But first of all, for the mathematically minded, I shall summarise what we know of each age. The Second Age is the simplest – it consists of exactly 3441 years. Leap-years occurred every fourth year, except at the end of a century. At the end of each millennium there was what we might call a double-leap-year, i.e. the year had 367 days in it. Tolkien doesn’t state this in so many words, but we know it must be true because he tells us that the millennial deficit of the calendar against the astronomical year was 4 hours, 46 minutes, and 40 seconds. Since, as can be calculated, one millennium on his calendar totalled 365,242 days (including the double-leap-year), and one thousand astronomical years add up to 365,242.2 days, that extra 0.2 of a day is very close indeed to Tolkien’s stated deficit. The upshot of all this is that the entire Second Age lasted for 1,256,797 days. The Third Age is slightly more complex, but not inordinately so. The basic rules were exactly the same, except that they were tampered with a number of times. Two extra days were arbitrarily added to the year 2059, making it a double-leap-year, and one extra day was added to 2360, which also therefore became a double-leap-year (it was already a leap-year of course). On the other hand, the year 3000 was not a double-leap-year (nor even an ordinary leap-year), because the authorities neglected to add the two extra days. The only other thing we have to take into account is that the Third Age was terminated, in Gondor, part of the way though the year 3021 – after just 85 days of it in fact, or just under three months. Although the official start of the Fourth Age was delayed in other parts of Middle-earth, we are following Gondor here, the seat of the kings. The complete total for the Third Age therefore turns out to be 1,103,117 days.