Hi Frank,I agree with your comments. I also cheated (a bit!). Knowing the answer and the range of possible assumptions for initial conditions and year lengths, I chose values to support the premise. The assumptions are reasonable considering what Dee knew at the time. Reality is different.
I prepared some supplementary slides to respond to questions like these. They are now posted at the same website http://www3.telus.net/public/rtbailey/GodsLongitude/ as "GodsLongSupp.ppt". One I have saved as the attached gif. This uses Meeus Algorithm for the vernal equinox to show how God's Longitude is changing with time. I expect that Luke used the same equation at www.gcstudio.com . This fourth order algorithm gives the average VE year but does not account for short term variations like nutation. That takes about 28 more terms in the algorithm.
Regards, Roger----- Original Message ----- From: "Frank King" <[EMAIL PROTECTED]>
To: "Roger Bailey" <[EMAIL PROTECTED]>Cc: "Sundial Mailing List (E-mail)" <[EMAIL PROTECTED]>; "Simon Cassidy" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Saturday, September 29, 2007 12:38 PM Subject: Re: God's Longitude and the Lost Colony of Virginia
Dear Roger, God's Longitude is indeed a fascinating topic. An intriguing side-issue is that an almost arbitrary 33-year run of the Gregorian Calendar shares an essential property of the Omar Khayyam Calendar: the date of the Vernal Equinox (or any other declination) is confined to a period of 24 hours. This means you can set up a sundial (at ANY longitude) that will show the date unambiguously for 33 years. The Paternoster Square noon mark on the new London Stock Exchange implements this idea down to and including showing 29 February. Of course it is not too satisfactory near the solstices because the declination changes too slowly but I really have put at least a scratch for every one of the 366 days of the year! It is good luck that whoever settled on 29 February as leap-year day chose a date close to an equinox when the declination is changing rapidly. YOUR PRESENTATION I greatly enjoyed looking at your slides. There were some lovely illustrations and it all seems great fun. I have one trifling comment... This refers to the slide which shows a blob diagram for 77 degrees west over the period 1579 to 2095 using the Omar Khayyam Calendar. This isn't quite right! You state that you use 1582 as the base year and take the instant of the vernal equinox that year as: 1582-03-21 23:58:10 UT Subject to the 10- or 11-day shift this is correct and the time is just before midnight UT of course. Given that, and using the Omar Khayyam Calendar, your blob diagram is confined to just UNDER 24 hours. The extreme times of day for the Vernal Equinox in the period you chose are respectively in 1587 (the latest time of day) and in 2078 (the earliest). In fact, using the Omar Khayyam Calendar, these extremes are just OVER 24 hours apart... The actual UT times of the vernal equinox in those extreme years are: 1587: 05:17:12 2078: 05:13:07 The dates are not shown because we are free to choose our own calendar but, using the Omar Khayyam Calendar, the first is 24h 4m 5s later than the second. When you shift westwards by the appropriate amount, the latest time will just be in the "next" day and the earliest time will just be in the "previous" day. The equivalent diagram that I showed in Cambridge DID span more than 24 hours but I didn't draw attention to this! Also I cheated (a bit!) by having a blob-diameter which was sufficiently large that it disguised the fact that the diagram spanned more than 24 hours! If we stick with your extremes, the compromise longitude is 5h 15m 9.5s west of Greenwich. [I take the average of 5:17:12 and 5:13:07.] This shifts us to 78 deg 47' 22.5" west which is a little further than we would like to fit the story! John Dee would not have access to www.gcstudio.com (where I got my data above) and would not be able to produce as precise a blob diagram as we can today. Moreover he probably didn't look as far ahead as 2078! LONG-TERM DRIFT The truth is that God's longitude is drifting very slowly eastwards but, even today, we can predict the rate of progress with only limited precision... The real problem is that the length of the day is changing unpredictably (which is why leap seconds are not published many years ahead) and if you don't know the length of the day you cannot say by what fraction of a day the year exceeds 365 days! What we can be sure of is that for the period 500 years either side of where we are now, this fraction averages a lot closer to 8/33 days (the Omar Khayyam value) than it does to 97/400 days (Pope Gregory's value).I would like to thank Frank King for the inspiration, Simon Cassidy for doing the historical research and uncovering the secret agenda...This is kind of you but Simon Cassidy was MY inspiration and I count myself only as a communicator!! Very best wishes Frank
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