Dear Steve, Michael, Werner and Fabio have provided some excellent responses to your question.
If you are ONLY interested in relating three ANGLES - solar longitude, solar declination and the obliquity - then this relationship is indeed all you need: sin(lambda).sin(obliquity) = sin(declination) Importantly, the cusps (starts) of the 12 Zodiacal months are DEFINED as being at 30-degree intervals round the ecliptic. If you wish to use one-third months, then using 10=degree intervals is the right thing to do. [ASIDE: I deliberately overlook numerous little details such as 12x30 not being quite 360 degrees because the sun doesn't QUITE get back to where it started, but you can usually ignore that unless you want to discuss fine details with Werner :-)] As every diallist knows, equal angles do not generally translate into equal intervals of time. The sun doesn't travel round the ecliptic at a uniform speed. Fabio's ring illustrates this beautifully BUT Fabio's French Republican Calendar also tells you about this, not just on the inside front cover but also... By looking at the information provided for each day, you can do some simple investigation as to how the lengths of the Zodiacal months vary... At the moment we are in Vintagarious, the first month, and you will see that each day has the symbol for Aries. Next month is Fogarious and you will see that each day has the symbol for Scorpio. The following month is Frostaious and you will see that each day has the symbol for Sagittarius. This seems too good to be true. Seemingly the 30-day months are precisely in sync with the Zodiacal months. Sadly this isn't quite the case because... The following month is Snowous and only the first 29 days shows the symbol for Capricorn. We are at our closest to the sun here and actually cover more than one degree a day. You will see Day 30 shows the symbol for Aquarius. The Calendar is running one day slow! Here is a table of the crude end-of-month errors in days slow (-) and days fast (+): Vintagearious 0 Fogarious 0 Frostarious 0 Snowous -1 Rainous -1 Windous -1 Buddal -1 Floweral 0 Meadowal +2 Reapidor +3 Heatidory +4 Fruitidor +5 I find it astonishing that it is only in the last four months that we end the month more than a day fast or slow. Of course we end the 12-month period five days early which is why the calendar ends with five (or six) Complementary Days. This is a nice simple way of showing that the angular rate of change in solar longitude doesn't vary very much! I find that the more I live with this Calendar the more it grows on me :-) You will find this too! Very best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
