The "Equation of Time" is weird... Since the summer solstice is also (coincidentally) near the earth's aphelion, this means that our orbital speed is low, which causes the apparent solar day to be a little *shorter*.
(When orbital speed is high, the earth has to turn just a teense more to "catch up" with the sun. On the other hand, if orbital speed was zero, then the solar day would equal the synodic day...for as long as it took for us to fall into the sun and burn to a crisp...)
So, you have two conflicting influences: the seasonal influence, which maximizes at the solstice, and the orbital influence, which maximizes at aphelion. As the two contend, I can easily see that there might be two (or more?) days when the sum of the forces is maximized.
Silas
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