A comment by Simon Cassidy about the future accuracy of calendars, (whether solar or lunar). There is very little point in trying to predict the future values of the real year and real month (in real days) with such authoritative looking and precise formulae as you (Peter) are using. There is no generally accepted theory of how the Earth's rotation changes and what mechanisms might be governing it. (Giordano Bruno would have loved this. He claimed Earth is a sentient animal just like us, with free-will in these matters.) Moreover, even if mechanisms are discoverable, they will be academic in the near future since it is becoming clear that human activities (which are presumably subject to free-will!) are beginning to exert a significant effect on the Earth's rotation. These human activities are now known to include the artificial greenhouse effect which is melting the Antarctic ice cap, and dam-building, both of which tend to slow the rotation by redistributing large masses of water closer to the equator. There is not even complete consensus in the field about whether it is impossible for the Earth's rotation (at the surface) to increase! For an excellent survey of this problem (but not an "orthodox" one) based on exhaustive consideration of historical astronomical data see R.R. Newton, "The Moon's Acceleration", 2 vols., 1984.