NOTE ON THE CALENDAR.
What every one learns from the almanac, over and above Easter and its consequences for the current year, is that what happens this year is no index at all to what will happen next year. And even those who preserve their almanacs, and compare them in long series, never have been able, so far as I know, to lay hands upon any law connecting the Easters of different years, without having had recourse to the very complicated law on which the whole calendar is constructed.
Nevertheless there does exist a simple relation which reduces the uncertainty in the proportion of five to two; so that by means of one past almanac, we may name two Sundays, one or the other of which must be Easter Sunday. I have never seen this relation noticed, though I have read much (for these days) on the calendar: has any one of your readers ever met with it?
Let us make a cycle of the days on which Easter day can fall, so that when we come to the last (April 25), we begin again at the first (March 22). Thus, six days in advance of April 23, comes March 25; seven days behind March 24, comes April 21.
The following is the rule, after which come two cases of exception:—
Take any year which is not leap year, then, by passing over eleven years, we either leave Easter day unaltered, or throw it back a week; and it is nearly three to one that we have to leave it unaltered. Thus 1941 is not leap year, and eleven years more give 1952; both have April 13 for Easter day; but of 1943 and 1954, the first gives April 25, the second April 18.
Take any year which is leap year, then, by passing over eleven years, we either throw Easter one day forward, or six days back; and it is about three to two that it will be thrown forward. Thus 1852 (leap year) gives April 11, but 1863 gives April 5.
But when, in passing over eleven years, we pass over 1700, 1800, or any Gregorian omission of leap year, the common year takes the rule just described for leap year; while, if we begin with leap year, the passage over eleven years throws Easter two days forward, or five days back. There is another class of single exceptions, occurring at long intervals, which it is hardly worth while to examine. The only case which occurs between 1582 and 2000, is when the first year is 1970.
Any number of instances may be taken from my Book of Almanacs, and the general rule may be easily seen to belong also to the old style. Those who understand the construction of the calendar will very easily find the explanation of the whole.
A. DE MORGAN.