Date: Mon, 16 Mar 1998 20:20:23 EST
Subject: The day of the week, July 24, 1837

My question:
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!

Colleen (student)

Hi Coleen

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.

1. 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:
mM
30
43
55
61
73
86
92
104
110
122
135
141
2. 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'.)
3. The day of the week is d + M + Y (mod 7), where 0 means Monday, 1 means Tuesday, ... , 6 means Saturday.
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.

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.

Cheers
Chris

Go to Math Central

To return to the previous page use your browser's back button.