This is not the ideal medium, because what you really want is a picture. It shows two circles, in the planes of the ecliptic and the equator, and intersecting at points representing the equinoxes. Got that? OK, now put the earth in the middle and the sun on the ecliptic circle at some point other than an equinox or a solstice. (Don't you just love putting the earth in the middle!) The angle, measured along the ecliptic circle, between the spring solstice and the sun is the solar longitude, which increases at a uniform rate through the year. Now, drop a perpendicular from the sun onto the plane of the equator and draw the line from the earth, through this, to the equator circle. The angle the sun has moved along the equator circle since the spring equinox is called the Hour Angle. It is this angle that we use in sundials, in conjunction with the earth's own rotation, to measure time. But, as you can see, it increases slower than the solar longitude between equinox and solstice, and faster between solstice and equinox. If you can't see it, try putting the sun very near the spring equinox. Drop that perpendicular (remember, the two circles' planes are at 23.4 degrees), and see that the distance along the equator is less than the distance along the ecliptic.
Voila! I have written a paper, which I intend to submit to the BSS Bulletin for publication, in which I describe a simple geometrical construction, suitable for any sundial with equi-spaced hour lines, which produces this equation of time angle for any date. I have another, even simpler, construction for the other component of the equation of time: that due to the eccentricity of our orbit. Jointly, they allow a sundial to show mean time. Hope this is clear Chris
