This can be a disheartening time of year. Summer's lease, as Shakespeare said, hath all too short a date, or as the poet John Clare, with more prolixity, expressed it:
Summer's pleasures they are
gone, like to visions every one,
And the cloudy days of autumn and of winter cometh on.
And to make matters worse, the evenings, as they say, are "drawing in".
Our perception that the rate at which the days grow shorter seems to accelerate with the advent of September is not an optical illusion. Nor is it a psychological effect induced by the return to school or work. Unlike so many other areas of life, that which seems to be is, in fact, exactly what is happening.
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. But as the months progress, 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 fact, is that during the second half of September the evenings shorten more rapidly than at any other time throughout the autumn.
But there is another sense in which September days are short. The 24hour day by which our lives is regulated is based on the average length of time between two consecutive transits of the Sun across the same meridian - if you like, the average length of time from noon to noon.
But this interval is not exactly constant: the length of the "solar day", as it is called, varies rhythmically throughout the year - one of the reasons being the fact that the Earth moves slightly faster in its orbit at certain times, when it is closer to the Sun, than it does at others.
The solar day is at its longest around Christmas, at about 24 hours and 30 seconds. It gradually shortens until late March, when it is only 23 hours 59 minutes and 41 seconds long, and then the solar day lengthens to reach 24 hours and 13 seconds by mid-June.
During the following three months the day shortens again, and the very shortest day of the year, a mere 23 hours, 59 minutes and 38 seconds in length, occurs on or about September 17th.