Date: Mon, 16 Mar 1998 20:20:23 EST|
Subject: The day of the week, July 24, 1837
What day of the week (Mon. Tues. Wed. etc...) was July 24th, 1837?
I think the level of the question is secondary.
Thank you to anyone who can answer this question!
The easiest way to find the day of the week is to consult a perpetual calendar; these can be found in reference books such as encyclopedias and almanacs. My Canadian World Almanac tells me that July 24, 1837 was a Monday.
There is a formula for the day of the week, but it is complicated by the irregular month-length of our calendar, by the leap-year rule, and by the convention that the extra day in a leap year comes on February 29.
To find the day of the week in the GREGORIAN (= our) calendar
for day = d, in month = m, in year = y, IN THIS CENTURY OR THE NEXT (between March 1, 1900 and February 28, 2100), compute the numbers M and Y as follows.
To modify the formula for use in other centuries (because three out of four century years are not leap years -- the rule is that a year divisible by 100 is a leap year exactly when it is divisible by 400), add 1 for 1800s (i.e. March 1, 1800 through Feb. 28 1900). add 2 for 1700s
add 3 for dates from October 15, 1582 (which was the first day of our (=Gregorian) calendar) through Feb. 28, 1700.
- We agree (because leap years have an extra day at the end of February) to let January and February be the be the 13th and 14th months of the year y - 1. Thus m runs from 3 (=March) to 14 (= Feb.). Define
M = 2m + [3(m+1)/5] - 1 (mod 7), where [3(m+1)/5] means the the whole number of times 5 goes into the product 3(m+1). If you don't like this formula, you can compute the 12 values of M once and for all:
- Y = y' + [y'/4] where y' = y when m is a number from 3 to 12 and y' = y-1 for m = 13, 14. (As before, [y'/4] means the whole number of times 4 goes into y'.)
- The day of the week is
d + M + Y (mod 7), where 0 means Monday, 1 means Tuesday, ... , 6 means Saturday.
subtract 1 for the 2100s,
subtract 2 for the 2200s
subtract 3 for the 2300s and 2400s.
EXAMPLE: For July 24, 1837, d=24, m=7, and y=1837. M=3 and Y= 1837 + [1837/4] = 3 + 459 = 3 + 4 = 0 (mod 7). Remembering to add 1 for the 1800s, date = 24 + 3 + 0 + 1 = 0 (mod 7), so MONDAY.