Dear Andrew, Thank you for your two messages, sent off-list but my response may be of trifling interest to others...
It is true that 128 tropical years is very close to 46751 days but when it comes to a real solar calendar (one you can look at and say "Oh, I see that today is 9 March") I regard this fact as a red herring. It is also very dubious long term. The simple question: "How many days are there in a tropical year?" has no useful answer beyond about three decimal places. The awkward fact is that neither the length of the year nor the length of the day is a constant. The length of the day changes in an especially horribly unpredictable manner which is why leap seconds are unpredictable. > I don't see where 36 fits in... This is a purely practical matter. If you sketch in my lines for, say, 12 noon on 1 March and 12 noon on 2 March each year for a number of years you will find that you are scribbling in two patches. The patches gradually fill in (unless you have a VERY sharp pencil) and expand. After 36 years you find that adjacent patches collide. They run into each other. In the region of overlap, you cannot tell whether the shadow refers to 1 March or 2 March. Your instrument is at the end of its design life and you have to redraw it for the next 36 years. Life becomes impossibly difficult around 2100 because of the omitted leap year then and the best thing you can do is redraw your instrument for the 36 years from 1 March 2103. My ghost will be lurking around to check that you get it right. > I also see that 33 tropical years is just > 11 and a bit minutes short of a whole number > (12053) of days. Is this connected? Yes. Now you are really getting somewhere and I am starting to salivate at the prospect of writing a juicy reply :-) > I seem to remember there are or were various > calendar proposals based on 33 year cycles... Yes. Such a calendar was devised by Omar Khayyam (and others) in 1079. This was and still would be an absolutely super calendar, MUCH better than the horrid muddle we have to live with! A 33-year cycle which includes 8 leap years would be perfect if the length of year was 365 plus 8/33 days and it jolly nearly is. You still get very long term drift and you cannot win against the unpredictability of the length of the day but, with such a calendar, my patches start colliding after more like 500 years rather than a miserable 36. Pope Gregory missed a trick. By 1582 the 33-year calendar had been known about for over 500 years. Moreover, Pope Gregory's Commission included Na'amat Allah an eastern patriarch who would certainly have known about the 33-year calendar. If I could do only one thing as Dictator Of The World it would be to introduce Omar Khayyam's calendar. Vote for me! All the best Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
