times have only meaning 
from the equal hours point of view.

J.P. Cornec 

Equation of time

[Charles Mollan, Samton Limited]

I have a photocopy of William Molyneux' "Sciothericum Telescopium" Dublin
1686, and can confirm that he uses the term "Equation of Time".  The title
of Chapter X is "Concerning the Astronomical Equation of Time and the Tables
thereof":

"Being now upon the business of Time, and the accurate observation thereof,
so as thereby to regulate curious Time-keepers; it will not be improper to
our subject to speak something of the Inequality of natural Days; a matter
that has exercised the thoughts of all Astronomers in all ages: And though
all have allowed that there really is such an Inequality, yet they have much
disagreed in assigning its quantity, or demonstrating the reason and
affections thereof; till at last our most Learned and Ingenious English
Astronomer, and my Honoured Friend Mr. John Flamsteed Math. Regius, has
determined the Controversy and by most evident demonstrations has put the
matter beyond further dispute, clearly evincing both the Reasons,
Affections, and Quantity of this Inequality. His Dissertation concerning
this is annex'd and publish'd at the end of the Opera Posthuma Jeremiae
Horroxcii, Lond. 1673.4to. From which (with my esteemed Friend's leave) I
shall present the Reader with the following Schemes and Demonstrations."...

**
(Dr) Charles Mollan
17 Pine Lawn
Newtownpark Avenue
Blackrock
Co. Dublin
Ireland
Tel (+353-1)-289-6186
Fax (+353-1)-289-7970
E-mail [EMAIL PROTECTED]

Equation of Time

[Frank Tapson]

I know WHAT the equation of time is.
What I would like to know is - WHY is it called that?
Isn't an equation supposed to contain an equals (=) sign?
Surely it is really a correction factor?
Should it not go something like:
Local Mean Time = Local Apparent Time + Correction
Anyone know anything about it?
Like WHO named it and WHEN?

Incidentally, if it were treated as suggested above, it would make sure that 
(whatever it was called) had the proper sign in front when it appeared in 
almanacs, and be far less confusing to navigators! At the moment many of 
them learn rules like "when the equation of time is positive you have to 
subtract it"!

O.K. that is the way it is and I cannot see it changing now however rational 
such a change might be, but I should like to know HOW did it ever come about?
With much curiosity
Frank
 **
 Frank Tapson
 C I M T
 School of Education
 University of Exeter
 EXETER
 EX1 2LU
 U K

 Tel: 01392 217113
 Fax: 01392 499398

 Try our Web site at
   http://www.ex.ac.uk/cimt/


 ***

Equation of time

[Frank Evans]

To John Harding's question concerning the sign of the equation of time
there is, for navigators of ships at least, a simple answer.  Any
instructional book on nautical astronomy will say that the equation of
time is defined as mean time minus apparent time, i.e. clock time minus
sun time.  So on days when the sun transits the meridian before noon
(local mean time) the sign is negative.  By the way, astro-navigators
are an endangered species in these days of satellites.  We should
treasure them, for they are the only creatures apart from us dialists
who believe the sun goes round the earth each day.

Frank Evans (former ship's navigator)

Equation of Time

[Chris Lusby]

Dear dialers,
Tom Semadeni <[EMAIL PROTECTED]> asks for clarification of a few points in
my earlier mail.

Firstly, I stated that an EoT table would have most error in 1903 and 2096.
The only factor I was considering was indeed the difference between the
calendar year and the mean tropical year. The only really easy way to
demonstrate this is with a graph of the solar longitude on, say, July 1st
each year. The graph steps by the equivalent of about quarter of a day every
year until a leap year, when it steps back by about three quarters of a day.
This sawtooth pattern is repeated every four years, but drifts by 3/4 of a
day per century, except of course that the years divisible by 100 but not
400 give it a kick in the opposite direction.

I'll try a picture. Each line represents 25 years, starting from 1600, the
distance along the line being the solar longitude on, say, 1st July. The ***
represent the range of longitudes during those 25 years:
  ***
   ***
***
 ***
***
 ***
  ***
   ***
  ***
   ***
***
 ***
***  1903 is at the left of this bunch - over 7 years since a leap
day.
 ***
  ***
   ***  2000 is right in the middle here.
***
 ***
  ***
   ***   2095 is at the right of this bunch - the last leap year for
eight years.
   ***
***
 ***
  ***
  ***
   ***
***
 ***
***
 ***
  ***
   ***
Hope that helped.

Tom also asked why one didn't simply have an analemma (figure of eight) at
noon, with single straight hour lines otherwise. Well, you could, but
converting from sun time to mean time would be a mental operation: the
shadow says 3:45, I follow the declination line back to the analemma,
estimate (how?) that it says the sun is 8 minutes fast (or is that slow -
easy to get confused), so the mean time is 3:37.
Too much work for most people, I would expect. Look at the URL (
http://www.uwrf.edu/sundial/ ) pointed to by John Shepherd's email for a
much more elegant solution.

Regards
Chris Lusby Taylor


=== 
Email:  [EMAIL PROTECTED]
 (Formerly [EMAIL PROTECTED])   
=== 

equation of time

[Frank Evans]

I don't know if Patrick Powers is right about astronomers differing from
(sextant age) navigators regarding the sign of the equation of time but
for navigators EoT has always been mean time minus apparent time.  My
British Admiralty Manual of Navigation, Volume 2, 1938 states simply:
The equation of time is defined as the excess of mean time over apparent
time. So there!

And as Evelyn Waugh said to his commanding officer who rebuked him for
drinking too much wine in the mess:  I do not intend to change the habit
of a lifetime for you!

Frank
-- 
Frank Evans

Equation of time

[François BLATEYRON]

Hi dear gnomonists...

Can someone help me with the calculation of the equation of time ?

I use the following equation:

E = 460 sin M - 592 sin 2 (w+M)  
in seconds

where M is (360/365.25)(t-t0) with t0 the instant of perihelion crossing
and w the perihelion longitude.

The curve obtained with this curve has the good shape but is a little
shifted. The maximum is the 21 of feb instead of the 11 of feb. The zero
crossings are on 22-april; 30-june and 6-sept instead of 16-april; 15-june
and 2-sept.

I can't find what is wrong... Is it t0 (3 january 1950) ? is it w ?
For w, I use :

w = 101°13'15" + 6189".T
with T the number of days ( from the 1 january 1900 at 0h ) divided by
365.25.

I would appreciate any help or results to compare. Thanks a lot.


Francois Blateyron
(and I wish everybody a happy new year with a lot of sunny days...)


E-mail : [EMAIL PROTECTED]
WWW : http://www.fc-net.fr/~frb/welcome.html

Equation of Time

[Ron Anthony]

Francois,

I saw your equation of time question on the remailer list.
The equation that I use is from a book called "Practical
Astronomy with your Calculator" and is more involved.  I
think that it is similar to yours but not sure.  Here is what
I use I hope there are no transcription errors.  For July 27th
1980 at noon eot = -6 min 25sec (Remember noon is July 27.5) I
have written it more in "computereze" than mathamatical.  There
is a more precise method but I think this is close enough for
sundials.

++ron


 1. Calculate the right ascension of the Sun in decimal hours:

  D = Number of days since January 0.0 = (209.5)

  Add/subtract number of days since/till 1990
  D = 209.5 - 3653  = -3443.5

  N = 360/365.242191 * D   = -3394.0767

  Subtract or add multiples of 360 until N is in the range
  0-360.
  N = 205.92332

  ' The following Three variables can be calculated for other
  ' epochs
  EL = 279.403303   ecliptic longitude at epoch 1990.0
  PL = 282.768422   ecliptic longitude of perigee
  OE = 23.441884ecliptic obliquity

  E  = .016713  eccentricity of the orbit
 
  M = N + EL - PL   = 202.5582
  If M is negative add 360

  EC =  360/PI * E * sin(M)  = -0.7347003

  L = N + EC + EL = 484.59192  Sun's geocentric ecliptic longitude
  If L more than 360, subtract 360
  L = 124.59192

  RA = atan( sin(L)*cos(OE)/cos(L)) = -53.068296
  Remove abiguity of atan
  RA = RA + 180 = 126.9317

  H = RA/15 = 8.462113


2. Take H as GST and convert to Universal Time.

  JD = Julian Date of 0hour on this calender date. = 247.5
  S  = JD - 2451545.0  = -7097.5
  T  = S/36525.0   = -0.194319
  T0 = 6.697374558 + (2400.051336 * T) + (0.25862 * T^2)

  T0 = -459.6781
  Reduce T0 to the range of 0-24 by adding or subtracting
  multiples of 24
  T0 = 20.321904

  UT = H - T0 = -11.859791
  Reduce UT to the range of 0-24 by adding or
  subtracting multiples of 24
  UT = 12.140209

  UT = UT * 0.9972695663 = 12.10706

  3. Calculate EOT in decimal hours

  EOT = 12 - UT   = -0 .10706 hours
  EOT = -6m 25.4s

Equation of Time

[Gianni Ferrari]

Dear friends,
I've followed with much interest the several 
messages arrived in last days on EoT calculation.
I've nothing to add to what the authors have written but I will 
note that the long calculation described not  always are useful  
if we wont only design a sundial.

The Sun's Right Ascension(RA) and Declination(D) and the EoT infact
change their values non only hourly in a day but also in the same 
hour and in the same day ( Calendar's date) in different years.
This because of the Equinoce's precession and of the existence of the 
February 29 in the leap years ( for example the RA can change in 
the same hour of the same day in different years as far as 0.60 
degree )

Given that a sundial is generally fixed and daily or annual 
corrections are non allowed, it's necessary to use (in the 
calculations) for every date average values of RA, D ( and EoT).
In such a way the sundial will mark always an imprecise time but
this time will be more  exact of the one marked by a sundial 
designed with the values( of RA, D, EoT) exactly calculated in a 
given year.

For this reason, and to speed up the work, I have developed the 
average values of AR,D and EoT in Fourier series with time measured
in days from the beginning of the year.
I've calculated, with great accuracy ,the values in all the days of 
the year for 32 consecutive years (1990-2021) and after I've found 
the average values for each day.
Later on I've developed AR, D, and EoT in Fourier series with 20
harmonics.
I've used the Jeffrey Sax's programs distributed by Willmann-Bell
and based on Astronomical Algorithms by J. Meeus -1991 . 
With a PC 386 the calculation took 40 minutes.

Given that the coefficients extinguish quickly  in my programs I use
only the first 6 terms with errors less then 0.11d. in RA, 0.06d.
in D and 0.1 min in EoT

EoT= E0+E1*cos(wt+F1) + E2*cos(2wt+F2) +.. + E6*cos(6wt+F6)

where   t is in days from the beginning of the year ( for 1/1 t=1)
w=2*3.141592653/Tropical_year_in days

The values of the coefficients are :
E0=0.01822 min  E1=7.36332 min  F1=86.37 degree
E2=9.9205   F2=110.35
E3=0.31794  F3=106.81
E4=0.21958  F4=130.06
E5=0.01470  F5=124.90
E6=0.00661  F6=149.45


With my best wishes for an Happy New Year

   Gianni Ferrari

equation of time

[fer j. de vries]

Dear gnomonists,

In this e-mail I have attached a gif-picture of the curve of the
equation of time for two years, 1902 and 2098.
They are calculated with the formula ( for the mentioned years) I
mentioned in my earlier e-mail this day.
You see the ( small) change in the curve in a periode of about 200
years.

I do hope many of you can really see this picture.

Fer J. de Vries.

Equation of Time

[Ron Anthony]

Prof Gregorio,

>> As far as the Equation of Time is concerned, the last
edition of the Explanatory Supplement to the Astronomical
Almanac reports (pag. 484) the following algorithm:<<

Thank you for the algorithm.  No matter how hard I try I cannot
make the algorithm yield the correct results.  I attribute this 
to my incorrect math assumptions.  Could you or someone else
walk thru the algorithm with a real date and time, (for 
example 12:00 July 27, 1980) to help me find my wrong thinking?

Does "remove multiples of 3600" mean  "reduce to the range of 
0 to 3600 by adding/subtracting multiples of 3600"?  Or is the 
range -3600 to 3600?

What is ET expressed in?  decimal hours?

++ron

Equation of Time

[DRTAIA]

Greetings, 
 
I am a new member and have what is probably a very simplistic  question.  My 
apologies in advance.
 
When considering a flat, fixed sundial (not an equatorial dial) it appears  
that to get the sundial as close as possible to watch time you set it to the  
latitude and then adjust it for the longitude when laying out the hour  lines.  
Having done all that, am I right in assuming that you are still at  the mercy 
of the Equation of Time and will need to add/subtract minutes to the  dials 
time to equal watch time?  - or is it somehow possible to adjust a  flat, fixed 
sundial to incorporate the equation of time also?
 
Thank you for any guidance/help you will tender.
 
Sincerely,
 
Duane Thomson



** See what's free at http://www.aol.com.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Equation of Time

[John Shepherd]

Thanks to Tom Semadeni for his kind words:

>Thanks to Chris, for the clever graphical explanation showing especially the
>discontinuities which support his recommendation to look at John Shepherd's
>work on the beautifully designed and executed Richard D. Swensen Sundial
>at the
>University of Wisconsin - River Falls.
>http://www.uwrf.edu/sundial/
>Not only is the sundial elegant, the web pages are too!
>
>

...
>
>Precision:
>The close-up photographs clearly show the precision of this Sundial (or
>heliochronometer [sun-time-measurer], I guess), indicating an optimized
>diameter for the gnomon.
>Perhaps Professor Shepherd would care to share his thinking on the topic of
>precision with us.
>

With a vertical sundial at our latitude (45 degrees N) the shadow length
varies considerably and therefore so does the distance moved by the shadow
on the wall in a minute.  So unless we were to vary the width of the bar
making the annalemmas (very costly) we had to chose a compromise for this
width and that of the pipes for the . The main factor turned out to be
visibility of the shadow and the annalemmas. We hung bar stock on the wall
and just looked at it from different distances:-) 1.25 by 0.75 inch turned
out to be best. Similarly we tried various pipes for the gnomon with
various terminations. When we viewed at the extreme hours we found the
discs and cross pieces on the end were too blured to see, hence the double
gnomon was born:-)

>Analemmae:
>It appears that the calculations were done in general; then the location,
>scale
>and orientation variables were set in; resulting in some sort of output that
>was used as input into a CAD program; which in turn gave those beautiful
>analemmae which were then "pasted" onto the wall using another scaling factor.
>Perhaps Professor Shepherd would describe how he went from those terrible
>recursive functions which produce the EoT to getting a template for those
>analemmae.
>

Actually as a Physicist part Astronomer the calculations were done first
using the Ephemeris Tables to calculate the Right Ascension/Declination of
the Sun at each hour for each day from this the direction of the Sun was
calculated for any latitude longitude and hence the intersection of the
shadow with the plane was found. Later I used "Compact data for navigation
& astronomy for the years 1991-1995" from the Royal Greenwich Observatory,
a set of tables that contain the Altitude azimuth data for the sun as a
function of time in polynomial form which is even easier to use for
computation. Hence I could calculate the direction of the sun for any time
on any date. I have since purchased the tables for 1996 - 2000. In plotting
the annalemas for different years I realized that there shape was year
independent which from our preceding discussion is not at first obvious:-)
The next task was to decide the scale which is determined by the size of
the gnomon. This is where the advantages of direct plotter output were
realized as I could draw many designs and pick the one I thought was best
for the size and shape of the wall. I also discovered that the previous
program based on the Ephemeris was in error having corrected for Sidereal
to solar time twice! This led to an error of 4 minutes at the end of the
day:-( In numerical work such as this its nice to have at least two
different ways of calculating something as an error check:-)

Once the size was decided I generated a file of x-y coordinates in inches
from the base of the Gnomon for every minute to generate a smooth curve.
Gene Olson then took this into his CAD program an generated the full size
drawings which he used as templates to bend the bar stock to.  You can see
a picture of Gene placing them on the wall at:
http://www.concentric.net/~mettlewk/sundial.htm


Thats probably more detail than most of you wanted.

Cheers,

John



Professor John P.G.Shepherd
Physics Department
University of Wisconsin-River Falls
410 S. 3rd. St.
River Falls,WI 54022

Phone (715)-425-3196, eve. (715)-425-6203
Fax (715)-425-0652

44.88 degrees N, 92.71 degrees W.

Re: Equation of Time

[Tom Semadeni]

Thanks to Chris, for the clever graphical explanation showing especially the
discontinuities which support his recommendation to look at John Shepherd's
work on the beautifully designed and executed Richard D. Swensen Sundial at the
University of Wisconsin - River Falls.
http://www.uwrf.edu/sundial/
Not only is the sundial elegant, the web pages are too!

The continuity of the analemma seems to respect Earth's rotation and revolution
with much more fidelity than tables which give the "accuracy" of the dial by
cataloguing the EoT with the (usually) Gregorian Calendar.  That is to say the
"in situ" analemmae prevent the inaccuracies introduced by the "calendar
problem" that Chris illustrates so clearly.

The only place where the "calendar problem" rears its ugly head on Shepherd's
dial is on the week indicators on the analemmae themselves.  Too bad, eh?
(That's the Canuck coming out, eh! )  The Standard Time vs Daylight Time
problem is neatly avoided.

Precision:
The close-up photographs clearly show the precision of this Sundial (or
heliochronometer [sun-time-measurer], I guess), indicating an optimized
diameter for the gnomon.
Perhaps Professor Shepherd would care to share his thinking on the topic of
precision with us.

Analemmae:
It appears that the calculations were done in general; then the location, scale
and orientation variables were set in; resulting in some sort of output that
was used as input into a CAD program; which in turn gave those beautiful
analemmae which were then "pasted" onto the wall using another scaling factor.
Perhaps Professor Shepherd would describe how he went from those terrible
recursive functions which produce the EoT to getting a template for those
analemmae.

Thank you.

--
Tom  Semadeni  O
[EMAIL PROTECTED]   o
aka I (Ned) Ames   .
Britthome Bounty   ><<*>
Box 176  Britt  ON   P0G 1A0
'Phone 705 383 0195 fax 2920
45.768* North   80.600* West

[Fwd: Equation of Time]

[Tom Semadeni]

Oops, I neglected to post this to the list.
Sorry, John.
t

--
Tom  Semadeni  O
[EMAIL PROTECTED]   o
aka I (Ned) Ames   .
Britthome Bounty   ><<*>
Box 176  Britt  ON   P0G 1A0
'Phone 705 383 0195 fax 2920
45.768* North   80.600* West


X-Mozilla-Status2: 
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Date: Sat, 20 Feb 1999 12:24:11 -0500
From: Tom Semadeni <[EMAIL PROTECTED]>
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Organization: Britthome Bounty
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To: John Shepherd <[EMAIL PROTECTED]>
Subject: Re: Equation of Time
References: <[EMAIL PROTECTED]> <[EMAIL PROTECTED]>
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Thanks, John for telling of the situation which led to tha Aha! of the pointed
double gnomon. The eye's extrapolation of the two shadows removes so much of the
uncertainty caused by the geometrical and physical optics of the formation of 
the
shadow.

John Shepherd wrote:

> With a vertical sundial at our latitude (45 degrees N) the shadow length
> varies considerably and therefore so does the distance moved by the shadow
> on the wall in a minute.  So unless we were to vary the width of the bar
> making the annalemmas (very costly) we had to chose a compromise for this
> width and that of the pipes for the . The main factor turned out to be
> visibility of the shadow and the annalemmas. We hung bar stock on the wall
> and just looked at it from different distances:-) 1.25 by 0.75 inch turned
> out to be best. Similarly we tried various pipes for the gnomon with
> various terminations. When we viewed at the extreme hours we found the
> discs and cross pieces on the end were too blured to see, hence the double
> gnomon was born:-)

snip

> Actually as a Physicist part Astronomer the calculations were done first
> using the Ephemeris Tables to calculate the Right Ascension/Declination of
> the Sun at each hour for each day from this the direction of the Sun was
> calculated for any latitude longitude and hence the intersection of the
> shadow with the plane was found. Later I used "Compact data for navigation
> & astronomy for the years 1991-1995" from the Royal Greenwich Observatory,
> a set of tables that contain the Altitude azimuth data for the sun as a
> function of time in polynomial form which is even easier to use for
> computation.

> Hence I could calculate the direction of the sun for any time

> on any date. I have since purchased the tables for 1996 - 2000. In plotting
> the annalemas for different years I realized that there shape was year
> independent which from our preceding discussion is not at first obvious:-)

Yes, except for the slowly changing change in magnitudes of obliquity and
eccentricity that Luke refers to.
It is so much easier for me, now, to fit the calendar to the analemma rather 
that
the other way around, in a way similar to your use of the weeks on the analemma
themselves.  The ONLY value to this, methinks, is to show the ability of a 
sundial
to act as a calendar. (I guess that it will also demonstrate the need for Pope
Gregory's modification to the Julian Calendar!)

< realized as I could draw many designs and pick the one I thought was best
> for the size and shape of the wall. I also discovered that the previous
> program based on the Ephemeris was in error having corrected for Sidereal
> to solar time twice! This led to an error of 4 minutes at the end of the
> day:-( In numerical work such as this its nice to have at least two
> different ways of calculating something as an error check:-)

Oops!
(Yes)

> Once the size was decided I generated a file of x-y coordinates in inches
> from the base of the Gnomon for every minute to generate a smooth curve.

You selected the "hour" first then did the minutes around the "hour" for each 
day
of the year to generate a figure-of-eight for that "hour"?  Then repeated the
process for all of the other "hours"?

> Gene Olson then took this into his CAD program an generated the full size
> drawings which he used as templates to bend the bar stock to.  You can see
> a picture of Gene placing them on the wall at:
> http://www.concentric.net/~mettlewk/sundial.htm
>
> Thats probably more detail than most of you wanted.

At the risk of being selfish on this list, this is a great "how to" explanation,
which I for one, appreciate very much, John.

Thank you

Tom

Re: equation of time

[Arthur Carlson]

Willy Leenders <[EMAIL PROTECTED]> writes:

> The equation of time has two causes. The first is that the orbit of
> the earth around the sun is an ellipse and not a circle. The second
> is that the plane of the earth's equator is inclined tot the plane
> of the earth's orbit.  Please can anyone explain me the second cause
> so that I can conceive it. I am not a astronomer!

I have given this question a lot of thought, but I realized when I was
asked about it a few days ago that I am still not satisfied with my
answer.  I have tried to explain it in detail on my page
"http://www.ipp.mpg.de/~Arthur.Carlson/sundial.html";, but that isn't
the intuitively obvious answer we would all like to have in order to
claim that we "understand" the effect.  If I had to answer in one
sentence, I might say that the effect arises because the sun moves
against the stars (in the Ptolemaic sense) on a circle (the ecliptic)
that differs from the coordinate system we use to define time (the
equatorial plane).  You can see that it is a "mathematical" effect, as
opposed to the "physical" effect of the eccentricity, by considering a
planet that does not rotate, so you can place the poles anywhere you
want.  The hour angle of the sun during the course of the year, except
at the solstices and equinoxes, will depend on your choice.

> You can do it in Dutch (for preference), in French, in German or in English.

I can offer you German, if you have trouble understanding the English.

Art Carlson

Re: equation of time

[Bel Murru]

plane of the earth's orbit.
Please can anyone explain me the second cause so that I can conceive it. I 
am not a astronomer!




If you have a globe that's tilted 23.45 degrees from vertical in its stand, 
and you spin it, that's its rotational plane, the plane of its equator.


If you move the globe around the table on its stand, that's the orbital 
plane.


It spins on one plane, and revolves around the sun on another.

A way to see it - Put a light bulb in the center of the room. Take your 
globe, holding the base level (parallel) to the floor, and the globe roughly 
in line with the bulb. Spin the globe and walk around the bulb. This is the 
interaction of the two planes.


Now put a dot on your location on the globe. Point the edge of the frame 
(the degree circle holding the globe) to the east. Keep it pointed east as 
you walk around the bulb. You'll notice that from your location on the 
globe, the bulb/sun would appear sometimes low, sometimes middle, sometimes 
high in the sky depending on where you are in your orbit.


If you were to make 365 steps around the bulb, and pinpointed the line of 
sight to the bulb from your position on the globe at your putative noon 
(perpendicularity to the day/night dividing line on the globe) you would 
trace a line of a certain length parallel to the earth's axis on the side of 
the globe. The ends of the line are the southern and northern limits of the 
sun's declination, the solstices. The middle of the line is the equinox.


If you could vary your speed accurately as you walked around the bulb in an 
ellipse and pinpointed your noon - quicker towards the minor axis and slower 
towards the major, you would find a figure eight instead of a line. This is 
the analemma. Many globes have it traced already at the right declinations, 
at noon on the International date line.


Hope this helps.

Ross Caldwell
__
Get Your Private, Free Email at http://www.hotmail.com

Re: equation of time

[Daniel Lee Wenger]

Willy

Simply put,

the actual sun moves irregularly in the ecliptic plane,

the mean sun may be thought to move uniformally in the earth's equatorial
plane.

In the first the ellipse is involved, in the second the obliquity of the
earth's axis is involved.

Dan Wenger

>The equation of time has two causes. The first is that the orbit of the
>earth around the sun is an
>ellipse and not a circle. The second is that the plane of the earth's
>equator is inclined tot the
>plane of the earth's orbit.
>Please can anyone explain me the second cause so that I can conceive it. I
>am not a astronomer!
>
>You can do it in Dutch (for preference), in French, in German or in English.
>
>Willy Leenders
>Hasselt
>Belgium


Daniel Lee Wenger
Santa Cruz, CA
[EMAIL PROTECTED]
http://wengersundial.com
http://wengersundial.com/wengerfamily

Re: equation of time

[Jeff Adkins]

I think this modeling explanation is as close as you'll get to a conceptual
view of the question (without mathematics or technical terminology).  Here are
some of the thoughts I've had about this type of visualization problem.

1. You could take a purely observational view and say, Haven't you noticed that
the sun is higher in the summer than in the winter?  If the sun is higher,
aren't sundial shadows shorter?  Then of course the EOT, which the position of
a sundial shadow taken at the same (clock) time of day for a year, must have a
vertical displacement to show this. This of course avoids the question of
**why** the sun is higher in the summer; but that isn't necessary from a purely
empirical view.

2. One thing I think is a big hurdle for people learning this for the first
time is they have difficulty relating the physical and mathematical models to
what they see personally in the sky (or on the ground--shadow-wise).  It is
important to note that the observer is "at the dot" and sees what a tiny person
(like an ant on the globe) would see.


This is the same kind of mental leap as was made by a student of mine several
years ago when I explained that the illustrations of the solar system in
textbooks are confusing because they are drawn as concentric circles, with the
observer far above the plane of the solar system.  The observer, however, is
**in** the plane of the solar system, so the proper way to look at one of these
drawings is to lay your face on the book where the earth is marked and look
around:  you don't see concentric circles; you see planets lined up in a single
path surrounding you (the ecliptic).

In the analemma case you must also visualize that your observations are on a
plane tilted at the same angle as the earth's rotation axis.  Once you are
convinced of this, the vertical motion of the sun in the analemma (which is the
horizontal axis in the EOT) becomes more apparent.

An analemma is an EOT folded in half.



Astronomy educators agree one of the best ways to introduce orbital
relationships is to have a large scale model in which the participant is one of
the celestial bodies (sun, moon, earth).

Bel Murru wrote:

> The second is that the plane of the earth's equator is inclined tot the
> >plane of the earth's orbit.
> >Please can anyone explain me the second cause so that I can conceive it. I
> >am not a astronomer!
> >
>
> If you have a globe that's tilted 23.45 degrees from vertical in its stand,
> and you spin it, that's its rotational plane, the plane of its equator.
>
> If you move the globe around the table on its stand, that's the orbital
> plane.
>
> It spins on one plane, and revolves around the sun on another.
>
> A way to see it - Put a light bulb in the center of the room. Take your
> globe, holding the base level (parallel) to the floor, and the globe roughly
> in line with the bulb. Spin the globe and walk around the bulb. This is the
> interaction of the two planes.
>
> Now put a dot on your location on the globe. Point the edge of the frame
> (the degree circle holding the globe) to the east. Keep it pointed east as
> you walk around the bulb. You'll notice that from your location on the
> globe, the bulb/sun would appear sometimes low, sometimes middle, sometimes
> high in the sky depending on where you are in your orbit.
>
> If you were to make 365 steps around the bulb, and pinpointed the line of
> sight to the bulb from your position on the globe at your putative noon
> (perpendicularity to the day/night dividing line on the globe) you would
> trace a line of a certain length parallel to the earth's axis on the side of
> the globe. The ends of the line are the southern and northern limits of the
> sun's declination, the solstices. The middle of the line is the equinox.
>
> If you could vary your speed accurately as you walked around the bulb in an
> ellipse and pinpointed your noon - quicker towards the minor axis and slower
> towards the major, you would find a figure eight instead of a line. This is
> the analemma. Many globes have it traced already at the right declinations,
> at noon on the International date line.
>
> Hope this helps.
>
> Ross Caldwell
> __
> Get Your Private, Free Email at http://www.hotmail.com

--
=-=-=-=-=-=-=-=-=-=-=-=-=
[EMAIL PROTECTED]
Jeff Adkins
Location: 38.00 N, 121.81 W
CA, USA, Earth, Sol III

Re: equation of time

[Luke Coletti]

Hello Willy,

The model I find useful actually applies to both effects, i.e.,
both eccentricity (the elliptical shape of our orbit) and obliquity (the
tilt of our axis relative to the plane of our orbit). Namely, the Sun's
daily position relative to the background of fixed stars appears to move
in a eastward direction and at a variable rate. If the Sun's apparent
motion eastward is variable then so to is the length of our apparent
solar day. The daily variation in the length of our solar day is
additive, the sum of which is the Equation of Time.

The question then becomes how do each of the two effects
(eccentricity and obliquity) produce this change in the apparent
eastward motion of the Sun. Obliquity causes this apparent motion to
vary because the Sun in its apparent eastward migration will move along
a path that is not always parallel to the direction of the Earth's
rotation. At the Solstices the track of the Sun IS parallel to the
direction of the Earth's rotation and the Sun appears to move fastest in
its apparent eastward direction resulting in the apparent solar day
being longer. The opposite is true at the Equinoxes.

There are several ways of describing the relative relationship(s) but I
like this one best.


-Luke


Willy Leenders wrote:
> 
> The equation of time has two causes. The first is that the orbit of the earth 
> around the sun is an
> ellipse and not a circle. The second is that the plane of the earth's equator 
> is inclined tot the
> plane of the earth's orbit.
> Please can anyone explain me the second cause so that I can conceive it. I am 
> not a astronomer!
> 
> You can do it in Dutch (for preference), in French, in German or in English.
> 
> Willy Leenders
> Hasselt
> Belgium

Re: Equation of time

[Gianni Ferrari]

Hello all,
on Sat, 4 Jan 1997 I sent a message to this list with the results of a
little research on the definition of the Equation of Time.
I send  it again (only partly) after having revised the results   (extended
to new books..)

I've  searched for EoT on many books on Sundials and on Astronomy and  I've
reached this conclusion : THERE IS E GREAT CONFUSON ON THIS SUBJECT

Let be
AT   the Local Apparent Time (often called True Time or Solar Time) (marked
by  a  Sundial)
MT   the Mean Solar Time (marked by standard clocks)

The results of my search are the following :

BOOKS ON SUNDIALS
n. 2 Italian books on Sundial   EoT=AT-MT  in
some pages and EoT=MT-AT  in others

n. 2 Italian books on Sundial   EoT=AT-MT
n. 4 Italian book  on SundialEoT=MT-AT

Rohr (It.& Engl.  Editions)   EoT=MT-AT
is said that in Anglo-Saxon Countries is   EoT=AT-MT

n. 1 English  book  on SundialEoT=MT-AT
n. 1 English  book  on SundialEoT=AT-MT

n. 2 Spanish book  on SundialEoT=AT-MT

n. 3 French book  on SundialEoT=MT-AT
n. 1 French book  on SundialEoT=AT-MT

Mayall-1994 - pag. 86
Waugh -1973 - pag.201
Duffett-Smith-1979 - pag.171EoT=MT-AT

Jhon Davis -The British Sundial Society Glossary  EoT=AT-MT


ASTRONOMY BOOKS
n. 6 handbook on Spherical .Astronomy  EoT=AT-MT

Meeus-Astronomical .Algh. - pag. 171 EoT=AT-MT
In the book is said that in older  and in French texts is EoT=MT-AT

H..Mills-Positional Astronomy  EoT=AT-MT  when
Sun transits  Meridian
(Very good explanations )

Explanatory Sup. Astronomical Almanac (ESAA)  pag. 5 - 74EoT=MT-AT

Total : 30 books or documents

RESULTS:
- in Astronomy handbooks the definition  EoT=AT-MT   wins (8 to 1)
( ALSO IF THIS IS NOT IN   ESAA  !! )
This occurrence probably because in Astronomy EoT was used ( and also now is
used at sea) to determine the True (Apparent)  Time when is known the Mean
Time (from Clock)

- in books on Sundials  (21) , where EoT is used to find the Clock's
Time knowing the Sundial's one (AT), the definition EoT=MT-ATwins ( 13
to 8)

--

For the use of EoT with Sundials I suggest that is preferred the definition
EoT=MT-AT

so EoT is the correction to "add" to Sundial's time (AT) to obtain the Mean
Time (MT) : MT=AT+EoT
see : Duffett-Smith, ESAA, Ferrari, Mayall, Rohr, Savoie, Waugh

- the values to use for tables or graphs have to be calculated in every day
in the instant of the Meridian transit of the True Sun ( True Noon) ( for
European countries also at 12h UT)
In such a way the values in the same day in different places of the world
are not equal but the differences are small ( max. 20 sec.)  (and therefore
the tables published in the books should not be used all over the world)


Gianni Ferrari

Re equation of time

[dougdot]

Hello all,
As a newcomer to dialling, I would like to know 
whether the "fast" or "slow" as shown on the graph is the same for the southern 
hemisphere as for the northern hemisphere.
Doug

Re: equation of time

[Aten Heliochronometers]

- Original Message - 
From: "Frank Evans" <[EMAIL PROTECTED]>
To: "Sundial" 
Sent: Wednesday, October 12, 2005 3:16 AM
Subject: equation of time


> Greetings fellow dialists
>
> In his recent article on the equation of time in BSS Bulletin 17 (iii),
> Chris Daniel writes that the earliest appearance of the analemma in a UK
> publication is perhaps the illustration in the second edition of Mrs.
> Gatty's sundial book, dated 1889. Here the figure and construction
> details are the work of Wigham Richardson, a Tyneside shipbuilder. In
> his diagram the familiar "figure of eight" is superimposed on the noon
> line. Of necessity such a construction demands a nodus on the gnomon and
> we may describe the arrangement as a graphic indicator of the equation
> of time through the year.
>
> Earlier, in 1881 Wigham Richardson made a sundial which he placed at the
> entrance to his shipyard. This dial bore a curve stretched over a
> straight line, which was also clearly an expression of the equation of
> time. Unfortunately neither the old photograph of the dial in situ nor
> the more recently repainted dial shows any indication of the months to
> which the parts of the curve are related. But they must originally have
> been present.
>
> Such a snake-like curve is not an indicator of the equation of time but
> a graphic illustration of its changes through the year.
>
> My question is: Was this, like Richardson's appendix in Mrs. Gatty's
> book, a first appearance of an equation of time line? Can anyone supply
> earlier earlier examples of such a line on dials either in the UK or
> elsewhere?
>
> Frank 55N 1W
>

Lloyd Mifflin (sp?) obtained a US patent for a sundial with an analemma in
or around
1867

Dave G.
http://atensundials.com


-

Re: equation of time

[tony moss]

Dave G. wrote:

>Lloyd Mifflin (sp?) obtained a US patent for a sundial with an analemma in
>or around 1867

USA patent No. 64,892 of 21st May 1867 to be exact although it wasn't the 
familiar full 'figure 8' shape he used.  Two profiled plates, each 
covering six months of the analemma, were fitted into a rotating holder 
to face the Sun in the middle of an equinoctial hour bow.

Picture from the original patent drawing for the curious on request.

Tony Moss.



-

Re: equation of time

[Roger W. Sinnott]

At 11:16 AM 10/12/2005 +0100, Frank Evans wrote:
>My question is: Was this, like Richardson's appendix in Mrs. Gatty's 
>book, a first appearance of an equation of time line? Can anyone supply 
>earlier earlier examples of such a line on dials either in the UK or 
>elsewhere?

Frank and others,

I think the lack of equation-of-time indicators on dials before the mid-1800s 
has a simple explanation:
Sundial time was considered CORRECT, and the mean solar time shown by clocks 
WRONG (or, at least, a mere approximation).

For example, I have several English almanacs for the year 1714. One of them is 
The Ladies Diary: or, the Woman's ALMANACK.  Next to many dates throughout the 
year, it has phrases such as:

  "Watches 3 minutes, 49 seconds too fast"  
  "Watches have gained of the Sun 2 minutes in 8 days"  
  "Watches will be 14 min. slower than a good Sun-dial"

Another one, John Wing's Almanack, says on the cover that it contains "an 
Equation Table, for the rectifying Pendulum Clocks and Watches."  
(Unfortunately, that particular table is missing from my copy.)

  -- Roger
   

-

Re: equation of time

[JOHN DAVIS]

Dear Frank et al,
 
The earliest datable dial with an EoT scale in Britain is (I believe) the 1685 double horizontal dial by Henry Wynne for Staunton Harold in Leicestershire.  But Thomas Tompion had published a table for pasting in his longcase clocks two years before.  The data almost certainly came from the first Astronomer Royal, John Flamsteed.  Tompion himself also put EoT tables on some of his dials but he didn't usually date them - the earliest which is positively datable is around 1702 but there may be ones from the 1690s.
 
For further details, see:
J. Davis: ‘The Equation of Time as represented on Sundials’  BSS Bulletin, 15(iv), pp 135-144, (2003).
and

J. Davis: ‘More on the Equation of Time on Sundials’, BSS Bulletin, 17(ii), pp. 66-75, (June 2005).
 
The early scales were usually labled "Watch fast/slow" or "Clock fast/slow".  Generally, it is not until the start of the 19th century that mean time is given precedence by changing the labels to "Dial fast/slow" or, sometimes, "Sun fast/slow"
 
I would be interested to hear from list members who know of other early dials with EoT scales. I have a database of many EoT scales, both from early almanacs and from 17th and 18th century dials: it is possible to see the way in which the actual values on dials lagged behind the latest versions calculated by the astronomers.
 
Regards,
 
John Davis
---
"Roger W. Sinnott" <[EMAIL PROTECTED]> wrote:
At 11:16 AM 10/12/2005 +0100, Frank Evans wrote:>My question is: Was this, like Richardson's appendix in Mrs. Gatty's >book, a first appearance of an equation of time line? Can anyone supply >earlier earlier examples of such a line on dials either in the UK or >elsewhere?Frank and others,I think the lack of equation-of-time indicators on dials before the mid-1800s has a simple explanation:Sundial time was considered CORRECT, and the mean solar time shown by clocks WRONG (or, at least, a mere approximation).For example, I have several English almanacs for the year 1714. One of them is The Ladies Diary: or, the Woman's ALMANACK. Next to many dates throughout the year, it has phrases such as:"Watches 3 minutes, 49 seconds too fast" "Watches have gained of the Sun 2 minutes in 8 days" "Watches will be 14 min.!
  slower
 than a good Sun-dial"Another one, John Wing's Almanack, says on the cover that it contains "an Equation Table, for the rectifying Pendulum Clocks and Watches." (Unfortunately, that particular table is missing from my copy.)-- Roger-Dr J DavisFlowton Dials

Re: equation of time

[Joe Montani]

From: "Roger W. Sinnott" <[EMAIL PROTECTED]>


For example, I have several English almanacs for the year 1714. One of them 
is The Ladies Diary: or, the Woman's ALMANACK.  Next to many dates 
throughout the year, it has phrases such as:


  "Watches 3 minutes, 49 seconds too fast"
  "Watches have gained of the Sun 2 minutes in 8 days"
  "Watches will be 14 min. slower than a good Sun-dial"


Dear Roger,

That is fascinating indeed!

Now, I appreciate that your point is/was that, in those days, sundial time
was considered the "correct" time; but, I come at this from a different
direction.  I wonder if you will please re-post those discrepancies, as
noted above, but with the DATES appropriate to the discrepancies,
or corrections.  I ask this because I am interested in knowing whether the
Equation of Time (EOT) was calculated at all correctly, back then.  To probe 
that,

we must know the dates for which the corrections pertained.

Nowadays, I do not use the tabulated EOT corrections which appear in the
usual sundial reference books, but I calculate them afresh, using the
(low-) precision formula on page C2 of THE ASTRONOMICAL ALMANAC.
The authors claim that the formula is good to about three seconds.
I find this useful for the rectification of Equatorial and Polar 
standard-time

dials I've designed.

If we had the dates for the corrections you've posted (or, perhaps, many 
more
such examples, please!), we could check the arithmetic of the compilers of 
that
almanac (or, more likely, of their sources...), and perhaps discover some 
details

of the algorithm they used, and the values assumed by them(or known to them)
for various astronomical quantities.  Could be a fascinating little study... 
.


Thank you so much for posting.

--Joe Montani / Tucson, AZ

Another one, John Wing's Almanack, says on the cover that it contains "an 
Equation Table, for the rectifying Pendulum Clocks and Watches."  
(Unfortunately, that particular table is missing from my copy.)

  -- Roger


Alas... can this be expeditiously reproduced by finding a copy (library?) 
elsewhere?  --Joe



-

Re: equation of time

[anselmo]

Roger,
 
> I think the lack of equation-of-time indicators on dials before the 
> mid-1800s has a simple explanation: Sundial time was considered 
> CORRECT, and the mean solar time shown by clocks WRONG (or, at least,
>  a mere approximation).

Well, I suppose there was some kind of transitional period, because
I've got a Spanish treaty on how to fix mechanical clocks from sundials
and correcting the equation of time dated in 1794... 
So what happened in these 80 years? I guess 
mechanical dials improved and then it made sense to make the
corrections, but at least astronomers knew about the equation
of time from a long time ago.

> Another one, John Wing's Almanack, says on the cover that it 
> contains "an Equation Table, for the rectifying Pendulum Clocks and 
> Watches." 

Mine is the opposite one!

Regards,

Anselmo



-

Re: equation of time

[Frans W. Maes]

Dear Frank & all,

[Sorry, previously sent to Frank only]

The Dutch sundial catalog (Zonnewijzers in Nederland, by Van Cittert-Eymers
& Hagen) mentions as the oldest public analemma in the country: an analemma
carved in stone at a sundial on a house in Jutphaas (south of Utrecht) from
1831 (cat.nr. Utrecht-8). The sundial was lost during the 1880's; the
analemma is in the Utrecht University museum.

The second-oldest public analemma in the Netherlands still exists on a
church in Enschede and dates from 1836. A picture can be seen in my website
www.fransmaes.nl/sundials , go to Pole style - vertical, and click the
fourth thumbnail on the first row.

The third-oldest analemma on a public dial is in Middelburg, dated 1842. It
has analemmas on all the hour lines.

Much older is a very elaborate copper horizontal dial, engraved around 1730
by David Coster, now in the Rijksmuseum (Amsterdam-4 in the book, with
picture). It has analemmas for all hours from 8 to 16.

Best regards,
Frans Maes


-

Re: equation of time

[Patrick Powers]

Message text written by "Frans W. Maes"
>Much older is a very elaborate copper horizontal dial, engraved around
1730
by David Coster, now in the Rijksmuseum (Amsterdam-4 in the book, with
picture). It has analemmas for all hours from 8 to 16.<

Hi Frans, this gets more and more interesting!  Thanks for that.   Just
whilst you must have been sending your reply to the list I was looking at
the web site of 
La Commission des Cadrans solaires du Québec
(URL: http://cadrans_solaires.scg.ulaval.ca/cadransolaire/toronto.html)
which has even more references

La CCSQ has the following text:

"Our French tradition, by its numerous authors of Gnomonics (Deparcieux
(1741); Rivard (1742); Delambre (1819); Gotteland and Camus (1993)), has
established that the analemma was invented in 1730, by the French
astronomer Grandjean de Fouchy . Is it the final argument? I doubt it very
much... And I am not alone for doing so!

Ms. Gotteland continues her researches on that topic, and she revealed, in
1993, that there was no evidence that Grandjean de Fouchy has ever
published a paper about his "invention". More, Mr Hagen, from the Dutch
Sundial Society, told her that he found three portable sundials, with an
analemma, and all of them were made before 1730:

- one armillary sphere on a painting from the Fine Arts Museum of
Amsterdam; 

- one table sundial, in the Greenwich Maritime Museum; let's recall that
its sundialist is Mr. Vogler, who deceased in 1725; 

- and one horizontal sundial, kept in the Rijksmuseum of Amsterdam, with
analemmas on each line of the hours. That sundial was carved in 1719 by
David Coster...(eleven years before the supposed invention of 1730)

According to Ms. Gotteland, de Fouchy would have been the first one, in
France, to use the analemma on his sundials, but he did not invent it!"

I wonder if there are any other references?
Patrick

-

RE: equation of time

[Roger Bailey]

Check the BSS glossary chronology on line. The French connection is listed
for 1740 "The modern figure-8 form of the analemma curve is conceived by
Jean Paul Grandjean de Fouchy, secretary of the Académie des Sciences,
Paris." It also earlier notes Flamsteed's EoT in 1675
http://www.sundialsoc.org.uk/glossary/chronology/chronology.htm

The analemma on the analemmatic dial at Brou in 1756 by J. J. de LaLande is
a latter addition , but LaLande's analemma noon mark on the floor of the
Ancien Hopital in Tonnerre is an original. I have seen the analemma but
don't have a picture or a good date reference. The green Michelin Guide for
Burgundy Jura says "Note the gnomon (sundial) on the paving, designed in the
18C by a Benedictine monk and the astronomer LaLande (1732-1807)".

Regards,

Roger Bailey
Walking Shadow Designs
N 48.6  W 123.4

-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] Behalf Of Patrick Powers
Sent: October 17, 2005 8:22 AM
To: SundialList
Subject: Re: equation of time


Message text written by "Frans W. Maes"
>Much older is a very elaborate copper horizontal dial, engraved around
1730
by David Coster, now in the Rijksmuseum (Amsterdam-4 in the book, with
picture). It has analemmas for all hours from 8 to 16.<

Hi Frans, this gets more and more interesting!  Thanks for that.   Just
whilst you must have been sending your reply to the list I was looking at
the web site of
La Commission des Cadrans solaires du Québec
(URL: http://cadrans_solaires.scg.ulaval.ca/cadransolaire/toronto.html)
which has even more references

La CCSQ has the following text:

"Our French tradition, by its numerous authors of Gnomonics (Deparcieux
(1741); Rivard (1742); Delambre (1819); Gotteland and Camus (1993)), has
established that the analemma was invented in 1730, by the French
astronomer Grandjean de Fouchy . Is it the final argument? I doubt it very
much... And I am not alone for doing so!

Ms. Gotteland continues her researches on that topic, and she revealed, in
1993, that there was no evidence that Grandjean de Fouchy has ever
published a paper about his "invention". More, Mr Hagen, from the Dutch
Sundial Society, told her that he found three portable sundials, with an
analemma, and all of them were made before 1730:

- one armillary sphere on a painting from the Fine Arts Museum of
Amsterdam;

- one table sundial, in the Greenwich Maritime Museum; let's recall that
its sundialist is Mr. Vogler, who deceased in 1725;

- and one horizontal sundial, kept in the Rijksmuseum of Amsterdam, with
analemmas on each line of the hours. That sundial was carved in 1719 by
David Coster...(eleven years before the supposed invention of 1730)

According to Ms. Gotteland, de Fouchy would have been the first one, in
France, to use the analemma on his sundials, but he did not invent it!"

I wonder if there are any other references?
Patrick

-

-

Re: equation of time

[fer de vries]

Friends,

There is some contradiction in the answers about the equation of time on a
sundial.

1 At first there is the proof of the existence of the EoT by Huygens, de 
Fouchy or Flamsteed.

As I think it was Huygens.

2 Second there are tables and graphs on or with a sundial to correct for EoT
in an indirect way.

3 Third there are sundials with curved hourlines to correct in a direct way
for the EoT.

The discussion on the sundial list now is like mentioned in point 3.



Hagen published in the bulletin of De Zonnewijzerkring in the following way:

The dial by Coster with EoT curves around each hourline is thought to be
from 1730( or earlier).
But Coster and/or Cruquius made a graph earlier around 1719.
BTW: the EoT curves on Coster's dial are only drawn for half a year, the
summer part.

The armillary with EoT correction is found  on a painting by Verkolje and
the painting is dated 1740.

I don't know anything about Vogler's dial.


So far for an EoT curve on a dial, to read directly the clock time, we are
still around 1730.

Best wishes, Fer.


Fer J. de Vries

De Zonnewijzerkring
mailto:[EMAIL PROTECTED]
http://www.de-zonnewijzerkring.nl

Eindhoven, Netherlands
lat.  51:30 N  long.  5:30 E

- Original Message - 
From: "Patrick Powers" <[EMAIL PROTECTED]>

To: "SundialList" 
Sent: Monday, October 17, 2005 5:21 PM
Subject: Re: equation of time



Message text written by "Frans W. Maes"

Much older is a very elaborate copper horizontal dial, engraved around

1730
by David Coster, now in the Rijksmuseum (Amsterdam-4 in the book, with
picture). It has analemmas for all hours from 8 to 16.<

Hi Frans, this gets more and more interesting!  Thanks for that.   Just
whilst you must have been sending your reply to the list I was looking at
the web site of
La Commission des Cadrans solaires du Québec
(URL: http://cadrans_solaires.scg.ulaval.ca/cadransolaire/toronto.html)
which has even more references

La CCSQ has the following text:

"Our French tradition, by its numerous authors of Gnomonics (Deparcieux
(1741); Rivard (1742); Delambre (1819); Gotteland and Camus (1993)), has
established that the analemma was invented in 1730, by the French
astronomer Grandjean de Fouchy . Is it the final argument? I doubt it very
much... And I am not alone for doing so!

Ms. Gotteland continues her researches on that topic, and she revealed, in
1993, that there was no evidence that Grandjean de Fouchy has ever
published a paper about his "invention". More, Mr Hagen, from the Dutch
Sundial Society, told her that he found three portable sundials, with an
analemma, and all of them were made before 1730:

- one armillary sphere on a painting from the Fine Arts Museum of
Amsterdam;

- one table sundial, in the Greenwich Maritime Museum; let's recall that
its sundialist is Mr. Vogler, who deceased in 1725;

- and one horizontal sundial, kept in the Rijksmuseum of Amsterdam, with
analemmas on each line of the hours. That sundial was carved in 1719 by
David Coster...(eleven years before the supposed invention of 1730)

According to Ms. Gotteland, de Fouchy would have been the first one, in
France, to use the analemma on his sundials, but he did not invent it!"

I wonder if there are any other references?
Patrick

-


-

Re: equation of time

[Frans W. Maes]

Hi Patrick & all,

More on Fer de Vries' point 3: the first analemma (EoT curve) on sundials.

Marinus Hagen wrote an extensive article on the sundials engraved by David
Coster in the Bulletin of the Dutch Sundial Society (1982, XII, p. 553-588).
His (tentative) conclusion is that the sundial with analemmas now in the
Rijksmuseum is the world's first. Coster's birth date is uncertain; probably
in the 1670's. The designer was either Nicolaas Cruquius (1678-1754) or
Willem 's Gravesande (1688-1742). Both lived in London for a while, were
members of the Royal Society, met Newton and knew about Flamsteed's EoT
data.

The sundial bears the coat-of arms of Count Unico Wilhelm van Wassenaer
Obdam. Based on the art-historical details, the sundial should be made
somewhere between 1719 and 1733. I do not know of a later article that
pinpoints the date to 1719.

Hagen quotes "Gnomonique" by G. Bigourdan (1922), who claims that Grandjean
de Fouchy (1707-1788) would have invented the analemma, but who does not
mention a date. Hagen writes that he could not find any article by Fouchy
about the analemma in the journal of the Paris Academy of Sciences, of which
Fouchy was secretary. So it would be interesting to know the source for the
claim from Québec.

To be continued?

Regards,
Frans Maes

- Original Message - 
From: "Patrick Powers" <[EMAIL PROTECTED]>
To: "SundialList" 
Sent: Monday, October 17, 2005 5:21 PM
Subject: Re: equation of time


Message text written by "Frans W. Maes"
>Much older is a very elaborate copper horizontal dial, engraved around
1730
by David Coster, now in the Rijksmuseum (Amsterdam-4 in the book, with
picture). It has analemmas for all hours from 8 to 16.<

Hi Frans, this gets more and more interesting!  Thanks for that.   Just
whilst you must have been sending your reply to the list I was looking at
the web site of
La Commission des Cadrans solaires du Québec
(URL: http://cadrans_solaires.scg.ulaval.ca/cadransolaire/toronto.html)
which has even more references

La CCSQ has the following text:

"Our French tradition, by its numerous authors of Gnomonics (Deparcieux
(1741); Rivard (1742); Delambre (1819); Gotteland and Camus (1993)), has
established that the analemma was invented in 1730, by the French
astronomer Grandjean de Fouchy . Is it the final argument? I doubt it very
much... And I am not alone for doing so!

Ms. Gotteland continues her researches on that topic, and she revealed, in
1993, that there was no evidence that Grandjean de Fouchy has ever
published a paper about his "invention". More, Mr Hagen, from the Dutch
Sundial Society, told her that he found three portable sundials, with an
analemma, and all of them were made before 1730:

- one armillary sphere on a painting from the Fine Arts Museum of
Amsterdam;

- one table sundial, in the Greenwich Maritime Museum; let's recall that
its sundialist is Mr. Vogler, who deceased in 1725;

- and one horizontal sundial, kept in the Rijksmuseum of Amsterdam, with
analemmas on each line of the hours. That sundial was carved in 1719 by
David Coster...(eleven years before the supposed invention of 1730)

According to Ms. Gotteland, de Fouchy would have been the first one, in
France, to use the analemma on his sundials, but he did not invent it!"

I wonder if there are any other references?
Patrick

-


-

Re: equation of time

[JOHN DAVIS]

Dear Sundialling colleagues,
 
A major article on the analemma and mean time sundials by Christopher Daniel (Chairman of the British Sundial Society) is currently being published in the BSS Bulletin.
 
Part 1 "The Equation of Time: The Invention of the Analemma. A brief history of the Equation of time" BSS Bulletin 17(iii) pp. 91-100 (September 2005).
 
Part 2 is currently in press for the December 2005 issue and is a further 11 pages. The paper quotes 104 references. It will include a nice colour photograph of the Coster dial of c.1726 referred to by Fer and others. It is also planned to publish the two parts together as a monograph early in 2006.
 
Regards,
 
John Davis
-Dr J DavisFlowton Dials

Re: Equation of Time

[fer j. de vries]

Frank Tapson wrote:
> 
> I know WHAT the equation of time is.
> What I would like to know is - WHY is it called that?
> Isn't an equation supposed to contain an equals (=) sign?
> Surely it is really a correction factor?
> Should it not go something like:
> Local Mean Time = Local Apparent Time + Correction


Hi Frank,

In my English-Netherlands dictionary the word equation is translated
with "vergelijking": that is something like A = B + C, 
but also with "correctie" : that is correction.
If this is all right the use of the words "equation of time" is correct.

Can it be a translation of "Equatio Temporis"?

Fer.

Re: Equation of Time

[Gordon T. Uber]

"Equation" refers to a difference or correction, as Fer J. de  Vries
has pointed out.

"a quantity added or subtracted in equating a computation" -
Webster's Third International Dictionary

Probably the first table of corrections for regulating a clock was
the "Tabula Aequationis Dierum" compiled by Christiaan Huygens
circa 1662.  Tables were published by John Flamsteed in 1666 and
John Smith in 1688. "A Table of the Equation of Days shewing How
much a good Pendulum Watch ought to be faster or slower than
a true Sun-Dial, every Day in the Year" was printed as early as 1683
for Thomas Tompion.  - from "The Grandfather Clock" by Earnest
Edwardes.

Gordon Uber


At 08:37 97/10/13 +0100, you wrote:
>I know WHAT the equation of time is.
>What I would like to know is - WHY is it called that?
>Isn't an equation supposed to contain an equals (=) sign?
>Surely it is really a correction factor?
>Should it not go something like:
>Local Mean Time = Local Apparent Time + Correction
>Anyone know anything about it?
>Like WHO named it and WHEN?

-- 
|  XII | Gordon T. Uber,  3790 El Camino Real, Suite 142
|XI| Palo Alto, CA 94306-3314,  email: [EMAIL PROTECTED]
|  X  \   /| CLOCKS and TIME: http://www.ubr.com/clocks/
| IX   \ / | Reynen & Uber WebDesign: http://www.ubr.com/rey&ubr

RE: Equation of Time

[Hooijenga R.]

** I read about this list on the "Sundials on the Internet" page by the
BSS. **

Hello Frank, and all,

As for the _name_, I think "equation" can mean something done, or
needed, to equate a thing to something else.
As Fer said, ' Can it be a translation of "Equatio Temporis"? '
Personally I would rather suspect it was the other way 'round, the Latin
expression being coined for international traffic.

As for the sign, that is an interesting point. It used to be the way you
would like to see it. Before the 1930's, you took the dial reading,
added the Equation, and wound up with clock time. The equation was
positive in February and negative in November.

By 1948, W.L.Kennon described the Equation the way we use it now. You
take clock time, add the variable Equation, and get the variable dial
time.
In 1940, dr. Minnaert, in his excellent "Natuurkunde van 't Vrije Veld"
("Open Air Physics"),  used the old sign for the equation. And as late
as 1953, P.Terpstra still did; really by then he should have known
better..
Towards the end of the 1930's there was one periodical (the name of
which escapes me momentarily) that carried two articles each using the
other sign of the Equation.

There is something to say for the modern standard. If you look at the
graph, what you see is Mean Time having a zero difference from day to
day, every day having equally many star seconds in it; and Apparant
(Dial) time meandering, slow and fast, about it. This is of course
really the way it works.
You could call the modern way the "Error curve" of the sundial, except
that this is not a very nice name for it.
The old way, then, could be called the "Correction curve" for the
sundial.

One last remark, of theoretical value only: there is a very slight
difference between the old and the new method, even if we reverse the
sign of one of them.
Example: the "old" way, we read, say, 9 AM on the dial, apply the
correction, say +10 minutes, and get 9:10 AM clock time.

If we reverse this to get the new method, we see that the Equation is
-10 minutes not for 9 AM clock time, but for 9:10 AM clock time.

Granted, the difference will be very very slight- in fact we happily use
the same Equation for the entire day, and would hardly compute fresh
Equations every 10 minutes. Still, a conceptual difference is there.

Happy dialling!
Rudolf

Equation of Time Formula

[Nicelli Alberto]

Hi all brothers dialists!
Who knows the exact  time and the exact ecliptic longitude of the
earth's perihelion ?  
I need these values to calculate myself the Equation of Time with this
formula I've obtained with a simple and traditional recipe : a little
bit of spherical geometry and another little bit of keplerian motion.
I submit it to your attention.
Maybe it is not so new or original as I believe, anyway is simple and
seems to work with good accuracy !

E.T. [minutes] = arctan { tan(M+L) } - arctan {cos O x tan
(M+L+180/pi x 2E x sin M ) }  

___
  (average Earth
rotation speed in deg/min)

where :

M=(average Earth revolution speed in deg/day) x (number of days since
perihelion time)
L= perihelion longitude 
O=obliquity of the ecliptic = 23,44 deg
E=terrestrial orbit eccentricity = 0,01672

and :

average earth rotation speed in deg/min=  0,250686
average earth revolution speed in deg/day =  0,985643

Thank you !
Alberto Nicelli
(45,5 N ; 7 E)
[EMAIL PROTECTED]

Heliochronometers: Equation of Time

[Chris Lusby]

Daniel Wegner ([EMAIL PROTECTED]) is only partly correct in
saying that an analemma must have an error due to leap years. The error can
be avoided.

It is true that tables of the Equation of Time are slightly inaccurate
because they take a mean value for the solar longitude on a named date (such
as February 17th), whereas the 4 year and 400 year cycles should be
allowed-for to be totally accurate. Fortunately for us, the peak error is
less in the next few years than at any other time in the 400 year cycle. How
convenient. The worst case is in 1903+400n and 2096+400n, when the longitude
is 7/8 of a day different from its mean value. But even 7/8 of a day
accounts for less than 30 seconds of EoT, so still allows a sundial to be
less than a minute out. Around the year 2000, the worst case is half this -
about 14 seconds.
If an EoT table is drawn graphically to allow a sundial reading to be
converted to mean time, then this too must have an error with the same 4 and
400 year cycles.

But if the sundial is marked with figure-of-eight hour lines, then there
need be no such error, since the sun's declination and longitude are related
by geometry, not by what we call the date. Even if we lost another 11 days
in a calendar reform (I am from England), such a sundial would continue to
read correct mean time. Therefore, I suggest that this is a purer and
altogether more satisfactory solution than an EoT table or figure. Except
for the little point that the EoT changes rather a lot, and the longitude
does not, at the solstices. Pity.

By the way, if you are ever making a circular date scale - to calibrate a
declination scale, for instance - you should divide it into 365.25 and make
February 29th be just the .25. This is the best simple way to allow for one
February 29th every four years.


Chris Lusby Taylor

=== 
Email:  [EMAIL PROTECTED]
 (Formerly [EMAIL PROTECTED])   
=== 

equation of time sundial

[Ken Baldwin]

Hello,

I'm a new list member, and have a beginner question:

Are there examples of sundials whose sole (or primary) purpose is to
compute the Equation of Time for the current date?

- I know that this information is often provided as a graph in the
furniture, but why should I have to know the date and perform the look-up
manually? Can't I use the position of the sun to do the computation for me?

- I know that the EOT correction can be incorporated into the layout of
(some) hour lines, but I'm more interested in having dials which show true
solar time. I'd like a separate device dedicated to computing the EOT.

- I know that I can construct an analemmic noon mark to show the EOT for
that day, since it's simply the east-west component of the analemma, but
I'd like a design that can be read at any daylight hour.

It seems to me that it should be possible to build such a dial, since the
EOT is a function of date, and date lines can be read from many sundials.
In principle, I can just re-label the date lines with corresponding EOT
values and interpolate.

I hope that makes sense. But since I haven't seen anything like that in
introductory sundial books, I must be missing something... Is it that the
shadow length can't be read accurately enough to get a reasonably precise
EOT estimate? Or is it just too hard to make a readable layout, given that
solar altitude is ambiguous between two dates, and that the component of
the EOT due to the eccentricity of the earth's orbit is out of phase with
the equinoxes and solstices?

Thanks in advance,
Ken Baldwin
Corvallis, OR USA
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Equation of time

[rsinnott]

Dear Francois,

>I can't find what is wrong... Is it t0 (3 january 1950) ? is it w ?
>For w, I use :
>
>   w = 101°13'15" + 6189".T
>with T the number of days ( from the 1 january 1900 at 0h ) divided by
>365.25.
>

I think your problem is the definition of T.  The longitude of perihelion 
increases very slowly -- by less than 2 degrees per century.  So it should be 
defined as the number of days from 1 Jan 1900 divided by 36525 days (instead of 
365.25 days).

Otherwise your method seems okay.

Best regards,

Roger Sinnott
Sky & Telescope

Re: Equation of time

[Paolo GREGORIO]

François BLATEYRON wrote:
> 
> Hi dear gnomonists...
> 
> Can someone help me with the calculation of the equation of time ?
> 
> I use the following equation:
> 
> E = 460 sin M - 592 sin 2 (w+M)
> in seconds
> 
> where M is (360/365.25)(t-t0) with t0 the instant of perihelion crossing
> and w the perihelion longitude.
> 
> The curve obtained with this curve has the good shape but is a little
> shifted. The maximum is the 21 of feb instead of the 11 of feb. The zero
> crossings are on 22-april; 30-june and 6-sept instead of 16-april; 15-june
> and 2-sept.
> 
> I can't find what is wrong... Is it t0 (3 january 1950) ? is it w ?
> For w, I use :
> 
> w = 101°13'15" + 6189".T
> with T the number of days ( from the 1 january 1900 at 0h ) divided by
> 365.25.
> 
> I would appreciate any help or results to compare. Thanks a lot.
> 
> Francois Blateyron
> (and I wish everybody a happy new year with a lot of sunny days...)
> 
> E-mail : [EMAIL PROTECTED]
> WWW : http://www.fc-net.fr/~frb/welcome.html

Dear Mr: Blateyron,

  first of all, my congratulations for your SHADOWS
program I have downloaded in the last week; I have
installed it on my computer and I will send you soon
my remarks.

  As far as the Equation of Time is concerned, the last
edition of the Explanatory Supplement to the Astronomical
Almanac reports (pag. 484) the following algorithm:

  1) Using the Julian Date (JD) and the universal time (UT)
 in hours, calculate the number of centuries from J2000
 with the relation

   T = (JD + UT / 24 - 2451545.0) / 36525.

  2) Calculate the solar mean longitude corrected for aberration

   L = 280°.460 + 36000°.770 T (remove multiples of 360°)

 then the mean anomaly G

   G = 357°.528 + 35999°.050 T (  "  )

 and finally the ecliptic longitude EL

  EL = L + 1°.915 * sin G + 0°.020 * sin 2G

   3) The equation of Time ET is given by

  ET = - 1°.915 * sin G - 0°.020 * sin 2G +

   + 2°.466 * sin 2 EL - 0°.053 * sin 4 EL 


  I hope this algorithm is sufficient for your needs, so we will
have soon a new release of your excellent program.

 Happy New Year!

   Prof. Paolo GREGORIO

Re: Equation of time

[diallist]

Hi all,

I thought I might as well throw a little something into the EOT calculation
brew by expanding on Prof. Gregorio's contribution.  The following series of
calculations, in addition to finding the EOT, will find the sun's
declination, semidiameter and, by iteration, sunrise and sunset for any
latitude and longitude.

What follows is not mine except for the correction I note in all capital
letters.  I got this from the U.S. Naval Observatory:
  
--
  JD = Julian DateUT = Universal Time (hrs) 

 T <- (JD + UT/24 - 2451545.0)/36525. Number of centuries from J2000.

 L <- 280.460 + 36000.770 * TSolar mean longitude, in degrees
 (remove multiples of 360 degrees from it.)

 G <- 357.528 + 35999.050 * TMean anomaly, degrees

 M <- L + 1.915 * sin (G) + 0.020 * sin (2*G)  Ecliptic long., degrees

 e <- 23.4393 - 0.01300 * T  Obliquity of ecliptic, degrees

 E <- -1.915 * sin (G) - 0.020 * sin(2*G) + 2.466*sin(2*M) - 0.053 *
sin(4*M)
     Equation of time

 GHA <- 15*UT -180 + E   Greenwich hour angle, degrees

 sin (DEC) <-  sin (e) * sin (M)   Declination of Sun

 SD <- 0.267 / ( 1 - 0.017 * cos (G) ) Semidiameter of Sun, degrees


 Define sunrise as the time when the apparent altitude (H) of the upper
limb of the Sun will be -50 arc minutes (34' for refraction + 16' for
semidiameter). Twilights are found for H = -6 degrees (civil), -12 degrees
(nautical), and -18 degrees (astronomical). Correct for height of the
observer if not at sea level.
 
 Obtain the time of rise/set, (UT) by iterating the equation 

  UT = UTo - (GHA + LON +/- t )   <-- THIS IS NOT CORRECT
  THE CORRECT EQUATION SHOULD BE
 UT = UTo - (GHA + LON +/- t ) / 15 

 with initial guess UTo = 12, using + for rise, - for set and t defined by: 

 cos t = (sin H - sin LAT sin DEC ) / (cos DEC cos LAT)

 replacing UTo by UT until their difference becomes small. 
 Convert UT to local timezone, applying Daylight Savings time if in effect. 



Back to me again!!  Regarding the iteration mentioned above.  It is not very
clear the way it was written but it is possible to figure out.  I found it
took about three iterations for the difference between UT and UTo to become
small.

Maybe one of you with a wiser head can think of a way to word the
instructions above more clearly regarding the iteration process.  I can give
one clue however, the new value for UT must be carried back to the top of
all the equations and run through again as well as replacing the initial
guess of 12.

Happy dialling!!!

Charles Gann


*   Sundials and The Author* 
* http://www.geocities.com/athens/1012 *

Re: Equation of time

[Andrew Pettit]

At 19:36 29/12/96 +0100, François BLATEYRON wrote:
>Hi dear gnomonists...
>
>Can someone help me with the calculation of the equation of time ?
>

Curiously enough it was "The Equation of Time" and its derivation that first
got me interested in Sundials. I thought - Oh yes, a piece of cake to apply
some simple Newtonian Mechanics and come up with an answer.

Well some considerable time later I concluded that it was not as easy as I
had at first thought! However, I have two references which may be of
interest to you or others on the mailing list:

1) "Practical Astronomy" by Robert H. Mills published by Albion (ISBN
1-898563-02-0 for hardback or 1-898563-00-4 for paperback) gives an analysis
of The Equation of Time.

2) There is a paper "The Equation of Time" in the Monhly Notices of the
Royal Astronomical Society" (1989) 238 1529-1535 submitted by David W.
Hughes, B. D. Yallop and C. Y. Hohenkerk. David Hughes is listed as being
from Sheffield University and the other two authors are from the Royal
Greenwich Observatory.

The Summary of this notice reads

"An Equation is developed which gives the Equation of Time as a function of
Universal Time. This enables it to be calculated for any epoch within 30
centuries of the present day, to a precision of about 3 s of time. We also
give several expressions for the Equation of Ephemeris Time which ignores
the distincion between the time-scale of the Ephemeris and Universal Time,
and so may be compared with expresions given in old text books."

I hope that these two references help - though I note that other side issues
such as the inner workings of Excel date functions may also cause some
anomolies

Best of luck

-Andrew
Pettit-

e-mail:  [EMAIL PROTECTED]

Postman Pat:   3, Lucastes Road, HAYWARDS HEATH, West Sussex, RH16 1JJ,
ENGLAND

Tel. UK:  (+44) (0)1444 453111

Re: Equation of time

[fer j. de vries]

François BLATEYRON wrote:
> 
> Hi dear gnomonists...
> 
> Can someone help me with the calculation of the equation of time ?
> 
> I use the following equation:
> 
> E = 460 sin M - 592 sin 2 (w+M)
> in seconds
> 
> where M is (360/365.25)(t-t0) with t0 the instant of perihelion crossing
> and w the perihelion longitude.
> 
> The curve obtained with this curve has the good shape but is a little
> shifted. The maximum is the 21 of feb instead of the 11 of feb. The zero
> crossings are on 22-april; 30-june and 6-sept instead of 16-april; 15-june
> and 2-sept.
> 
> I can't find what is wrong... Is it t0 (3 january 1950) ? is it w ?
> For w, I use :
> 
> w = 101°13'15" + 6189".T
> with T the number of days ( from the 1 january 1900 at 0h ) divided by
> 365.25.
> 
> I would appreciate any help or results to compare. Thanks a lot.
> 
> Francois Blateyron
> (and I wish everybody a happy new year with a lot of sunny days...)
> 
> E-mail : [EMAIL PROTECTED]
> WWW : http://www.fc-net.fr/~frb/welcome.html


Francois,

The factor 6189" change in 'w' in one year is very high.
See also the remark of Roger Sinnot.

To compute the equation of time as well the suns declination out of a
daynumber in a given year I use a formala for that year.
This formula for 1998, a year between 2 leap years, is :

Fomulae to compute the equation of time and the suns declination out of
a daynumber:

L   =   DAYNR*360/365.2422 - 80.535132 DEGREES

EQUATION=   - 107.0605*SIN( L) - 428.6697*COS( L)
+ 596.1009*SIN(2L) -   2.0898*COS(2L)
+   4.4173*SIN(3L) +  19.2776*COS(3L)
+  12.7338*SIN(4L) SECONDS (of time)

LAMBDA  = L +   0.4277*SIN( L) +   1.8664*COS( L)
+   0.0180*SIN(2L) +   0.0087*COS(2L)  DEGREES

EPSILON = 23.43954 DEGREES

DECLINATION = ARCSIN(SIN LAMBDA * SIN EPSILON) DEGREES

Strictly these formulae are for 1998 and for 12.00 UT, but for sundials
you can use them during a long time.
See also 'Cousins', page 236, for such a fomula for the year 1931.

In my sundial program I use a procedure to compute this formula for a
certain year.

I learned this methode from one of the members of "De Zonnewijzerkring"
(the Dutch Sundial Society).
He also calculated the errors of this methode.
The error in the equation of time is about + or - 3 seconds.
For sundials this is very accurate.



To Paolo Gregorio I have the question if it is known what the errors are
with the formula given in your message?



Happy new year to all,

Fer J. de Vries, Netherlands.

Re: Equation of Time

[Warren Thom]

Gianni Ferrari wrote:
> 
> Dear friends,
> I've followed with much interest the several
> messages arrived in last days on EoT calculation.

I too, find this discussion interesting.  It also requires us to
ask "What is significant?" in effects on time measurement.

So far we have centered our concerns with astronomical variations.
What about geographical concerns?  The fact that the Earth is
an ellipseoid (not a sphere) should be of some concern, but when?
Don't forget the different definitions we can have for sunset, or
our altitude above sea level.

With the help of the basic programs from Sky & Telescope, I have 
worked on the question of how many full moons will fall on Christmas
in the next 100 years. (3-2015,2072,2091) Someone at church said
we would not have a full moon on Christmas for over 100 years---I 
knew that was not likely.  There are several programs for date, time,
right ascension, and declination. The URL for Sky & Telescope is: 



> I've calculated, with great accuracy ,the values in all the days of
> the year for 32 consecutive years (1990-2021) and after I've found
> the average values for each day.
> Later on I've developed AR, D, and EoT in Fourier series with 20
> harmonics.

Excellent problem for computer solution. Nice job.

Are these questions moot for sundial design? (Don't stop the thread 
though.)  Having followed the articles in the Compendium on error
analysis of sundials (and from practical experience) a difference
of one millimeter on a gnomon is a greater problem than most of our
cercerns above. But this is an interesting discussion.

My .02 cents---Warren Thom

Re: equation of time

[diallist]

At 07:35 PM 12/31/96 +0100, you wrote:
>Dear gnomonists,
>
>In this e-mail I have attached a gif-picture of the curve of the
>equation of time for two years, 1902 and 2098.
>They are calculated with the formula ( for the mentioned years) I
>mentioned in my earlier e-mail this day.
>You see the ( small) change in the curve in a periode of about 200
>years.
>
>I do hope many of you can really see this picture.
>
>Fer J. de Vries.
>
>Attachment Converted: D:\EUDORA\ATTACH\equatime.gif
>

Fer,

Thanks for the informative GIF which compares the EOT for 1902 and 2098.

Two questions:

1.  What drawing program did you use to make the GIF.  I've been wanting to
draw a nice EOT graph for use on my website, but the only drawing program I
have requires me to manually input the individual points that make up the
curve.  Does your drawing software allow the use of equations to
automatically draw the desired curve?

2.  Eventually, I want to add a page to my website devoted to the EOT.
Since the GIF you so graciously provided is so informative, I wonder if I
might have your permission to use it on my website?  With credit given to
you of course.

Charles


*   Sundials and The Author* 
* http://www.geocities.com/athens/1012 *

Re: Equation of Time

[diallist]

>Date: Wed, 01 Jan 1997 05:11:37 -0500
>To: "Gianni Ferrari" <[EMAIL PROTECTED]>
>From: [EMAIL PROTECTED]
>Subject: Re: Equation of Time
>
>At 07:25 PM 12/31/96 +0100, you wrote:
>
>>EoT= E0+E1*cos(wt+F1) + E2*cos(2wt+F2) +.. + E6*cos(6wt+F6)
>>
>>where   t is in days from the beginning of the year ( for 1/1 t=1)
>>  w=2*3.141592653/Tropical_year_in days
>>
>>The values of the coefficients are :
>>  E0=0.01822 min  E1=7.36332 min  F1=86.37 degree
>>  E2=9.9205   F2=110.35
>>  E3=0.31794  F3=106.81
>>  E4=0.21958  F4=130.06
>>  E5=0.01470  F5=124.90
>>  E6=0.00661  F6=149.45
>>
>>
>>  With my best wishes for an Happy New Year
>>  
>> Gianni Ferrari
>>
>>
>>
>
>Dear Gianni,
>
>Would you be so kind as to explain exactly what you mean by
>
> "Tropical_year_in days"
>
>Thank you very much.
>
>Charles
>
>


*   Sundials and The Author* 
* http://www.geocities.com/athens/1012 *

Re: Equation of time

[Paolo GREGORIO]

François BLATEYRON wrote:
> 
> Hi dear gnomonists...
> 
> Can someone help me with the calculation of the equation of time ?

Dear François,

  I beg your pardon for my delay, but I have been very
busy in the last hours, since I have been shovelling
snow away..

  I agree with the Roger Sinnot and Fer De Vries remarks;
the Explanatory Supplement (1961-1977 editions) gives for
the mean longitude of perihelion the expression

  w = 101° 13' 15".04 + 6189".03 * T + 1".63 * T^2

where the time interval from the epoch is denoted by T and
measured in Julian centuries of 36525 ephemeris days, that
is to say

 T = (JD - 2415020.0) / 36525

  Everything else seems to be okay; happy year to all!

 Paolo GREGORIO

Re: Equation of time

[Paolo GREGORIO]

Ron Anthony wrote:
> 
> Prof Gregorio,
> 
> >> As far as the Equation of Time is concerned, the last
> edition of the Explanatory Supplement to the Astronomical
> Almanac reports (pag. 484) the following algorithm:<<
> 
> Thank you for the algorithm.  No matter how hard I try I cannot
> make the algorithm yield the correct results.  I attribute this
> to my incorrect math assumptions.  Could you or someone else
> walk thru the algorithm with a real date and time, (for
> example 12:00 July 27, 1980) to help me find my wrong thinking?
> 
> Does "remove multiples of 3600" mean  "reduce to the range of
> 0 to 3600 by adding/subtracting multiples of 3600"?  Or is the
> range -3600 to 3600?
> 
> What is ET expressed in?  decimal hours?
> 
> ++ron

Dear Ron,

  in the algorithms suggested by the Explanatory
Supplement, the solar mean longitude and the mean
anomaly must be reduced in the interval 0-360 degrees
(and NOT 0-3600 degrees); it was probably a misunderstanding,
due to e-mail transmission.

  In order to convert a Gregorian calendar date into a
Julian date (at Greenwich mean noon), you can use the
form (valid for calendar dates since March, 1900, personal
communication of T.C. Van Flandern & K.F.Pulkkinen, US Naval
Observatory, Washington)

 JD = 367*Y-7*(Y+(M+9)/12)/4+275*M/9+D+1721014

where Y=year, M=month number, D=day (all integers).

  In the above formula, division by integers implies truncation
of the quotients to integers; no decimals are carried. You can also
use the method (less suitable for computers) suggested by Peter
Duffet-Smith in his excellent book "Practical Astronomy with
Your Calculator", Cambridge University Press, 2nd edition, 1981.

  Finally, the EOT of the Expl.Supplement algorithm is expressed
in degrees; you may convert it in hours (or primes or seconds)
remenbering that

 24 hours = 360 degrees  (1 hour = 15 degrees)

or

 1 degree = 1/15 hour = 4 primes = 240 seconds

  I hope that these specifications are sufficient for you; if
something is not completely clear, don't fear, e-mail...

   With my best regards,

   Paolo GREGORIO

Re: Equation of time

[Ron Anthony]

 Prof Gregorio,


>>0-360 degrees (and NOT 0-3600 degrees); it was probably a misunderstanding,
due to e-mail transmission.<<

Yes, that was the problem.  I used Charles Gann's copy of the formula.  For
July 27, 1980 at 12:00 I got -6m 27.6s. This compares to -6m 25.4s I got   
using the longer formulas from "Practical Astronomy with Your Calculator".  

Thank you for your help.  I have enjoyed this EOT discussion very much.


++ron

Ron Anthony
Concord California USA

Re: equation of time

[fer j. de vries]

Ross McCluney wrote:
.
> EOT = .170 sin (4*pi*(J - 80)/373) - .129 sin (2*pi*(J - 8).355)
> 
> where the arguments of the sine functions are in radians and J is the
> number of days since December 31, and EOT is given in decimals hours.
> .


Dear Ross,

I received your formula for the EoT as above.

I assume the last term must be ( J - 8 ) / 355.

I was curious about this formula, because I didn't expect the numbers
373 and 355 on those places. I expected the number of days in a year.
( 365 or 365.25 ).

So I calculated the results of the formula and my computer compared them
with the results of my procedures.
The + and - differences are shown below for the years 1997 - 2012.
When you accept this accuracy you may use this formula during a long
time.  
( My value - your value )

1997  19.38 sec at day 1.5   -45.34 sec at day 365.5
1998  26.37 sec at day 1.5   -38.26 sec at day 365.5
1999  33.37 sec at day 1.5   -31.17 sec at day 365.5
2000  40.39 sec at day 1.5   -24.30 sec at day 366.5
2001  19.12 sec at day 1.5   -45.61 sec at day 365.5
2002  26.10 sec at day 1.5   -38.54 sec at day 365.5
2003  33.10 sec at day 1.5   -31.45 sec at day 365.5
2004  40.12 sec at day 1.5   -24.57 sec at day 366.5
2005  18.86 sec at day 1.5   -45.89 sec at day 365.5
2006  25.83 sec at day 1.5   -38.82 sec at day 365.5
2007  32.83 sec at day 1.5   -31.74 sec at day 365.5
2008  39.85 sec at day 1.5   -24.84 sec at day 366.5
2009  18.59 sec at day 1.5   -46.16 sec at day 365.5
2010  25.57 sec at day 1.5   -39.10 sec at day 365.5
2011  32.56 sec at day 1.5   -32.02 sec at day 365.5
2012  39.57 sec at day 1.5   -25.12 sec at day 366.5

Lateron in the century the max error isn't always at the first or last
day but can fall on another day. See example for 2097.


2097  26.41 sec at day 71.5  -52.29 sec at day 364.5

The change in the error from year to year shows the change in the real
EoT, because your formula always give the same values.

Don't look at the decimals, the computer just printed them as well.

 
Fer J. de Vries.

Re: equation of time

[Luke Coletti]

[EMAIL PROTECTED] wrote:
> 
> Thanks for the informative GIF which compares the EOT for 1902 and 2098.
> 
> Two questions:
> 
> 1.  What drawing program did you use to make the GIF.  I've been wanting to
> draw a nice EOT graph for use on my website, but the only drawing program I
> have requires me to manually input the individual points that make up the
> curve.  Does your drawing software allow the use of equations to
> automatically draw the desired curve?
> 

Hello,
One option you might want to try is Gnuplot(ver3.6), a freely
available
plotting program that includes GIF as one of the output formats. The
attached GIF image was created using Gnuplot using the approximation
formulas given. Datafiles are easily read and displayed too. The URL for
more info on Gnuplot:

http://www.cs.dartmouth.edu/gnuplot_info.html


Regards,

Luke Coletti

Re: Equation of Time

[Gianni Ferrari]

Warren Thorn  wrote :

> With the help of the basic programs from Sky & Telescope, I have 
> worked on the question of how many full moons will fall on Christmas
> in the next 100 years. (3-2015,2072,2091) Someone at church said
> we would not have a full moon on Christmas for over 100 years---I 
> knew that was not likely.  There are several programs for date, time,
> right ascension, and declination. The URL for Sky & Telescope is: 
> 
> 

In "Astronomical Tables of Sun, Moon and Planets" by J. Meeus  and using
the Jeffrey Sax's programs distributed by Willmann-Bell and based on
Astronomical Algorithms by J. Meeus 
I've found that Full Moon will fall in Christmas day 5 times in next
century .  
Exactly in 2015 (11h 13m UT), 2034 (8h 56m), 2053 (9h, 24m) ,2072(7h 18m),
2091(22h 02m) 
: the intervals respect the Saros Cycle
The Full Moon will fall in the Holy Night ( as in 1996 at 20h 42m UT) only
4 times : 2007 ( 1h 17m) ,2026 (1h 29m), 2045 (0h 45m), 2093 (3h 53m) .

Perhaps at church someone said that  we would not have a full moon on
Christmas for over 100 years  (also in Italy I've heared this news by
radio) because  for the persons not keened on astronomy the Holy Night
begins about at 18h (12/24) and ends about 6h (12/25) and in this period
there is no Full Moon ( at Greenwich obviously) .

Please accept my apologies since this note not concerns Sundials

Ciao  Gianni

Re: Equation of Time

[Andrew Pettit]

At 17:57 03/01/97 +0100, Gianni Ferrari wrote:
>Warren Thorn  wrote :
>
>> With the help of the basic programs from Sky & Telescope, I have 
>> worked on the question of how many full moons will fall on Christmas
>> in the next 100 years. (3-2015,2072,2091) Someone at church said
>> we would not have a full moon on Christmas for over 100 years---I 
>> knew that was not likely.  There are several programs for date, time,
>> right ascension, and declination. The URL for Sky & Telescope is: 
>> 
>> 
>
>In "Astronomical Tables of Sun, Moon and Planets" by J. Meeus  and using
>the Jeffrey Sax's programs distributed by Willmann-Bell and based on
>Astronomical Algorithms by J. Meeus 
>I've found that Full Moon will fall in Christmas day 5 times in next
>century .  
>Exactly in 2015 (11h 13m UT), 2034 (8h 56m), 2053 (9h, 24m) ,2072(7h 18m),
>2091(22h 02m) 
>: the intervals respect the Saros Cycle
>The Full Moon will fall in the Holy Night ( as in 1996 at 20h 42m UT) only
>4 times : 2007 ( 1h 17m) ,2026 (1h 29m), 2045 (0h 45m), 2093 (3h 53m) .
>
>Perhaps at church someone said that  we would not have a full moon on
>Christmas for over 100 years  (also in Italy I've heared this news by
>radio) because  for the persons not keened on astronomy the Holy Night
>begins about at 18h (12/24) and ends about 6h (12/25) and in this period
>there is no Full Moon ( at Greenwich obviously) .
>
>   Please accept my apologies since this note not concerns Sundials
>   
>   Ciao  Gianni
>
I do not wish to sound impolite but isn't there a reasonably well known
thoery that the lunar cycle repeats every 19 years. This is known as the
Metonic Cycle and was first devised about 430 BC by Meton of Athens.

100 divided by 19 is about five and a quarter so, if there is ever a Full
Moon on Christmas Day, approximately three centuries in four will have five
Full Moons on Christmas Day and approximately one century in four will have six.

OK I realise that the cycle is not exactly nineteen years and  dare say that
one could argue about exactly what is meant by a Full Moon occurring on
Christmas Day but once in a thousand years seems a little far fetched.

As I said earlier I hope that this obsevation does not appear impolite - or
even wrong in which case I will "have egg all over my face!!!"

I hope that this is of asstistance.

Regards
-Andrew
Pettit-

e-mail:  [EMAIL PROTECTED]

Postman Pat:   3, Lucastes Road, HAYWARDS HEATH, West Sussex, RH16 1JJ,
ENGLAND

Tel. UK:  (+44) (0)1444 453111

Equation of time EoT

[fer j. de vries]

Dear all,

In a message to Gianni Ferrari I wrote about the change in the
definition for EoT by the IAU in 1930.
But I made typing errors.
 
The formal definition was EoT = TM - TA.
In 1930 changed into  EoT = TA - TM.
TM is mean time
TA is local time.

Sorry for my errors.

Fer.

RE: Equation of Time

[Carl & Barbara Sabanski]

Sunny Day Duane?

As you suggest it is possible to incorporate the Equation of Time into a
garden variety horizontal sundial.  However it must be done to each
individual hour line in the form of an analemma, which is in the shape of an
"8".  If used, it is normally done only on the full hours.  I am sure you
have seen this.  I many cases the graph of the Equation of Time is included
in the dial plate.  When reading the sundial the graph is used to estimate
the correction required on a particular day.  You can see this at:

http://www.mysundial.ca/sdu/sdu_correct_a_dial_2.html

There is a more complex horizontal sundial that will indicate standard time.

Happy Dialling!

Carl Sabanski
www.mysundial.ca
"Get Hooked on Gnomonics!"
  -Original Message-
  From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
Behalf Of [EMAIL PROTECTED]
  Sent: Friday, June 01, 2007 2:57 PM
  To: sundial@uni-koeln.de
  Subject: Equation of Time


  Greetings,

  I am a new member and have what is probably a very simplistic question.
My apologies in advance.

  When considering a flat, fixed sundial (not an equatorial dial) it appears
that to get the sundial as close as possible to watch time you set it to the
latitude and then adjust it for the longitude when laying out the hour
lines.  Having done all that, am I right in assuming that you are still at
the mercy of the Equation of Time and will need to add/subtract minutes to
the dials time to equal watch time?  - or is it somehow possible to adjust a
flat, fixed sundial to incorporate the equation of time also?

  Thank you for any guidance/help you will tender.

  Sincerely,

  Duane Thomson






--
  See what's free at AOL.com.
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Equation of Time

[Roger Bailey]

Hello Duane,

This is a good question, one that has challenged us since the railways forced 
the introduction of standard time. My initial advice is to "Get over it!". 
Sundials show solar time, in tune with the rotations and orbits of our 
universe. Clock time is defined by law and international conventions. This is 
fine for catching an airplane but it is a totally  arbitrary system of time. 
There are translations available but the bottom line is the clocks are wrong. 
Go with the sun.

I have mellowed a bit and now accept  that there are good reasons to show clock 
time on a sundial. The advice that you have been getting for slewing for 
longitude and adding an EOT correction is appropriate. This used to be what we 
were stuck with to show mean clock time. But things have changed with the 
wonderful subtle design by Hendrik Hollander, a mean time sundial with conical 
gnomon. This dial looks quite normal, with straight lines and smooth curves but 
it incorporates the equation of time and shows clock time. Hendrik won the 
prestigious "Sawyer Dialing Prize" last year for this concept and has published 
the details in in the NASS Compendium, Sept 2006. The latest Compendium digital 
edition, June 2007, included software by Brian Albinson to design such a 
Hollander mean time dial for your location. Google "Hendrik Hollander sundial" 
for more leads. 

My final recommendation is to not construct a sundial based on Hollander's 
concepts until you can explain the hidden subtly to your friends and family. 
Actually this is not a recommendation but a challenge. I am not there yet. 

Welcome to the Sundial Mailing List,

Roger Bailey
Walking Shadow Designs www.walkingshadow.info 
NASS Secretary www.sundials.org 



- Original Message - 
  From: [EMAIL PROTECTED] 
  To: sundial@uni-koeln.de 
  Sent: Friday, June 01, 2007 1:57 PM
  Subject: Equation of Time


  Greetings, 

  I am a new member and have what is probably a very simplistic question.  My 
apologies in advance.

  When considering a flat, fixed sundial (not an equatorial dial) it appears 
that to get the sundial as close as possible to watch time you set it to the 
latitude and then adjust it for the longitude when laying out the hour lines.  
Having done all that, am I right in assuming that you are still at the mercy of 
the Equation of Time and will need to add/subtract minutes to the dials time to 
equal watch time?  - or is it somehow possible to adjust a flat, fixed sundial 
to incorporate the equation of time also?

  Thank you for any guidance/help you will tender.

  Sincerely,

  Duane Thomson





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11:22 AM
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Re: Equation of Time

[Aten Heliochronometers]

Hi Duane:

  Another way to incorporate the equation of time into a sundial is to use the 
"analemma" - a graphic representation of the EofT - placed on a pivoting 
surface with a gnomon/sight to produce a shadow or solar image on the analemmic 
surface - the pivot is scaled relative to a fixed, marked surface to show the 
time in standard hours/mins. during daylight.  This is generally known as a 
heliochronometer - you can see the ones I make at http://atensundials.com . I 
like this design because it is simple and one design works at any longitude and 
latitudes between 20 and 50 degrees North or South without much loss of 
accuracy at the extreme ranges.  

Cheers!
Dave G.
---
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Re: Equation of Time

[Mike Shaw]

Duane,

The easiest way, I think, is to combine the longitude correction and the 
Equation of Time graph.
You can then just apply one correction without the need to calculate in the 
longitude correction into the dial.

See: http://homepage.ntlworld.com/jmikeshaw/page13.html for an adjustable one.

Mike Shaw

53.37N
3.02W

www.wiz.to/sundials

---
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RE: Equation of Time

[Roger Sinnott]

Duane,

In addition to all the other comments, I'd like to mention this possibility:

An ordinary garden sundial with triangular gnomon is usually mounted on a solid 
pedestal with the horizontal plane fixed.  If instead you place it on an 
"equatorial table," the sundial can wobble about an axis through the north and 
south celestial poles.  By controlling this wobble with the seasons, you can 
easily counteract the equation of time and make the sundial show mean time 
without any mental corrections at all.

Equatorial tables, or platforms, have been around since they were invented by a 
French genius, Adrien Poncet, and described in the January 1977 issue of Sky & 
Telescope, pages 64-67. The prototype that I made then is sitting on the table 
in front of me now, and it seems ideal for carrying a horizontal sundial!  This 
is Poncet's concept:  If a rigid body (in this case the entire sundial) is 
supported at three points, one acting as a fixed pivot and the other two 
constrained to slide on a fixed plane (that of the celestial equator), the body 
can only rotate around the polar axis (defined by the gnomon's shadow-casting 
upper edge).

Since 1977, many versions of the Poncet platform have been devised and produced 
commercially. They tend to get more complicated when you need them to carry 
heavy telescopes, such as Dobsonians, and track smoothly enough for 
time-exposure imaging.  But for a sundial Poncet's original design seems quite 
adequate. All you would need is a cam of the proper shape to raise or lower one 
end of the table (by no more than 4 degrees) to correct for the equation of 
time.

Using a knob attached to this cam, you could dial in the current month and day 
and that's it! (And if you forget to reset the date for a week or two, the 
readings will still be quite close.)

   -- Roger


Greetings,

I am a new member and have what is probably a very simplistic question.  My 
apologies in advance.

When considering a flat, fixed sundial (not an equatorial dial) it appears that 
to get the sundial as close as possible to watch time you set it to the 
latitude and then adjust it for the longitude when laying out the hour lines.  
Having done all that, am I right in assuming that you are still at the mercy of 
the Equation of Time and will need to add/subtract minutes to the dials time to 
equal watch time?  - or is it somehow possible to adjust a flat, fixed sundial 
to incorporate the equation of time also?

Thank you for any guidance/help you will tender.

Sincerely,

Duane Thomson


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

Re: Equation of Time

[Karl Billeter]

On Fri, Jun 01, 2007 at 04:57:24PM -0400, [EMAIL PROTECTED] wrote:
> Having done all that, am I right in assuming that you are still at  the mercy 
> of the Equation of Time and will need to add/subtract minutes to the  dials
> time to equal watch time?  - or is it somehow possible to adjust a  flat,
> fixed sundial to incorporate the equation of time also?

Yes you are right, and yes, you can incorporate the EOT.  Curved lines is the
simplest way but you need to keep track of which half of the year you are in
and the dial tends to be cluttered.  Have a look at the Sawyer Equant dial at
http://www.precisionsundials.com for a clever technique of rotating a
horizontal dial.
  
Karl
---
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Re: Equation of Time

[Dave Bell]

Roger Sinnott wrote:
> Duane,
>
> In addition to all the other comments, I'd like to mention this possibility:
>
> [F]or a sundial Poncet's original design seems quite adequate. All you would 
> need is a cam of the proper shape to raise or lower one end of the table (by 
> no more than 4 degrees) to correct for the equation of time.
>
> Using a knob attached to this cam, you could dial in the current month and 
> day and that's it! (And if you forget to reset the date for a week or two, 
> the readings will still be quite close.)
>
>-- Roger
>   
Nice idea, Roger!
A variant on that would be to use a long, straight shaft for the polar 
axis and gnomon, letting the horizontal dial hang from the axis.
The adjustment would be very slight, barely noticeable as off-level...



Dave

---
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RE: Equation of Time

[Edley McKnight]

Hi Duane, Roger, and all,

A true equatorial mount is truly fine if you have one, A simple hinge mounted 
in parallel with the earth's axis at some point below the horizontal surface, 
allowing the dial to tip a little one way or the other will allow adjusting for 
both 
Longitude and the Equation of Time.  One could consider the sundial to be a 
slightly slow or fast clock and set it daily for the correct time, like any 
other 
clock. (even daylight saving's time if the tilt is large enough) Mounting an 
east west hinge below that would allow adjusting for errors in Latitude as 
well.  Setting up such a table is a fun thing to test various designs or 
sundials 
found.  I call it an "Latitude/Longitude table".

BTW, Even Pillar or Shepherd's dials made for other places seem to work 
just fine locally when rotated on such a table, set for the correct Lat/Long 
rather than dangled by their cords.  Has anyone else observed this?

I still like Hendrik Hollander's cone gnomon design the best currently.

Enjoy the Light!

Edley McKnight

> Duane,
> 
> In addition to all the other comments, I'd like to mention this
> possibility:
> 
> An ordinary garden sundial with triangular gnomon is usually mounted
> on a solid pedestal with the horizontal plane fixed.  If instead you
> place it on an "equatorial table," the sundial can wobble about an
> axis through the north and south celestial poles.  By controlling this
> wobble with the seasons, you can easily counteract the equation of
> time and make the sundial show mean time without any mental
> corrections at all.
> 
> Equatorial tables, or platforms, have been around since they were
> invented by a French genius, Adrien Poncet, and described in the
> January 1977 issue of Sky & Telescope, pages 64-67. The prototype that
> I made then is sitting on the table in front of me now, and it seems
> ideal for carrying a horizontal sundial!  This is Poncet's concept: 
> If a rigid body (in this case the entire sundial) is supported at
> three points, one acting as a fixed pivot and the other two
> constrained to slide on a fixed plane (that of the celestial equator),
> the body can only rotate around the polar axis (defined by the
> gnomon's shadow-casting upper edge).
> 
> Since 1977, many versions of the Poncet platform have been devised and
> produced commercially. They tend to get more complicated when you need
> them to carry heavy telescopes, such as Dobsonians, and track smoothly
> enough for time-exposure imaging.  But for a sundial Poncet's original
> design seems quite adequate. All you would need is a cam of the proper
> shape to raise or lower one end of the table (by no more than 4
> degrees) to correct for the equation of time.
> 
> Using a knob attached to this cam, you could dial in the current month
> and day and that's it! (And if you forget to reset the date for a week
> or two, the readings will still be quite close.)
> 
>-- Roger
> 
> 
> Greetings,
> 
> I am a new member and have what is probably a very simplistic
> question.  My apologies in advance.
> 
> When considering a flat, fixed sundial (not an equatorial dial) it
> appears that to get the sundial as close as possible to watch time you
> set it to the latitude and then adjust it for the longitude when
> laying out the hour lines.  Having done all that, am I right in
> assuming that you are still at the mercy of the Equation of Time and
> will need to add/subtract minutes to the dials time to equal watch
> time?  - or is it somehow possible to adjust a flat, fixed sundial to
> incorporate the equation of time also?
> 
> Thank you for any guidance/help you will tender.
> 
> Sincerely,
> 
> Duane Thomson
> 
> 
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 


---
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RE: Equation of Time

[Simon \[illustratingshadows]

not only altitude dials, but azimuth dials also. I
have a chapter in Illustrating More Shadows showing
the portability and rules for portability of both dial
types, from the equator to the pole, and the
correlation with calendar curves on an hour angle
dial.

The DeltaCAD macros for the Shepherd and the winged
azimuth dial's both animate over latitude, and it
interesting to see the evolution fro the equator to
the pole, and in the case of the azimuth dial, even
more fun when given a longitude correction.

Simon



--- Edley McKnight <[EMAIL PROTECTED]> wrote:

> Hi Duane, Roger, and all,
> 
> A true equatorial mount is truly fine if you have
> one, A simple hinge mounted 
> in parallel with the earth's axis at some point
> below the horizontal surface, 
> allowing the dial to tip a little one way or the
> other will allow adjusting for both 
> Longitude and the Equation of Time.  One could
> consider the sundial to be a 
> slightly slow or fast clock and set it daily for the
> correct time, like any other 
> clock. (even daylight saving's time if the tilt is
> large enough) Mounting an 
> east west hinge below that would allow adjusting for
> errors in Latitude as 
> well.  Setting up such a table is a fun thing to
> test various designs or sundials 
> found.  I call it an "Latitude/Longitude table".
> 
> BTW, Even Pillar or Shepherd's dials made for other
> places seem to work 
> just fine locally when rotated on such a table, set
> for the correct Lat/Long 
> rather than dangled by their cords.  Has anyone else
> observed this?
> 
> I still like Hendrik Hollander's cone gnomon design
> the best currently.
> 
> Enjoy the Light!
> 
> Edley McKnight
> 
> > Duane,
> > 
> > In addition to all the other comments, I'd like to
> mention this
> > possibility:
> > 
> > An ordinary garden sundial with triangular gnomon
> is usually mounted
> > on a solid pedestal with the horizontal plane
> fixed.  If instead you
> > place it on an "equatorial table," the sundial can
> wobble about an
> > axis through the north and south celestial poles. 
> By controlling this
> > wobble with the seasons, you can easily counteract
> the equation of
> > time and make the sundial show mean time without
> any mental
> > corrections at all.
> > 
> > Equatorial tables, or platforms, have been around
> since they were
> > invented by a French genius, Adrien Poncet, and
> described in the
> > January 1977 issue of Sky & Telescope, pages
> 64-67. The prototype that
> > I made then is sitting on the table in front of me
> now, and it seems
> > ideal for carrying a horizontal sundial!  This is
> Poncet's concept: 
> > If a rigid body (in this case the entire sundial)
> is supported at
> > three points, one acting as a fixed pivot and the
> other two
> > constrained to slide on a fixed plane (that of the
> celestial equator),
> > the body can only rotate around the polar axis
> (defined by the
> > gnomon's shadow-casting upper edge).
> > 
> > Since 1977, many versions of the Poncet platform
> have been devised and
> > produced commercially. They tend to get more
> complicated when you need
> > them to carry heavy telescopes, such as
> Dobsonians, and track smoothly
> > enough for time-exposure imaging.  But for a
> sundial Poncet's original
> > design seems quite adequate. All you would need is
> a cam of the proper
> > shape to raise or lower one end of the table (by
> no more than 4
> > degrees) to correct for the equation of time.
> > 
> > Using a knob attached to this cam, you could dial
> in the current month
> > and day and that's it! (And if you forget to reset
> the date for a week
> > or two, the readings will still be quite close.)
> > 
> >-- Roger
> > 
> > ____
> > Greetings,
> > 
> > I am a new member and have what is probably a very
> simplistic
> > question.  My apologies in advance.
> > 
> > When considering a flat, fixed sundial (not an
> equatorial dial) it
> > appears that to get the sundial as close as
> possible to watch time you
> > set it to the latitude and then adjust it for the
> longitude when
> > laying out the hour lines.  Having done all that,
> am I right in
> > assuming that you are still at the mercy of the
> Equation of Time and
> > will need to add/subtract minutes to the dials
> time to equal watch
> > time?  - or is it somehow possible to adjust a
> flat, fixed sundial to
> > incorporate the equation of time also?
> > 
> > Thank you for any guidance/help you will tender.
> > 
> > Sincerely,
> > 
> > Duane Thomson
> > 
> > 
> >
> ---
> >
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> > 
> 
> 
> >
---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 
> 

---
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RE: Equation of Time

[Edley McKnight]

Hi Simon,

Ahhh!  Thanks much for the information!  So, nearly any sundial, if 
competently made can be used nearly anywhere on earth, if oriented 
properly.  That is good to hear.

Thanks again!

Edley McKnight.

> not only altitude dials, but azimuth dials also. I
> have a chapter in Illustrating More Shadows showing
> the portability and rules for portability of both dial
> types, from the equator to the pole, and the
> correlation with calendar curves on an hour angle
> dial.
> 
> The DeltaCAD macros for the Shepherd and the winged
> azimuth dial's both animate over latitude, and it
> interesting to see the evolution fro the equator to
> the pole, and in the case of the azimuth dial, even
> more fun when given a longitude correction.
> 
> Simon
> 
> 
> 
> --- Edley McKnight <[EMAIL PROTECTED]> wrote:
> 
> > Hi Duane, Roger, and all,
> > 
> > A true equatorial mount is truly fine if you have
> > one, A simple hinge mounted 
> > in parallel with the earth's axis at some point
> > below the horizontal surface, 
> > allowing the dial to tip a little one way or the
> > other will allow adjusting for both 
> > Longitude and the Equation of Time.  One could
> > consider the sundial to be a 
> > slightly slow or fast clock and set it daily for the
> > correct time, like any other 
> > clock. (even daylight saving's time if the tilt is
> > large enough) Mounting an 
> > east west hinge below that would allow adjusting for
> > errors in Latitude as 
> > well.  Setting up such a table is a fun thing to
> > test various designs or sundials 
> > found.  I call it an "Latitude/Longitude table".
> > 
> > BTW, Even Pillar or Shepherd's dials made for other
> > places seem to work 
> > just fine locally when rotated on such a table, set
> > for the correct Lat/Long 
> > rather than dangled by their cords.  Has anyone else
> > observed this?
> > 
> > I still like Hendrik Hollander's cone gnomon design
> > the best currently.
> > 
> > Enjoy the Light!
> > 
> > Edley McKnight
> > 
> > > Duane,
> > > 
> > > In addition to all the other comments, I'd like to
> > mention this
> > > possibility:
> > > 
> > > An ordinary garden sundial with triangular gnomon
> > is usually mounted
> > > on a solid pedestal with the horizontal plane
> > fixed.  If instead you
> > > place it on an "equatorial table," the sundial can
> > wobble about an
> > > axis through the north and south celestial poles. 
> > By controlling this
> > > wobble with the seasons, you can easily counteract
> > the equation of
> > > time and make the sundial show mean time without
> > any mental
> > > corrections at all.
> > > 
> > > Equatorial tables, or platforms, have been around
> > since they were
> > > invented by a French genius, Adrien Poncet, and
> > described in the
> > > January 1977 issue of Sky & Telescope, pages
> > 64-67. The prototype that
> > > I made then is sitting on the table in front of me
> > now, and it seems
> > > ideal for carrying a horizontal sundial!  This is
> > Poncet's concept: 
> > > If a rigid body (in this case the entire sundial)
> > is supported at
> > > three points, one acting as a fixed pivot and the
> > other two
> > > constrained to slide on a fixed plane (that of the
> > celestial equator),
> > > the body can only rotate around the polar axis
> > (defined by the
> > > gnomon's shadow-casting upper edge).
> > > 
> > > Since 1977, many versions of the Poncet platform
> > have been devised and
> > > produced commercially. They tend to get more
> > complicated when you need
> > > them to carry heavy telescopes, such as
> > Dobsonians, and track smoothly
> > > enough for time-exposure imaging.  But for a
> > sundial Poncet's original
> > > design seems quite adequate. All you would need is
> > a cam of the proper
> > > shape to raise or lower one end of the table (by
> > no more than 4
> > > degrees) to correct for the equation of time.
> > > 
> > > Using a knob attached to this cam, you could dial
> > in the current month
> > > and day and that's it! (And if you forget to reset
> > the date for a week
> > > or two, the readings will still be quite close.)
> > > 
> > >-- Roger
> > > 
> > >

RE: Equation of Time

[Roger Sinnott]

Dave, Edley, and others,

Thanks for the excellent suggestions!

Edley's idea is simple and elegant.  The only slight drawback I see is that the 
base of the sundial has to be made thick enough to accommodate the hinge.

Dave's idea is also nice, and it avoids the need for a thick base.  Adrien 
Poncet liked to refer to his invention as a "no axis" telescope mount (meaning 
that the polar axis was not a physical thing but was implied by the 3-D 
geometry and degrees of freedom of the parts).  That is helpful in a 
telescope/camera mount because it means the equatorial table can have a very 
low profile.  But a sundial of this type has a solid gnomon anyway, so why not 
make use of it, as Dave's idea does!

In a separate e-mail, Patrick Powers commented that the usual garden sundial 
has a thick gnomon (in which you read the shadow from one edge of the gnomon in 
the morning and the other edge in the afternoon). So the gnomon theoretically 
needs to tilt *with* the base, rather than being independently fixed while the 
base tilts under it.

I'm trying to come up with the mathematical shape of a suitable cam for 
controlling the base tilt in a sundial of this general type, during the course 
of a year. So far, no luck.  It may be easier to go ahead and make one 
empirically.

-- Roger


>From Edley McKnight:

A true equatorial mount is truly fine if you have one, A simple hinge mounted 
in parallel with the earth's axis at some point below the horizontal surface, 
allowing the dial to tip a little one way or the other will allow adjusting for 
both Longitude and the Equation of Time.  One could consider the sundial to be 
a slightly slow or fast clock and set it daily for the correct time, like any 
other clock. (even daylight saving's time if the tilt is large enough) Mounting 
an east west hinge below that would allow adjusting for errors in Latitude as 
well.  Setting up such a table is a fun thing to test various designs or 
sundials found.  I call it an "Latitude/Longitude table".

BTW, Even Pillar or Shepherd's dials made for other places seem to work just 
fine locally when rotated on such a table, set for the correct Lat/Long rather 
than dangled by their cords.  Has anyone else observed this?

I still like Hendrik Hollander's cone gnomon design the best currently.
-
>From Dave Bell:

A variant on that would be to use a long, straight shaft for the polar
axis and gnomon, letting the horizontal dial hang from the axis.
The adjustment would be very slight, barely noticeable as off-level...
-

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

RE: Equation of Time

[Edley McKnight]

Hi Roger, Patrick, Dave and all,

My idea was to tilt the whole sundial, gnomon, base and all.  It is as if it 
were remounted at a 
longitude where the local time was the same as the corrected time here.

In light of that, couldn't a wide gnomon standard horizontal dial be considered 
two dials 
mounted close to each other?  In that case the tilt of the dial would still 
keep the two 
gnomons parallel to the earth's axis, thus correcting both.

Well, of course it wouldn't be a horizontal dial anymore, but I wouldn't be 
that picky.

The single rod gnomon that the balance of the dial hangs from would work nicely 
too, thanks 
Dave

Edley.

> Dave, Edley, and others,
> 
> Thanks for the excellent suggestions!
> 
> Edley's idea is simple and elegant.  The only slight drawback I see is
> that the base of the sundial has to be made thick enough to
> accommodate the hinge.
> 
> Dave's idea is also nice, and it avoids the need for a thick base. 
> Adrien Poncet liked to refer to his invention as a "no axis" telescope
> mount (meaning that the polar axis was not a physical thing but was
> implied by the 3-D geometry and degrees of freedom of the parts). 
> That is helpful in a telescope/camera mount because it means the
> equatorial table can have a very low profile.  But a sundial of this
> type has a solid gnomon anyway, so why not make use of it, as Dave's
> idea does!
> 
> In a separate e-mail, Patrick Powers commented that the usual garden
> sundial has a thick gnomon (in which you read the shadow from one edge
> of the gnomon in the morning and the other edge in the afternoon). So
> the gnomon theoretically needs to tilt *with* the base, rather than
> being independently fixed while the base tilts under it.
> 
> I'm trying to come up with the mathematical shape of a suitable cam
> for controlling the base tilt in a sundial of this general type,
> during the course of a year. So far, no luck.  It may be easier to go
> ahead and make one empirically.
> 
> -- Roger
> 
> 
> >From Edley McKnight:
> 
> A true equatorial mount is truly fine if you have one, A simple hinge
> mounted in parallel with the earth's axis at some point below the
> horizontal surface, allowing the dial to tip a little one way or the
> other will allow adjusting for both Longitude and the Equation of
> Time.  One could consider the sundial to be a slightly slow or fast
> clock and set it daily for the correct time, like any other clock.
> (even daylight saving's time if the tilt is large enough) Mounting an
> east west hinge below that would allow adjusting for errors in
> Latitude as well.  Setting up such a table is a fun thing to test
> various designs or sundials found.  I call it an "Latitude/Longitude
> table".
> 
> BTW, Even Pillar or Shepherd's dials made for other places seem to
> work just fine locally when rotated on such a table, set for the
> correct Lat/Long rather than dangled by their cords.  Has anyone else
> observed this?
> 
> I still like Hendrik Hollander's cone gnomon design the best
> currently.
> - >From
> Dave Bell:
> 
> A variant on that would be to use a long, straight shaft for the polar
> axis and gnomon, letting the horizontal dial hang from the axis. The
> adjustment would be very slight, barely noticeable as off-level...
> -
> 
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 


---
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RE: Equation of Time

[Edley McKnight]

Hi Folks, just a short note on hinging in latitude/EOT corrections.

I tend to think of the hinge as one side of a parallelogram with the gnomon as 
the opposite side.  The parallelogram extending down through the dial plate 
and base.  When any set of parallel lines is rotated around one of them, they 
still stay parallel, further, if only a subset of these lines is rotated, all 
of them 
are still parallel.  So, really, the hinge could be just below an edge of the 
dial 
plate if the dial plate is allowed to swing to positive and negative angles. So 
long as the hinge is parallel to the gnomon.  A half circle with a screw clamp 
or any number of other ways could be used to set the angle/time.  I hope this 
makes sense.  It is all equivalent to translating the dial in Longitude( 
rotating 
around the earth's axis as a hinge).

Enjoy the Light!

Edley.
---
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Re: Equation of Time

[Chris Lusby Taylor]

This has been an excellent discussion. As several of my designs purport to be 
readable to a couple of minutes, I, too, had been exploring ways to correct for 
the EoT.

The Poncet platform rotates the entire sundial about a polar axis, but has to 
be made for a specific latitude, so cannot be mass-produced. A 
latitude-independent version is described in US patent 09874026 filed just last 
year (see http://www.patentstorm.us/patents/7035005-description.html) Patrick 
is correct in saying that if the gnomon has two edges you must rotate it, not 
just the dial, as the orientation of the edges would remain correct, but their 
position in space would not.

An alternative that I've investigated is to use two wedges, similar to those 
Bill Gottesman uses for the latitude adjustment of his sundials (also patented: 
see
 http://www.precisionsundials.com/equant%20dial.htm).
The wedge angle can be vey small - just 2 degrees. But having to set three 
alignments seems an unacceptable burden.

My latest approach is to take the "Housewife's Trick" from AP Herbert: just 
turn the whole horizontal sundial about a vertical axis, so the dial plate 
remains horizontal but the gnomon and the 12 o'clock line are no longer 
North-South. This is very much easier to do than any of the other suggestions. 
But, is it accurate?

Of course not - an article in The Compendium a few years ago analysed it and 
rejected it. But The Compendium is written with a USA perspective. AP Herbert 
was English. The housewives to whom he referred were at 51 or more degrees 
North. Does this make a difference?

Yes, it does. By rotating the sundial appropriately, the maximum time error can 
be made to be less than one minute except in July when it may be as much as 90 
seconds. Well, for my money that's a pretty good result. I'm sorry it doesn't 
work as well in the USA because you're too near the equator. For us in northern 
Europe I suggest it is quite good enough. The further north you are, the less 
the error. Should I patent it, or at least the calculation of the "appropriate" 
angle? I think I'm too late. It appears that it's common knowledge amongst 
housewives in this country.

Chris Lusby Taylor
51.4N 1.3W

  - Original Message - 
  From: Edley McKnight 
  To: Roger Sinnott ; sundial@uni-koeln.de 
  Sent: Tuesday, June 05, 2007 6:59 AM
  Subject: RE: Equation of Time


  Hi Folks, just a short note on hinging in latitude/EOT corrections. 


  I tend to think of the hinge as one side of a parallelogram with the gnomon 
as the opposite side.  The parallelogram extending down through the dial plate 
and base.  When any set of parallel lines is rotated around one of them, they 
still stay parallel, further, if only a subset of these lines is rotated, all 
of them are still parallel.  So, really, the hinge could be just below an edge 
of the dial plate if the dial plate is allowed to swing to positive and 
negative angles. So long as the hinge is parallel to the gnomon.  A half circle 
with a screw clamp or any number of other ways could be used to set the 
angle/time.  I hope this makes sense.  It is all equivalent to translating the 
dial in Longitude( rotating around the earth's axis as a hinge). 


  Enjoy the Light! 


  Edley. 


--


  ---
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---
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Re: Equation of Time

[Edley McKnight]

Hi Chris,

Really Cool Chris!  So all those houswives have been correct enough all this 
time!  Thanks!

Edley.
 
> This has been an excellent discussion. As several of my designs
> purport to be readable to a couple of minutes, I, too, had been
> exploring ways to correct for the EoT. 
> 
> The Poncet platform rotates the entire sundial about a polar axis, but
> has to be made for a specific latitude, so cannot be mass-produced. A
> latitude-independent version is described in US patent 09874026 filed
> just last year (see http://www.patentstorm.us/patents/7035005-
> description.html)Patrick is correct in saying that if the gnomon has
> two edges you must rotate it, not just the dial, as the orientation of
> the edges would remain correct, but their position in space would not.
> 
> 
> An alternative that I've investigated is to usetwo wedges, similar to
> those Bill Gottesman uses for the latitude adjustment of his sundials
> (also patented: see
> http://www.precisionsundials.com/equant%20dial.htm). The wedge angle
> can be vey small -just 2 degrees. But having to set three alignments
> seems an unacceptable burden. 
> 
> My latest approach is to take the "Housewife's Trick" from AP Herbert:
> just turn the whole horizontal sundial about a vertical axis, so the
> dial plate remains horizontal but the gnomon and the 12 o'clock line
> are no longer North-South. This is very much easier to do than any of
> the other suggestions. But, is it accurate? 
> 
> Of course not - an article in The Compendium a few years ago analysed
> it and rejected it. But The Compendium is written with a USA
> perspective. AP Herbert was English. The housewives to whom he
> referred were at 51 or more degrees North. Does this make a
> difference? 
> 
> Yes, it does. By rotating the sundial appropriately, the maximum time
> error can be made to be less than one minute except in July when it
> may be as much as 90 seconds. Well, for my money that's a pretty good
> result. I'm sorry it doesn't work as well in the USA because you're
> too near the equator. For us in northern Europe I suggest it is quite
> good enough. The further north you are, the less the error. Should I
> patent it, or at leastthe calculation of the "appropriate" angle? I
> think I'm too late. It appears that it's common knowledge amongst
> housewives in this country. 
> 
> Chris Lusby Taylor 
> 51.4N 1.3W 
> 
> - Original Message - 
> From: Edley McKnight 
> To: Roger Sinnott ; sundial@uni-koeln.de 
> Sent: Tuesday, June 05, 2007 6:59 AM 
> Subject: RE: Equation of Time 
> Hi Folks, just a short note on hinging in latitude/EOT
> corrections. 
> 
> I tend to think of the hinge as one side of a parallelogram with
> the gnomon as the opposite side. The parallelogram extending down
> through the dial plate and base. When any set of parallel lines is
> rotated around one of them, they still stay parallel, further, if
> only a subset of these lines is rotated, all of them are still
> parallel. So, really, the hinge could be just below an edge of the
> dial plate if the dial plate is allowed to swing to positive and
> negative angles. So long as the hinge is parallel to the gnomon. A
> half circle with a screw clamp or any number of other ways could
> be used to set the angle/time. I hope this makes sense. It is all
> equivalent to translating the dial in Longitude( rotating around
> the earth's axis as a hinge). 
> 
> Enjoy the Light! 
> 
> Edley. 
> 
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial 
> 
> 


---
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RE: Equation of Time

[Roger Sinnott]

Chris,

Concerning equatorial tables, people seem to be looking at recent patents for 
ELABORATE designs (conical rollers and such).  But the original Poncet table is 
quite simple. I made my 1977 prototype out of wood, with a piece of Formica for 
the inclined plane on which one end of the table slides.  My unit has no curved 
surfaces at all.

I've used mine for astrophotography at latitudes other than 42 N (for which it 
was constructed).  Shoving a small rock under the north or south end will tilt 
the whole unit appropriately.  I made a couple of small "alignment wedges" on 
which I can place a bubble level for setting the proper base tilt when away 
from home.  I took it to Turkey for the 1999 eclipse (latitude 39 N) and to the 
Winter Star Party in Florida (latitude 25 N) a few years later. The only 
restriction is that it won't work too near the Earth's equator.

I think there's definitely a sundial application here, and I hope to make one 
in the coming weeks to show to the list.

-- Roger


From: [EMAIL PROTECTED] [EMAIL PROTECTED] On Behalf Of Chris Lusby Taylor 
[EMAIL PROTECTED]
Sent: Tuesday, June 05, 2007 5:30 AM

This has been an excellent discussion. As several of my designs purport to be 
readable to a couple of minutes, I, too, had been exploring ways to correct for 
the EoT.

The Poncet platform rotates the entire sundial about a polar axis, but has to 
be made for a specific latitude, so cannot be mass-produced. A 
latitude-independent version is described in US patent 09874026 filed just last 
year (see http://www.patentstorm.us/patents/7035005-description.html) Patrick 
is correct in saying that if the gnomon has two edges you must rotate it, not 
just the dial, as the orientation of the edges would remain correct, but their 
position in space would not.

An alternative that I've investigated is to use two wedges, similar to those 
Bill Gottesman uses for the latitude adjustment of his sundials (also patented: 
see
 http://www.precisionsundials.com/equant%20dial.htm).

---
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RE: Equation of Time

[dbell]

> Concerning equatorial tables, people seem to be looking at recent patents
> for ELABORATE designs (conical rollers and such).  But the original Poncet
> table is quite simple. I made my 1977 prototype out of wood, with a piece
> of Formica for the inclined plane on which one end of the table slides.
> My unit has no curved surfaces at all.

I agree - all I see lately are roller bearing designs, not the sliding
plane. Smooth, frictionless motion is NOT needed here!

> I took it to Turkey for the 1999
> eclipse (latitude 39 N)

We went to Romania for 1999... Did you get out before the quake?

Dave

---
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RE: Equation of Time

[Mac Oglesby]

Hi Roger,

Any chance you could post pictures of your prototype? Maybe even drawings?

Best wishes,

Mac Oglesby





>Chris,
>
>Concerning equatorial tables, people seem to be looking at recent 
>patents for ELABORATE designs (conical rollers and such).  But the 
>original Poncet table is quite simple. I made my 1977 prototype out 
>of wood, with a piece of Formica for the inclined plane on which one 
>end of the table slides.  My unit has no curved surfaces at all.
>
>I've used mine for astrophotography at latitudes other than 42 N 
>(for which it was constructed).  Shoving a small rock under the 
>north or south end will tilt the whole unit appropriately.  I made a 
>couple of small "alignment wedges" on which I can place a bubble 
>level for setting the proper base tilt when away from home.  I took 
>it to Turkey for the 1999 eclipse (latitude 39 N) and to the Winter 
>Star Party in Florida (latitude 25 N) a few years later. The only 
>restriction is that it won't work too near the Earth's equator.
>
>I think there's definitely a sundial application here, and I hope to 
>make one in the coming weeks to show to the list.
>
> -- Roger
>
>
>From: [EMAIL PROTECTED] [EMAIL PROTECTED] On 
>Behalf Of Chris Lusby Taylor [EMAIL PROTECTED]
>Sent: Tuesday, June 05, 2007 5:30 AM
>
>This has been an excellent discussion. As several of my designs 
>purport to be readable to a couple of minutes, I, too, had been 
>exploring ways to correct for the EoT.
>
>The Poncet platform rotates the entire sundial about a polar axis, 
>but has to be made for a specific latitude, so cannot be 
>mass-produced. A latitude-independent version is described in US 
>patent 09874026 filed just last year (see 
>http://www.patentstorm.us/patents/7035005-description.html) Patrick 
>is correct in saying that if the gnomon has two edges you must 
>rotate it, not just the dial, as the orientation of the edges would 
>remain correct, but their position in space would not.
>
>An alternative that I've investigated is to use two wedges, similar 
>to those Bill Gottesman uses for the latitude adjustment of his 
>sundials (also patented: see
>  http://www.precisionsundials.com/equant%20dial.htm).
>
>---
>https://lists.uni-koeln.de/mailman/listinfo/sundial

---
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RE: Equation of Time

[Edley McKnight]

Hi Roger,

Yes, Now that the concept finally comes fully in to mind, this is a great idea! 
 
As you say only about 4 degrees of rotation, a small width of incllined plane 
for the two sliding contacts, would do it for just EOT correction.  Quite 
compactly too.  To handle both Longitude and EOT just about anywhere it 
would be much larger.  3 hours in a time zone plus daylight saving time plus 4 
degrees, What, 65 degrees or so??? total swing.  We would need very strong 
bolts holding the sundial and maybe a mirror to view the dial? 
I guess we could probably handle the 19 degrees or so of Daylight saving time 
and EOT with this inclined plane Poncet mount.  Who knows when Daylight 
saving time will happen in your zone next time? 
Some of the more current designs that have the hour lines spaced evenly 
along a line or circular curve would allow us to just slide a straight or 
curved 
plate to correct for all three corrections.  I think my future designs will 
tend in 
that direction.

Thanks for your persistance, sorry it took so long to soak in!

Edley.

> Chris,
> 
> Concerning equatorial tables, people seem to be looking at recent
> patents for ELABORATE designs (conical rollers and such).  But the
> original Poncet table is quite simple. I made my 1977 prototype out of
> wood, with a piece of Formica for the inclined plane on which one end
> of the table slides.  My unit has no curved surfaces at all.
> 
> I've used mine for astrophotography at latitudes other than 42 N (for
> which it was constructed).  Shoving a small rock under the north or
> south end will tilt the whole unit appropriately.  I made a couple of
> small "alignment wedges" on which I can place a bubble level for
> setting the proper base tilt when away from home.  I took it to Turkey
> for the 1999 eclipse (latitude 39 N) and to the Winter Star Party in
> Florida (latitude 25 N) a few years later. The only restriction is
> that it won't work too near the Earth's equator.
> 
> I think there's definitely a sundial application here, and I hope to
> make one in the coming weeks to show to the list.
> 
> -- Roger
> 
> 
> From: [EMAIL PROTECTED] [EMAIL PROTECTED] On
> Behalf Of Chris Lusby Taylor [EMAIL PROTECTED] Sent:
> Tuesday, June 05, 2007 5:30 AM
> 
> This has been an excellent discussion. As several of my designs
> purport to be readable to a couple of minutes, I, too, had been
> exploring ways to correct for the EoT.
> 
> The Poncet platform rotates the entire sundial about a polar axis, but
> has to be made for a specific latitude, so cannot be mass-produced. A
> latitude-independent version is described in US patent 09874026 filed
> just last year (see
> http://www.patentstorm.us/patents/7035005-description.html) Patrick is
> correct in saying that if the gnomon has two edges you must rotate it,
> not just the dial, as the orientation of the edges would remain
> correct, but their position in space would not.
> 
> An alternative that I've investigated is to use two wedges, similar to
> those Bill Gottesman uses for the latitude adjustment of his sundials
> (also patented: see
>  http://www.precisionsundials.com/equant%20dial.htm).
> 
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
> 


---
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RE: Equation of Time

[Roger Sinnott]

Mac and others,

Here is a first attempt, using Google Sketchup.

 -- Roger


Hi Roger,

Any chance you could post pictures of your prototype? Maybe even drawings?

Best wishes,

Mac Oglesby


<>---
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Re: Equation of Time

[Dave Bell]

Roger Sinnott wrote:
> Mac and others,
>
> Here is a first attempt, using Google Sketchup.
>
>  -- Roger
>
> 
>   
> Nice!! So, you have two matching inclined surfaces, one on the pedestle, and 
> one on the "carrier".
>   
If you were doing this for a telescope, I guess you'd put two Teflon 
pads on the carrier's surface.
For this application, more friction is actually beneficial, so that's 
not necessary.

I've seen Poncet mounts that use a ball/socket for the pivot point. How 
are you suggesting the pivot be made?
Maybe a rounded pin into a conical hole in a hardwood block? And it 
looks like the pin would lie in an equatorial plane, parallel to the 
polar end plane...

Is there a height alignment requirement for the pivot point, relative to 
the inclined plane?
Horizontally, it should be centered, but I have a feeling it needs to be 
placed at the right height on the meridian end, as well.

Great sketch - I have to get around to learning Sketchup!

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

---
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RE: Equation of Time

[Roger Sinnott]

Dave Bell wrote:
>
> Nice!! So, you have two matching inclined surfaces, one on the pedestle,
>and one on the "carrier".

Actually no, there is only one surface (the big one in front) that *has* to be 
inclined.  I gave the rear one a similar tilt to catch the pivot point more 
securely and prevent the upper table from sliding foward under gravity. But its 
angle is not critical.

>
>If you were doing this for a telescope, I guess you'd put two Teflon
>pads on the carrier's surface. For this application, more friction is actually
>beneficial, so that's not necessary.

Good points.

>I've seen Poncet mounts that use a ball/socket for the pivot point. How
>are you suggesting the pivot be made? Maybe a rounded pin into a
>conical hole in a hardwood block? And it looks like the pin would lie in
>an equatorial plane, parallel to the polar end plane...

The pivot can be almost anything -- even a nail through the upper table. Its 
angle is nothing special.

>Is there a height alignment requirement for the pivot point, relative to
>the inclined plane? Horizontally, it should be centered, but I have a
> feeling it needs to be placed at the right height on the meridian
>end, as well.

Nope -- the height is not important, nor does it have to be centered. But you 
are right that the unit will be more stable this way. If the table tilts too 
much, as can happen when star-tracking with a heavy camera or telescope on top, 
things can get out of balance and there is a risk of the upper board toppling 
off.  But this problem shouldn't arise in a sundial with an equation-of-time 
correction, and maybe not with a daylight-saving-time correction either.

>Great sketch - I have to get around to learning Sketchup!

I first heard of SketchUp about a year ago, on this list, and I've been having 
a BLAST with it!

 -- Roger



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RE: Equation of Time

[Roger Sinnott]

>From Edley McKnight:
>Hi Roger and all,
>
>Not ever having seen one, I'd imagined it as a horizontal slice through an 
>equatorial
>dial, with the pivot on the gnomon and the sliding on the dial face, but this 
>looks
>easier to adjust.  I would imagine now that so long as the pivot point and the 
>inclined
>plane contact points all start out in a horizontal triangle that it would 
>work.  The inclined
>plane appears to be parallel with the equatorial plane, yes?

Hi Edley,

The pivot and contacts on the inclined plane don't *have* to define a 
horizontal plane, but they might as well, since they are being used to carry a 
horizontal sundial.  Also, everything will be more stable that way.

You're right, the inclined plane must be parallel to the plane of the celestial 
equator (and Earth's equator). Therebore, this original form of Poncet table 
works well at high and temperate latitudes. But when you get close to the 
Earth's equator (say, within the latitude band from 15 N to 15 S),  the 
inclined plane would become so steep that it wouldn't support the table 
properly.

   -- Roger



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Equation of time cam

[Frederick Jaggi]

Apparently the long now people sell a copy of the cam. See:

http://www.levenger.com/PAGETEMPLATES/PRODUCT/Product.asp? 
Params=Category=5-23|PageID=4871|Level=2-3

Fred Jaggi
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Re: Heliochronometers: Equation of Time

[Luke Coletti]

Hello,

I have found the best method of correcting for the periodic variability
of the EoT relative to the calendar is to take the EoT as a four year
average. The temporal variability, as has been discussed in earlier
threads, is chiefly due to the phase relation between obliquity and
eccentricity as caused by the precession of the equinoxes and the
shifting of perihelion. The magnitude of obliquity and eccentricity
changes too but on a slower time scale. 

Best Regards,

Luke Coletti


Chris Lusby wrote:
> 
> Daniel Wegner ([EMAIL PROTECTED]) is only partly correct in
> saying that an analemma must have an error due to leap years. The error can
> be avoided.
> 
> It is true that tables of the Equation of Time are slightly inaccurate
> because they take a mean value for the solar longitude on a named date (such
> as February 17th), whereas the 4 year and 400 year cycles should be
> allowed-for to be totally accurate. Fortunately for us, the peak error is
> less in the next few years than at any other time in the 400 year cycle. How
> convenient. The worst case is in 1903+400n and 2096+400n, when the longitude
> is 7/8 of a day different from its mean value. But even 7/8 of a day
> accounts for less than 30 seconds of EoT, so still allows a sundial to be
> less than a minute out. Around the year 2000, the worst case is half this -
> about 14 seconds.
> If an EoT table is drawn graphically to allow a sundial reading to be
> converted to mean time, then this too must have an error with the same 4 and
> 400 year cycles.
> 
> But if the sundial is marked with figure-of-eight hour lines, then there
> need be no such error, since the sun's declination and longitude are related
> by geometry, not by what we call the date. Even if we lost another 11 days
> in a calendar reform (I am from England), such a sundial would continue to
> read correct mean time. Therefore, I suggest that this is a purer and
> altogether more satisfactory solution than an EoT table or figure. Except
> for the little point that the EoT changes rather a lot, and the longitude
> does not, at the solstices. Pity.
> 
> By the way, if you are ever making a circular date scale - to calibrate a
> declination scale, for instance - you should divide it into 365.25 and make
> February 29th be just the .25. This is the best simple way to allow for one
> February 29th every four years.
> 
> Chris Lusby Taylor
> 
> ===
> Email:  [EMAIL PROTECTED]
>  (Formerly [EMAIL PROTECTED])
> ===

Re: Heliochronometers: Equation of Time

[Luke Coletti]

Hello,

Below are some data that may help you, the calculation date is
Jan 1 Noon UT, EoT values are in the form TA-TM. The value of the EoT
corresponds to a date/time i.e., a calendar and since there is not a
whole number of days in our orbital period I think you can see how the
EoT becomes unsynced. I'm not sure I fully understand your question of
averages, but try looking at the average of the EoT deltas for each four
year period and compare it to each of yearly values within the cycle.
Hope this helps...


Regards,

Luke Coletti


Column 1: day of year, Column 2: year, Column 3: days in year
Column 4: days from J2000, Column 5: Solar Day Length, secs
Column 6: EoT, secs, Column 7: EoT delta, secs

1 2000 366+0.0 -28.5750 -198.0059  +0.00
1 2001 365  +366.0 -28.3493 -219.3062 -21.300274
1 2002 365  +731.0 -28.4230 -212.3139 -14.307972
1 2003 365 +1096.0 -28.4950 -205.3031  -7.297152 
1 2004 366 +1461.0 -28.5650 -198.2742  -0.268264
1 2005 365 +1827.0 -28.3388 -219.5665 -21.560536
1 2006 365 +2192.0 -28.4127 -212.5768 -14.570837
1 2007 365 +2557.0 -28.4848 -205.5685  -7.562580
1 2008 366 +2922.0 -28.5551 -198.5422  -0.536216
1 2009 365 +3288.0 -28.3283 -219.8264 -21.820466
1 2010 365 +3653.0 -28.4024 -212.8393 -14.833377
1 2011 365 +4018.0 -28.4747 -205.8336  -7.827690
1 2012 366 +4383.0 -28.5451 -198.8098  -0.803855
1 2013 365 +4749.0 -28.3177 -220.0860 -22.080063
1 2014 365 +5114.0 -28.3920 -213.1015 -15.095591
1 2015 365 +5479.0 -28.4645 -206.0984  -8.092480
1 2016 366 +5844.0 -28.5350 -199.0771  -1.071182
1 2017 365 +6210.0 -28.3072 -220.3453 -22.339328
1 2018 365 +6575.0 -28.3816 -213.3634 -15.357478
1 2019 365 +6940.0 -28.4542 -206.3629  -8.356951
1 2020 366 +7305.0 -28.5250 -199.3441  -1.338196

Re: Heliochronometers: Equation of Time

[Pete Swanstrom]

My apologies for such late input to this thread, I have been a little behind
in my e-mail!  I encountered many of these problems and the same questions
when designing my Analemmic Equatorial sundial
( http://netnow.micron.net/~petes/sundial ).  I hope the following
will help.

Luke Coletti wrote:

    I have found the best method of correcting for the periodic variability
of the EoT relative to the calendar is to take the EoT as a four year
average.

 

Tom Semadeni wrote:

How do you do that?  Do you pick a 12 month year which straddles the
mid point between two leap years, like Jun 30, 97 to Jun 30, 98?



The method I used to derive "average" date points for my analemmic gnomon,
and a table of the resultant values, may be found at  http://netnow.micron.net/~petes/sundial/dialcalc.htm
.  As others have stated, this does not affect the shape of the analemma,
just the location of the date's position on the analemma.  This normally
does not affect the time accuracy of the analemmic sundial, except near
the solstices; a 1 day error near the winter solstice would affect the
indication of time by 1/2 minute .

Luke Coletti wrote:

 The temporal variability, as has been discussed in earlier
threads, is chiefly due to the phase relation between obliquity and
eccentricity as caused by the precession of the equinoxes and the
shifting of perihelion. The magnitude of obliquity and eccentricity
changes too but on a slower time scale.



I prepared several graphs last year, prior to the NASS conference, using
Luke Coletti's Solar Calculator program ( http://www.gcstudio.com/suncalc.html
- Thanks Luke! ) and Excel to show how the effects of changing obliquity
and eccentricity of the Earth's orbit may be expected to change the accuracy
of my sundial long-term.  The graphs show the necessary shape of the
analemmic gnomon for the years 2000 BC, , 2000 AD, 4000 AD and 6000
AD.  I found them rather interesting, and so I hope you will forgive
me for attaching them to this e-mail.

Thanks.  Pete S.  ( http://netnow.micron.net/~petes )

Attachment converted: MAC Hard Disk:Millen.gif (GIFf/JVWR) (000127E6)

Re: Heliochronometers: Equation of Time

[Tom Semadeni]

Chris Lusby's post is instructive and I'd like to learn more.

Chris Lusby wrote:

> It is true that tables of the Equation of Time are slightly inaccurate
>
> because they take a mean value for the solar longitude on a named date
> (such
> as February 17th), whereas the 4 year and 400 year cycles should be
> allowed-for to be totally accurate. Fortunately for us, the peak error
> is
> less in the next few years than at any other time in the 400 year
> cycle. How
> convenient. The worst case is in 1903+400n and 2096+400n, when the
> longitude
> is 7/8 of a day different from its mean value. But even 7/8 of a day
> accounts for less than 30 seconds of EoT, so still allows a sundial to
> be
> less than a minute out. Around the year 2000, the worst case is half
> this -
> about 14 seconds.

Where do the 1903 and 2096 come from?   Am I correct in assuming that
ALL of the EoT discrepancy above comes from the (longitude-mean day)
delta?

> But if the sundial is marked with figure-of-eight hour lines, then
> there
> need be no such error, since the sun's declination and longitude are
> related
> by geometry, not by what we call the date. Even if we lost another 11
> days
> in a calendar reform (I am from England), such a sundial would
> continue to
> read correct mean time. Therefore, I suggest that this is a purer and
> altogether more satisfactory solution than an EoT table or figure.
> Except
> for the little point that the EoT changes rather a lot, and the
> longitude
> does not, at the solstices. Pity.

I often see the figure-of-eight hour lines and don't understand why just
one along the noon hour line isn't used.  Is it only the practical
matter that the observer isn't "there" at noon when he/she is observing
at say 3pm?  Or can the noon observation NOT be used to "calibrate" the
observations for the rest of the day, at least?

Thanks for your help
t
--
Tom  Semadeni  O
[EMAIL PROTECTED]   o
aka I (Ned) Ames   .
Britthome Bounty   ><<*>
Box 176  Britt  ON   P0G 1A0
'Phone 705 383 0195 fax 2920
45.768* North   80.600* West

Re: Heliochronometers: Equation of Time

[Tom Semadeni]

Luke Coletti wrote:

> Hello,
>
> I have found the best method of correcting for the periodic 
> variability
> of the EoT relative to the calendar is to take the EoT as a four year
> average.

How do you do that?
Do you pick a 12 month year which straddles the mid point between two leap 
years,
like Jun 30, 97 to Jun 30, 98?

Or do you calculate the "average" of something(s) and if so what?  Perhaps the
average of the 4 results of the noon EoT's for each day of the year.  I.E.,
calculate the average of the noon results of the EoT for Jan 1,96; Jan 1,97; Jan
1,98 and  Jan 1,99. Then do this for every day of the year and list the average
across every day. Leap day?

Or, is there a clever way of just "slipping" one day in the tabular values 
between
the results of the EoT and the calendar day 4 times and then averaging. This 
would
seem to work and the algorithm wouldn't be too daunting.

> The temporal variability, as has been discussed in earlier
> threads, is chiefly due to the phase relation between obliquity and
> eccentricity as caused by the precession of the equinoxes and the
> shifting of perihelion. The magnitude of obliquity and eccentricity
> changes too but on a slower time scale.

Does this mean that the daily values in the EoT, irrespective of the "calendar
problem", generate some sort of periodic function when taken over the Period of 
a
Year (of what sort?) but not quite?  That is, on the anniversaries the EoT isn't
quite where it was a Year ago due to the slow change in the absolute values of 
the
obliquity and eccentricity?

I missed the earlier thread that you referred to. Perhaps you could direct me to
an URL which quantifies your two marvellously concise sentences above.  I think
that I'm getting in over my head and need to do some figuring!

Thank you

Tom Semadeni

>
>
> Best Regards,
>
> Luke Coletti
>
> Chris Lusby wrote:
> >
> > Daniel Wegner ([EMAIL PROTECTED]) is only partly correct in
> > saying that an analemma must have an error due to leap years. The error can
> > be avoided.
> >
> > It is true that tables of the Equation of Time are slightly inaccurate
> > because they take a mean value for the solar longitude on a named date (such
> > as February 17th), whereas the 4 year and 400 year cycles should be
> > allowed-for to be totally accurate. Fortunately for us, the peak error is
> > less in the next few years than at any other time in the 400 year cycle. How
> > convenient. The worst case is in 1903+400n and 2096+400n, when the longitude
> > is 7/8 of a day different from its mean value. But even 7/8 of a day
> > accounts for less than 30 seconds of EoT, so still allows a sundial to be
> > less than a minute out. Around the year 2000, the worst case is half this -
> > about 14 seconds.
> > If an EoT table is drawn graphically to allow a sundial reading to be
> > converted to mean time, then this too must have an error with the same 4 and
> > 400 year cycles.
> >
> > But if the sundial is marked with figure-of-eight hour lines, then there
> > need be no such error, since the sun's declination and longitude are related
> > by geometry, not by what we call the date. Even if we lost another 11 days
> > in a calendar reform (I am from England), such a sundial would continue to
> > read correct mean time. Therefore, I suggest that this is a purer and
> > altogether more satisfactory solution than an EoT table or figure. Except
> > for the little point that the EoT changes rather a lot, and the longitude
> > does not, at the solstices. Pity.
> >
> > By the way, if you are ever making a circular date scale - to calibrate a
> > declination scale, for instance - you should divide it into 365.25 and make
> > February 29th be just the .25. This is the best simple way to allow for one
> > February 29th every four years.
> >
> > Chris Lusby Taylor
> >
> > ===
> > Email:  [EMAIL PROTECTED]
> >  (Formerly [EMAIL PROTECTED])
> > ===

--
Tom  Semadeni  O
[EMAIL PROTECTED]   o
aka I (Ned) Ames   .
Britthome Bounty   ><<*>
Box 176  Britt  ON   P0G 1A0
'Phone 705 383 0195 fax 2920
45.768* North   80.600* West

Re: Heliochronometers: Equation of Time

[Tom Semadeni]

Hi Pete,
Thanks very much for your help in calculating the "average over 4
years-sort of" analemma  as shown in your
 http://netnow.micron.net/~petes/sundial/dialcalc.htm.  Luke Coletti
also sent me a really helpful table off-list.

And I like your Bi-Millennial figures-of-eight, indicating the
non-trivial precessional change that Luke mentions.  This whole
discussion has changed my paradigm to one of fitting the current
calendar to the analemma rather than the reverse.  I think that I was
sucked into the much more artificial reverse by the practice of
calculating EoT as a function of calendar dates, rather that as a
function of local max (noon) elevation.  I guess that it is instructive
to remember what the independent variable really is in this case!

The dials athttp://netnow.micron.net/~petes/sundialare beauties.

Have a look at my big "Sundial"  at:
http://sciencenorth.on.ca/AboutSN/polaris/index.html

Merci, eh.

Tom

RE: Re equation of time

[David Pratten]

Title: Message



Dear 
Doug,
 
The 
factors that make the sundial 'fast' or 'slow' are not dependent on 
latitude.  
 
See http://www.sunlitdesign.com/infosearch/equationoftime.htm and 

 
http://www.sunlitdesign.com/products/thesunapi/documentation/sdxEOT.htm for 
a function to calculate the Equation of Time  If you note the parameters to 
this function you will see that latitude is not necessary for calculating 
it.
 
David

  
  -Original Message-From: 
  [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On 
  Behalf Of dougdotSent: Wednesday, 16 October 2002 7:26 
  AMTo: sundial@rrz.uni-koeln.deSubject: Re equation of 
  time
  Hello all,
  As a newcomer to dialling, I would like to know 
  whether the "fast" or "slow" as shown on the graph is the same for the 
  southern hemisphere as for the northern hemisphere.
  Doug

Re: Equation of Time Formula

[Gordon T. Uber]

See "Astronomical Algorithms" by Jean Meeus, published
by Willmann-Bell.  He has a chapter on the Equation of Time.
Formulas and parameters for almost everything astronomical.

See: http://www.willbell.com/

Gordon

At 14:55 97/12/09 +0100, you wrote:
>Hi all brothers dialists!
>Who knows the exact  time and the exact ecliptic longitude of the
>earth's perihelion ?  
>I need these values to calculate myself the Equation of Time with this
>formula I've obtained with a simple and traditional recipe : a little
>bit of spherical geometry and another little bit of keplerian motion.

>Thank you !
>Alberto Nicelli
>(45,5 N ; 7 E)
>[EMAIL PROTECTED]

-- 
|  XII | Gordon T. Uber,  3790 El Camino Real, Suite 142
|XI| Palo Alto, CA 94306-3314,  email: [EMAIL PROTECTED]
|  X  \   /| CLOCKS and TIME: http://www.ubr.com/clocks/
| IX   \ / | Reynen & Uber WebDesign: http://www.ubr.com/rey&ubr

RE: Equation of Time Formula

[Jorge Ramalho]

--
From:  Nicelli Alberto[SMTP:[EMAIL PROTECTED]
Sent:  terça-feira, 9 de dezembro de 1997 13:55
To:  'sundial@rrz.uni-koeln.de'
Subject:  Equation of Time Formula

Hi all brothers dialists!
Who knows the exact  time and the exact ecliptic longitude of the
earth's perihelion ?  

Alberto,
Try this one:

282.9050112d

auguri
jorge

38N 9W

Re: Equation of Time Formula

[Luke Coletti]

Nicelli Alberto wrote:

> Hi all brothers dialists!
> Who knows the exact  time and the exact ecliptic longitude of the
> earth's perihelion ?

The time(s) of perihelion and the other three principle orbital
positions can be found at the following URL:

http://aa.usno.navy.mil/AA/data/docs/EarthSeasons.html

The USNO Astronomical Almanac in section C has the necessary formula
to compute Ecliptic Longitude, Meeus is another excellent reference.


Regards,

Luke Coletti

FourierSeries for Equation of Time

[Gianni Ferrari]

Dear friends,
I could read only few days ago the many messages that have been 
sent to
the List regarding the development of the Equation of Time in Fourier series.
I thank in particular John Pickard to have taken up again the matter and
Fer de Vries and Luke Coletti to have recalled and explained my note of 1996.
>From the reading of the letters I have been pushed to return to my old
programs, to repeat all the calculations and to seek the value of the
errors that we find when we use the developments.
I try here to organize my results and apologize immediately for the length
of  this message and for the repetition of some parts in comparison to that
I have written in 1996

THE REASON TO USE THE FOURIER SERIES
When, in 1984, I begun to write my first programs for the calculation of
sundials I used a ZX SPECTRUM and the speed of calculation was very low
(more than 2000 times inferior to my actual PC). Therefore the precise
calculation of the Right Ascension (RA) ,of the Declination (Dec.) of the
Sun and of the Equation of Time (TEq) took too much time.
To reduce this time of calculation I have need of more fast procedures than
those standards and so I have thought to use the Fourier series of RA, Dec
and TEq.
For the same reason I have used, in the series, the mode Modulus-Phase
instead of that Sine-Cosine reducing in this way to the half the number of
the trigonometric functions to calculate.
Since then I use in my programs this method even if, with the speed of
calculation of today, the reason for which I begun to use them, has fallen.

THE FOURIER SERIES
A periodic function (that is a function that repeat itself equal after a
certain period T), given analytically can be developed as an infinite sum
of sine and cosine terms.
If we limit the number of the terms of the sum (harmonics) we have some
errors (differences between the exact values and the sums) : greater it is
the number of the considered terms smaller is the error.
If the function is not known but of it we know only a certain number R of
values (that it assumes in different instants) we can, with opportune
methods, to get a Fourier series truncated to the term R/2 (that is a sum
of Fourier of R/2 terms)
The Fourier s. may be written in two forms.
It forms sine-cosine
y = V0 +A1*Cos(wt) +B1*Sen(wt)+A2*Cos(2wt)+B2*Sen(2wt) + A3*Cos(3wt) +.

and the form Modulus-Phase 
y = V0 +M1*Cos(wt+F1) + M2*Cos(2wt+F2) + M3*Cos(3wt+F3) +...

where
w = 2*pigrec/T rad = 360/T degrees
V0 = mean value of the function in the period 
M  are the amplitude of the harmonics and F the phases (in rad or degrees)
The passage from one form to the other can be done applying the formula 
Cos(a+b)=Cos(a)*Cos(b)-Sen(a)*Sen(b)

THE CALCULATIONS
To get the Fourier series of the Equation of Time I have done in this way.
I have calculated, with great precision, for every day of the year (at
12h), the values of the TEq
I have repeated the calculation for 32 years (from 1990 to 2021) (I could
use any number of years but I have restricted the period to my life : I am
60 now).
I have calculated, for every day, the mean value finding in this way 365
values of the TEq .
With these values I have finally calculated the first 20 terms (20
harmonics) of the Fourier Sum that approach the mean Teq.

I have repeated the  procedure for the RA and for the Dec.


To make the calculations I have written a program in which I use, in the
first part, the algorithms of J.Meeus.

For the RA it is necessary to make the development only of the difference
between the RA and the mean anomaly of the Sun. For this to the results of
the development it is necessary to add the value:
Mean Anomaly = w*(t-Tequinox) where Tequinox is the instant of the Spring
Equinox 

THE RESULTS
I have used:
w = 360/Tropical year in days = 360/365.2421897=0.98564736 degrees / day
time = t = time from the beginning of the year to the midday 
If N is the progressive number of the day (1 for 1 January, 32 for 1
February etc.) we have:
t = N - 0.5
For the calculation of the RA I have used as instant of the Spring Equinox
the value 78.82215 (gotten by the mean course) 

The values of the coefficients (last calculation February 1998), rounded
off, are the followings:

Equation of Time  TEq
V0 = 0
M1 = 7.3670 minutes F1 = 86.33 degrees
M2 = 9.9182 minutes F2 = 110.97 degrees
M3 = 0.3060 minutes F3 = 105.12 degrees
M4 = 0.2027 minutes F4 = 130.65 degrees
M5 = 0.0008 minutes F5 = -73.40 degrees
M6 = 0.0069 minutes F6 = -98.81 degrees

Declination  Dec
V0 = 0.3838 degrees
M1 = 23.2623 degreesF1 = -169.390 degrees
M2 = 0.3552 degrees F2 = -174.537 degrees
M3 = 0.1342 degrees F3 = -146.899 degrees
M4 = 0.0326 degrees F4 = 4.904 degrees
M5 = 0.0358 degrees F5 = -5.565 degrees
M6 = 0.0324 degrees F6 = -6.757 degrees

Right Ascension RA
V0 = -1.9015 degrees
M1 = 1.8101 degrees F1 = -95.769 degrees
M2 = 2.4153 degrees F2 = -69.272 degrees
M3 = 0.0294 degrees