Thibaud Taudin-Chabot wrote "it is simple arithmetic: our watch shows mean time, so the mean of the correction should be 0, otherwise your watch is fast or slow after a year."
I thought just the same when I first saw the question - but then I thought again. I believe that the above condition means that the average length of the day (or hour, minute, second ...) shown by solar time must be the same as by the mean sun or corresponding clock. But you could declare solar noon today - at the meridian or allowing for the difference in longitude - to be at 12:02 or 11:57 or at any other time without affecting the going either of the sun or the clock. Therefore one can offset the EoT curve by a fixed amount with impunity in this respect. In fact this is exactly what we do by adopting a time at a longitude different from our own - or still more drastically by introducing daylight saving. I believe that the EoT curve IS chosen so that the average IS zero, which is the same as saying that if both its two sinusoidal components were reduced in amplitude to zero, then it would lie along the straight line of zero correction. This is entirely logical as if the magnitude were zero then it would make no sense to have a non-zero EoT. Adding up the two sine waves, at frequencies of 1/year and 2/year with their different zero cross points and amplitudes, quite naturally results in the curve we know with its particular crossing points. These dates are therefore not arbitrary but derive from the relationships of the phases (as they relate to our calendar) and the amplitudes of the two contributing components of its cause, the orbital eccentricity and the inclination. Andrew James 01 18 W 51 04 N
