Lewis Carroll devised a mechanism to work out the day of the week given a particular date and was published in Science in 1887. Here is a PHP function that works out the day of the week given the date that uses the same mechanism that Lewis Carroll devised. The mechanism isn't very complicated, but rather than explain it twice I have just put a lot of comments in the code to indicate what is happening.

```
function dayOfWeek($date)
{
$total = 0;
$date = explode('/', $date);
if ( $date[0] <= 1752 ) {
// if the date is prior to 1752 then subtract the centry from 18
$centry = substr($date[0], 0, 2);
$total = (18 - $centry);
} else {
// otherwise do it this way
// extract Centry
$centry = substr($date[0], 0, 2);
// divide by 4 - take remainder by 3 multiply by 2
$total = ((3 - ($centry%4)) * 2);
}
// if total is more than seven then divide by 7 and take remainder
if ( $total > 7 ) {
$total = $total % 7;
}
// extract year
$year = $date[0] % 100;
// divide by 12, add this to remainder, add number of 4's in the remainder
$year = (((int)($year/12)) + ($year%12) + ((int)(($year%12)/4)));
// add the year to the total
$total = $centry + $year;
// if total is more than seven then divide by 7 and take remainder
if ( $total >= 7 ) {
$total = $total % 7;
}
// extract month
$month = $date[1];
// pick month from table
$monthTable = array(0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5);
$month = $monthTable[(int)$month - 1];
// add month to total
$total = $total + $month;
// extract day
$day = $date[2];
// if the year is a leap year, and the month is January or February then minus 1.
if ( $date[0]%4==0 ) {
if ( $date[0]%100 == 0 ) {
if ( $date[0]%400 == 0 ) {
if ( $date[1] == 1 || $date[1] == 2 ) {
$day = $day - 1;
}
}
} else {
if ( $date[1] == 1 || $date[1] == 2 ) {
$day = $day-1;
}
}
}
// add to total
$total = $total + $day;
// if total is more than seven then divide by 7 and take remainder
if ( $total >= 7 ) {
$total = $total % 7;
}
// convert day number into day
$days = array('Sunday', 'Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday');
return $days[$total];
}
```

Use the function by giving it a date in the format of YYYY/MM/DD. Here are a couple of examples.

```
echo dayOfWeek('1979/07/13');
echo ' ';
echo dayOfWeek('2008/05/12');
echo ' ';
echo dayOfWeek('1640/02/06');
```

Prints out:`Wednesday Monday Thursday`

The month table is taken from an example page by the University of Sydney. This page is also useful if you want to know how the algorithm works in detail.

Note that if the date is prior to 1752 then you need to subtract the number by 18. This is because the Gregorian calendar was modified in 1752 by dropping the days between September 3 and 13. However, not all countries participated in this update.