Equinox refers to a time when the length of the night is approximately equal to the length of the day as measured from sunrise to sunset.

Equi-umbra refers to a time when the length of the horizontal shadow of a vertical object is equal to its height.

Equi-umbra thus refers to the time when the angle (altitude) of the sun is equal to 45 degrees.

Each day the sun rises to its highest altitude at Midday.

Midday (Solar Noon or Transit) in the Northern hemisphere, North of the Tropic of Cancer, is when the sun is exactly due south .In the Southern hemisphere below the Tropic of Capricorn it is when the sun is due North.
NB. Midday (Solar Noon or Transit) rarely occurs exactly at 12.00 noon local time, but at some time before or after depending on the location and the time of year (see later).

The altitude of the sun at Midday depends on the time of year and the latitude of the location.

At Midsummer (the summer solstice) the sun at Midday is at its highest altitude of the year.

At Midwinter (the winter solstice) the sun at Midday is at its lowest altitude of the year.

In some parts of the world (within most of the Arctic and Antarctic circles) the sun never reaches 45 degrees at Midday at any time of the year, even Midsummer.

In contrast, even in Midwinter, in most of the area between the Tropic of Cancer and the Tropic of Capricorn the sun is never less than 45 degrees at Midday.

In the rest of the world the altitude of the sun is higher than 45 degrees for a certain length of time during the summer.
In this region, as with Equinoxes, there are two Equiumbra days in a year> - one before the summer solstice - Spring Equi-umbra and one after, Autumn Equi-umbra. Like Equinoxes the dates of Equiumbra at a particular location are around the same each year, occasionally varying by a day, depending on the particular year and the latitude and longitude of the location.

Unlike for Eqinoxes, the dates of Equiumbra are strongly dependent on the latitude of the particular location.

The exact dates of Equiumbra are specific for a particular local location.

Spring Equi-umbra in a particular localation is the first day after Midwinter when the length at Midday of the horizontal shadow of a vertical object is equal, or very slighly less, than its vertical height.

On this day, the VERTICAL ANGLE (ALTITUDE) of the sun at Midday when it is exactly South, is equal, or more, than 45 degrees, whereas on the day before it was less than 45 degrees.

Autumn or Autumnal Equi-umbra is the last day of the year after Midsummer when the altitude of the sun at Midday is equal or more than 45 degrees. The following day it is less than 45 degrees and the shadows of vertical objects at Midday again begin to become longer than their vertical heights

In the Northern Hemisphere, Midsummer falls around June 20 and Midwinter around 20 December. In the Southern hemisphere it is the reverse.

Thus in the Northern Hemisphere the date of Spring Equiumbra in most cases occurs in the months January to June and the Autumn Equiumbra in the months July to December. In the Southern Hemisphere it is again the reverse.

For example:

Miami Florida	Spring Equi-umbra	January 24	Autumn Equi-umbra	November 17
Washington DC	Spring Equi-umbra	March 5	Autumn Equi-umbra	October 8
Anchorage Alaska	Spring Equi-umbra	May 4	Autumn Equi-umbra	August 7
La Quiaca Argentina	Spring Equi-umbra	July 3	Autumn Equi-umbra	June 9
Buenos Aires	Spring Equi-umbra	August 25	Autumn Equi-umbra	Abril 16
Ushuaia	Spring Equi-umbra	October 18	Autumn-Equi-umbra	February 22

What / When are Morning Equi-umbra and Afternoon Equi-umbra ?

On each day between the Spring and Autumn Equi-umbra there are two moments, one before Midday (Morning Equi-umbra) and one after Midday (Afternoon Equi-umbra) when the Altitude of the Sun is 45 degrees and the length of the horizontal shadow of an object is equal to its vertical height.

The times of Morning and Afternoon Equi-umbra vary strongly with the date and the latitude and longitude of the place.

The intervals of time betwen the Equiumbra and Midday (Solar Noon or Transit) are equal.

For example:

From: United States Naval Observatory (USNO)

N 38-53 W 77-02    Washington DC    2009 July 4

	Time (EST)	Altitude
Sunrise	04.50	0.0
Morning Equi-umbra	08.54	45.1
Midday (Noon / Transit)	12.13	73.9
Afternoon Equi-umbra	15.31	45.1
Sunset	19.35	0.0

S 34-30 W 58-20     Buenos Aires     2010 January 01

	Time (h.mins UT/GMT)	Altitude
Sunrise	08.46	0.0
Morning Equi-umbra	12.36	45.0
Midday(Noon / Transit)	15.57	78.5
Afternoon Equi-umbra	19.17	45.1
Sunset	23.08	0.0