These are just the basics – in order to keep the ecclesiastical Moon and Equinox reasonably aligned to the astronomical ones, periodic adjustments have to be made which make the actual calculation much more complicated (for a good look at how things get complicated fast, check out this article on the Cycle of Epacts, which will tax your appetite for minutiae like you wouldn't believe).

He's not kidding.

"Let us suppose that Easter is to be kept (as is at least implied by the British Act of Parliament regulating its date) on the Sunday after the astronomical full moon, and that this full moon, as sometimes happens, occurs just before midnight on Saturday evening in the western districts of London or New York. The full moon will therefore happen a little after midnight in the eastern districts, so that Easter, if regulated strictly by the paschal full moon, must be kept on one Sunday in the western and on the following Sunday in the eastern districts of the same city. Lest it be thought that this is carrying astronomical exactness to extremes, we may say that, if Easter were dependent on the astronomical moons, the feast could not always be kept on the same Sunday in England and America. Seeing, therefore, that astronomical accuracy must at some point give way to convenience and that an arbitrary decision on this point is necessary, the Church has drawn up a lunar calendar which maintains as close a relation with the astronomical moons as is practicable, and has decreed that Easter is to be kept on the Sunday after the fourteenth day of the paschal moon as indicated by this calendar."

In other words, if you want to see what science brutalized into the service of religion looks like, read on:

"In the year 1800, both the Lunar and Solar Equations (i.e. the addition and subtraction of 1) occur and no change of Epacts takes place. In 1900 the Solar Equation occurs and we must again subtract 1 from the Epacts. No change takes place in 2000 or in 2100, the former being a leap year and the latter having both equations. In 2200 and in 2300, we must again subtract 1, while in 2400, in which the Lunar Equation occurs and is not neutralized as usual by the Solar Equation, we add 1 to all the Epacts. The accompanying table [below] gives the Epact of every year from 1 B.C. to A.D. 3099.

Examples. (1) To find the Epact of the year 3097. Golden Number is 1, since (3097+1)÷19 = 163, with 1 as remainder. Epact corresponding to Golden Number 1 after 2900 is XXV; therefore the Epact of 3097 is XXV."

Long division and roman numerals, ladies and gentlemen.

Yes, it's true that the whole structure of astronomical mechanical complications – whether in the Strasbourg cathedral clock, or in watches like Caliber 89 – is a manifestation of a world view. That worldview – of an orderly clockwork universe, with tidy nests of ratios that can be encoded in gear trains – never really existed; the real universe is chaotic and probabilistic. But it is a beautiful vision, albeit it says more ultimately about how we would like the universe to be than how it actually is. There is a poignancy, whether intentional or not, in the fact that there is, at the very heart of the Caliber 89 – a monument to the dream of the music of the spheres – a mechanism that acknowledges that that beautiful dream is also an impossible one.

That's damn beautiful, actually.

Incidentally, those sotheby's auction catalogues are spectacular, particularly the "noteworthy timepieces" ones. I own three of them; they're generally available on that other auction site for pennies on the dollar.