# Page:Popular Science Monthly Volume 18.djvu/784

As every common year consists of fifty-two weeks and one day, supposing the 1st of January of any year to fall upon Sunday, A will be the Sunday letter for that year. The last day of that year will also be Sunday, and Monday will be the 1st of January of next year; and, as A is always affixed to the first day of the year, G will become the Sunday letter for that year. The next year will begin with Tuesday, which will make its Sunday letter F, etc.; hence, if there were no leap-year, the Sunday letter of each succeeding year would be removed one letter further backward, and in seven years the cycle would be complete, and the Sunday letter of the eighth year would again be A. But, as every leap-year has fifty-two weeks and two days, the letter C, which always belongs to the 28th of February, is also affixed to the 29th, which puts the Sunday letter for the remainder of the year one letter further back. Leap-year has therefore two Sunday letters instead of one, as in common years. This change takes place every four years; the other, as we have seen, would take place in seven years. Hence a complete cycle of the Sunday letter consists of the multiple of seven and four ${\displaystyle =}$ twenty-eight years; i. e., in any given century, the Sunday letters will again follow each other in exactly the same order every twenty-eight years.