Mathematical_Recreations-Kraitchik-2e

110 Mathematical Recreations
year just 365 days and making every fourth year a leap year
of 366 days. The Julian calendar spread abroad with other
important features of Roman culture, and was generally used
until 1582.
The Julian year was a little too long, and by 1582 the ac'
cumulated error amounted to 10 days. A second reform,
instituted by Pope Gregory XIII, compensated for the error
and required that for the future the last year of each century
should not be a leap year unless the number of the century
were divisible by 4. Thus, 1700, 1800, 1900, 2100,· .. are
not leap years, but 2000 is.
Gauss gave a formula for finding the day of the week corresponding
to a given date. This formula is:
W 55 D+ M + C+ Y (modulo 7),
where W is the day of the week (starting with Sunday = 1),
D is the day of the month, and M, C, and Yare numbers depending
on the month, the century and the year, respectively.
The values of M, C, and Yare given in the tables
on page 111.
In determining the value of Y, the number of the year
must be diminished by one if the month is January or
February.
Many tables and mechanisms have been devised to solve
this problem. We shall give two of the simplest, which are
nomograms.
The first is shown in Figure 17.
To find the day of the week corresponding to a given date,
on Figure 17, proceed as follows:
1. Write the given date as a set of four numbers - the
day of the month (called the Date in the first scale of the
nomogram), the month (third scale), the first two numbers
of the year (called the Century in the fourth scale), and the
last two numbers of the year (called the Year in the first