E. S. Burns

“ It had been discovered that the lunar year was eleven days shorter than the solar year; so that, if a new moon occurred upon any given day of any solar year, on the same day of the next solar year the moon would be eleven days old, on the same day of the second year twenty-two days old, etc. Examination showed that the new moon would again occur upon the same day of the solar year in the course of nineteen years. Hence the lunar cycle consists of nineteen years. The other ancient cycles are unimportant for our present purpose ”

“ Several of the ancient cycles were, however, used by the early Church in fixing what are called the "movable feasts"; these being regulated not by the solar year, as Christmas or the 4th of July is, but by the lunar year. But, as most of these feasts depend upon or are regulated by Easter, we need consider this one only. In the early days the churches of Asia kept their Easter upon the day on which the Jews celebrated their passover, i. e., on the fourteenth day of their first month, which began with the new moon next after the vernal equinox. ”

“ After the Julian calendar had been used several centuries, the improved state of astronomy disclosed the fact that computed time did not keep pace with actual time, because the year did not consist of three hundred and sixty-five days and six hours but was about eleven minutes ten seconds less. Hence, by inserting an extra day for leap year, we gain upon true time forty-four minutes, forty seconds, which makes an error of a day in about one hundred and thirty-one years ”

“ Calling this one hundredth year a common year gives a gain of one day, or 24 hours, which puts computed time ahead of actual time, 24-18·6 5·4 hours, which, in 400 years, equals 21·6 hours, gain. Calling the four hundredth a leap-year brings back computed time 24 21·6 2·4 hours behind real time. To lose a whole day at this rate will require 10 400 4,000 years. ”

“ The advanced state of astronomical science and the experience of those who have gone before us have enabled us to reduce all that pertains to this subject to so complete a system that we lose sight of its magnitude and importance; we forget the slow progress and toilsome research which the great minds of past centuries had to undergo to reach the present state of correctness. ”

“ To appreciate even faintly this magnitude, we must transport ourselves backward a few thousand years, and forget, if we can, the improvements of modern astronomy, the developments of mathematics, and, above all, the universality and ubiquity of modern almanacs. ”

“ 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 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. ”

“ Upon the same principle the dominical letter for the years of any other century can be found. But, as the number to be deducted for centurial years, not leap-years (equal 14) , is an exact multiple of 7, the remainder will be the same whether it is deducted or not, and hence no account need be made of it, for it is by the remainder and not by the quotient that the Sunday letter is fixed. ”