How was the time of equinox measured in ancient times? In the book "The Crime of Claudius Ptolemy" by Robert Newton, on page 81, it reads as follows:


  When we measure the time of a solstice, we measure the time when the
  meridian elevation angle of the sun has an extreme value, a maximum in
  the summer, and a minimum in the winter.... When we measure the time
  of an equinox, on the other hand, we measure the time when the
  meridian elevation takes on a specified value.


What does he mean by a "specified value". What specified value?

Also, how would the ancients have determined the time of the maximum, or the specified value? Time devices in ancient Greece, like water clocks, I suppose would have significant errors. Would they just start the water clock when the sun rose, then marked its level when the "specified value" occurred? That method would seem to have a lot of error.
The "specified value" would be the latitude of the observer, and would be the average of the maximum and minimum values observed at the solstice.

The altitude of the sun above the horizon is measured when it is due South. This is what "meridian elevation" means. So no clock is required. However this method can at best determine the date of the equinox. Precise observations over several years could be combined to obtain an time of equinox.

The position of the sun above the horizon can be simply determined by measuring the length of a shadow. However Ptolemy had access to astrolabes and quadrants for more accurate measurement of the sun's position.