[syhprum (OP)]

I am always surprised how much faster the length of daylight changes between the equinoxes in mid April dawn appears to come rapidly much earlier day but come the end of June things steady down.
From my long gone schooldays I seem to remember something about d/dt am I on the right track?.

[David Cooper]

Your question looks as if it's been written while multitasking and then posted without reading it back, so it's hard to make full sense of it. At the equinoxes you get the fastest change and at the solstices you momentarily get no change other than that caused by the Earth's orbit not being quite circular. I would guess that it would follow a sine wave as you suggest, if you removed the eliptical orbit aspect.

[syhprum (OP)]

What I was trying to say was that the length of the daylight changes more rapidly  between the equinoxes than it does at the time of equinoxes   

[evan_au]

Does this visual calculator help answer the question?
Pick your lattitude using the slider, and it shows how the hours of the day vary throughout the year.
http://astro.unl.edu/classaction/animations/coordsmotion/daylighthoursexplorer.html

It does look like a sine/cosine thing (unless you pick a latitude inside the arctic/antarctic circles, where the days and nights can exceed 24 hours).
But like a sine/cosine, the length of day changes most rapidly when it is near the mid-line, which happens at the equinoxes (equinox=equal night & day).

[syhprum (OP)]

My post was somewhat muddled because I had just got back from a 20 hour Indianapolis to home trip I should of course spoken of solsticeses instead equinoxes

[David Cooper]

It's easy enough to get words like those switched with each other in that way even when you know them perfectly well - I would guess that the brain's always being reprogrammed as connections break and repeatedly have to be mended or fortified, and technical terms which you don't use day in day out do seem to be quite fragile.