The hounds of spring

Not before time, the hounds of spring are on winter's traces. Today's been mild and sunny hereabouts - for the first time I've been able to just stand still stand outside without feeling cold or wet and actually feel some warmth in the sun. A day to throw open the windows and let some fresh air into the house (although discovering a long-dead mouse in the utility room and throwing it out probably did more for the sum total of household freshness). It's a month away from midwinter and there's a real feeling in the air that the seasons are turning.

All of which set me to brooding on something which I'd never quite got my head round - why is the rate of change in day length slowest around the midwinter and midsummer solstices? It's particularly noticeable if, like me, you're impatient to see a bit more daylight after the gloom of midwinter. I had some vague notions of why this might be so, but had never pinned it down. The other week, coincidentally, I was looking at a diagram describing how the amount current or voltage created by the spinning armature of an Alternating Current generator as it rotates through a magnetic field varies over time. It's a circular motion and the effect is described by a sine wave, with the rate of change constantly speeding up and slowing down. Thinking of day length, determined by circular motions, as changing in a similar unequal fashion due to trigonometry makes it a bit easier to understand. A further complication is that the rate of change of day length is asymmetric (i.e. the time of sunrise and of sunset do not change by equal amounts) - if you want to worry about that further variation, there's a fuller explanation here.

For the faint east quickens, the wan west shivers,
Round the feet of the day and the feet of the night.