
"It's weird  you know, I could swear it was a Sunday…" 
Yesterday was Sunday, and I was woken
early by the sun shining in the window and the birds (no respecters of late
night World Cupviewing schedules) making a racket. As I lay there, it occurred
to me that we are close to Waterloo day.
One thing about Waterloo which is
important (or seems so) is that it took place on a Sunday. Is there not a
reference to the priest at Plancenoit insisting on ringing the bells for
morning mass? Whatever, it was a Sunday – you will struggle to find any
description of the event which does not mention this.
This year 18^{th} June is a
Wednesday, and next year – the 200^{th} anniversary – will be a
Thursday. So, in my halfawake state, I reasoned that somehow or other I should
be able to reconcile the 4day slippage over two centuries. If I failed, there
was always the chance that I would drift off to sleep again, so how could I
lose?
Righto – concentrate, I told myself.
Your standard year is 365 days, which
is 52 weeks and 1 day, so that gives you a 1 day slip forward each year – and
then there’s leap years. OK – no problem – every 4^{th} year we get an
extra day, so on the face of it that’s 5 days forward every 4 years (or 2 days
back, if that’s easier – which it probably isn’t). Aha – snag. I was vaguely aware that something funny
happens at the end of each century – leap years aren’t so straightforward as
this. I realized that this wasn’t going to work until I’d done a
little selfeducation on the nippy question of what happens about extra days at
centuryend.
[This
is a common enough situation – I regularly find that unlocking the window latch
requires an expanding series of preliminary jobs until I have to move the entire house
four centimetres to the left before I start.]
Not to worry, I reasoned – let’s gloss
over the century issue for the time being, and see how far out I am. Then I can
check the details and balance everything up. At this stage I wasn’t going to
get back to sleep. OK – 100 years is 25 lots of 4 years, which (as I had
already decided) means a total slip forward of 25 x 5 days, which is 125 days,
which is 17 weeks 6 days, which is a slip forward of 6 days or a slip back of 1
day. That’s not too difficult, though the birds were putting me off a bit. This
means that my crude version of the leap year rule gives a backward slip of 2
days in 200 years, which would move the anniversary of our Sunday battle to
Friday.
Drat. We already know it’s going to be
a Thursday in 2015. I’ve lost a day somewhere – or have I gained a day? At this
point I decided
(a) it’s less confusing if I always
count the slippage forward
(b) I’d better get up and switch the
computer on. Not knowing what happens to leap years at the end of a century is
not too pressing a matter if it only affects us once every 100 years, but
clearly this is a gap in my toolbox.
First pseudocode rule I found was reasonably
simple, even at that time of the morning:
if year is not divisible by
4 then common year
else if year is not
divisible by 100 then leap year
else if year is not
divisible by 400 then common year
else leap year
But then I found that it isn’t as
simple as that – and we get into Gregorian and Julian calendars, and all sorts
of alternative calendars, some of which I have never heard of. I think that my
world conforms to the Revised Julian, and the full definition for this is:
The Revised Julian calendar adds
an extra day to February in years that are integer multiples of four, except
for years that are integer multiples of 100 that do not leave a remainder of
200 or 600 when divided by 900. This rule agrees with the rule for the
Gregorian calendar until 2799. The first year [in which] dates in the Revised
Julian calendar will not agree with those in the Gregorian calendar will be
2800, because it will be a leap year in the Gregorian calendar but not in the
Revised Julian calendar.
This rule gives an average year length of 365.242222
days. This is a very good approximation to the mean tropical year, but because the vernal
equinox year is slightly longer, the Revised Julian calendar does not do as
good a job as the Gregorian calendar of keeping the vernal equinox on or close
to March 21.
In fact, I believe these two versions both give the same answer
for this particular problem – i.e. 1900 was not a leap year, but 2000 was. So
let’s look at this again – 2 x 25 lots of 4 years, each 4 years giving us 5
days slip forward, is 250 days, which is 35 weeks 5 days, but in fact the year
1900 should not have been a leap year, so deduct 1 day, giving 35 weeks 4 days.
4 days forward from Sunday gets us to Thursday for the 200^{th}
anniversary, which is correct.
Thank goodness for that. Since there was no point in going back
to bed at this point, I got sidetracked into reading about exactly when
centuries end, and I leave you with the following statement from The Times of 26^{th} December
1799, which does not seem to invite further comment:
We have uniformly rejected all letters and declined all discussion
upon the question of when the present century ends, as it is one of the most
absurd that can engage the public attention, and we are astonished to find it
has been the subject of so much dispute, since it appears plain. The present
century will not terminate till January 1, 1801, unless it can be made out that
99 are 100... It is a silly, childish discussion, and only exposes the want of
brains of those who maintain a contrary opinion to that we have stated.