The evenings, as they say, are drawing in. But it is not an optical illusion, nor a psychological effect induced by the return to school or work, that the rate at which the days grow shorter seems to accelerate with each passing week. That, in fact, is just what happens in the early autumn.
After the summer solstice, the time of sunset advances a little every day. The change is very gradual at first, the sunset on a date in mid-July, for example, being only a few minutes earlier than it may have been a week before.
As the months progress, however, the gap from week to week becomes much wider, until by mid-September sunset becomes earlier by about 17 minutes every week. Then the rate of advance begins to ease again, and the change from week to week is very gentle as we approach the winter solstice in December. What it means, in simple terms, is that during the second and third weeks of September the evenings shorten more rapidly than at any other time throughout the autumn.
But in late October every year, the evenings shorten with a sudden lurch, for reasons of custom and alleged convenience rather than any law of nature or astronomy. Tonight, as I am sure you will remember, we must put our clocks back by an hour.
Have you ever wondered why it should be by precisely this amount of time? The hour, in fact, is an entirely arbitrary unit, in contrast to the day, the month and the year, all of which have astronomical connections. But the 60-minute hour appears to have no connection whatsoever with the natural world.
The origins of the 24-hour day, and any reasons for the choice of this particular number, are lost in the mists of time. We do know, however, that even after the number 24 became established, all the hours were not of equal length: the two daily periods of light and darkness were each divided into 12 equal parts called temporal hours, an arrangement with the inconvenient consequence that the length of an hour varied from day to night, and also with the changing seasons.
The man credited with reforming this very awkward system of unequal hours was the 13th-century Arabian mathematician Abul Hassan. With what in retrospect seems more like common sense than genius, he suggested that an hour should be a fixed period based on "a twelfth part of the daylight at the equinoxes when the day and night are of equal length". And so, more or less, it has remained until this very day.