The Julian and Gregorian calendars are frequently represented by the abbreviations O. S. and N. S., old style, new style, and as the older historical dates are usually expressed in O. S., it is sometimes convenient to transform a date from the one calendar to the other. This is readily done by the formula
G = J + (N - 2) - N/4,
where G and J are the respective dates, N is the number of the century, and the remainder is to be neglected in the division by 4. For September 3, 1752, O. S., we have
| G | = | Sept. 14 |
| J | = | Sept. 3 |
| N - 2 | = | + 15 |
| - N/4 | = | - 4 |
and September 14 is the date fixed by act of Parliament to correspond to September 3, 1752, O. S. Columbus discovered America on October 12, 1492, O. S. What is the corresponding date in the Gregorian calendar?
62. The day of the week.—A problem similar to the above but more complicated consists in finding the day of the week on which any given date of the Gregorian calendar falls—e. g., October 21, 1492.
The formula for this case is
7q + r = Y + D + (Y - 1)/4 - (Y - 1)/100 + (Y - 1)/400
where Y denotes the given year, D the number of the day (date) in that year, and q and r are respectively the quotient and the remainder obtained by dividing the second member of the equation by 7. If r = 1 the date falls on Sunday, etc., and if r = 0 the day is Saturday. For the example suggested above we have