Natal Math Revisited
It has been pointed out to me (by Jim Eshelman) that what I said about Ephemeris Time and ephemerides last issue was slightly in error. I said older ephemerides are for 0 or 12 hours Universal Time (since the term Ephemeris Time was only adopted in 1958). Jim pointed out that even though older ephemerides say they are set for Universal Time, they are actually for 0 or 12 hours Ephemeris Time.
As I have said before, Ephemeris time is more uniform than Universal Time. The procedures used in generating ephemerides, even the older ones, assume this more uniform time. Unless a special correction is made before computing positions, any ephemeris run for an even hour is using Ephemeris Time. To get an ephemeris for an even hour of Universal Time, you have to compute the positions for a time differing from that hour by the correction delta T. This was not done in the older ephemerides (delta T is only estimated a year or two in advance), so they are really for 0 or 12 hours Ephemeris Time. This means precisionists using such ephemerides should make the Ephemeris Time correction for planetary interpolations.
I also left out of the article last issue the procedures for getting the East Point and Vertex. The East Point, sometimes called the Equatorial Ascendant, is the Ascendant you would have had if you had been born on the equator. It can be obtained in any table of houses by a single (not double) interpolation.
If your table of houses includes 0° latitude, as does that in the American Ephemeris and Book of Tables, just look up (interpolate) the Ascendant for your natal sidereal time for 0° latitude.
For me, with a natal Sidereal Time of 12:14:5, the Ascendant at 0° is: 3 Cap 40 - 2 Cap 45 = 55’ * 0.5208 (ST fraction) = 29’ + 2 Cap 45 = 3 Cap 14.
If your table of houses does not include 0°, add six hours to your natal sidereal time and look up (interpolate) the Midheaven for this new time.
For me, this would be 12:14:5 + 6:0:0 = 18:14:5 ST. The Midheaven obtained is: 3 Cap 40 - 2 Cap 45 = 55’ * .5208 (ST fraction) = 29’ + 2 Cap 45 = 3 Cap 14.
The answer should be the same either way. That is your East Point.
The procedure for the Vertex is slightly more complicated. First, get the co-latitude of birth. The co-latitude is the natal latitude subtracted from 90°.
For me, the co-latitude = 90° - 32° 13’ = 57° 47’ North.
Next, add 12 hours to the natal sidereal time.
For me, that gives 12:14:5 + 12:0:0 = 24:14:5 = 0:14:5.
In the table of houses, look up (interpolate) the Ascendant at this new sidereal time at the co-latitude. That is the Vertex.
For me, that is:
Asc. 57° N = 4 Leo 9 - 3 Leo 29 = 40’ * .5208 = 21’ + 3 Leo 29 = 3 Leo 50.
Asc. 58° N = 5 Leo 5 - 4 Leo 26 = 39’ * .5208 = 20’ + 4 Leo 26 = 4 Leo 46.
Asc. at 57° 47’ N = 4 Leo 46 - 3 Leo 50 = 56’ * 0.7833 (47/60 Latitude fraction) = 44’ + 3 Leo 50 = 4 Leo 34 = Vertex.
A slightly different way of doing the same thing is to use the natal IC as a Midheaven in looking up the Ascendant at the co-latitude of birth. This gets one to the same result as adding 12 hours to the sidereal time but now we interpolate a fraction of Midheaven interval instead of sidereal time interval. This is actually easier in tables of houses that give cusps for every even degree on the Midheaven (such as Dalton’s).
The Vertex, on the west side of the chart, is like an extra Descendant. Dr. Dobyns prefers to put the Antivertex in the chart, which is like an extra Ascendant. The Antivertex is the same degree and minute as the Vertex and the opposite sign.
Since there are two ways to get the East Point it sometimes confuses people. Remember, it is the Ascendant of 0 latitude by the first method, and it is the Midheaven 6 hours of sidereal time later by the second.
If you look at or visualize a model of the celestial sphere, you can see the same point on the ecliptic become an Ascendant by going to 0° latitude and a Midheaven by rotating the sphere 6 hours (one quarter turn).
With the East Point and Antivertex now added to the planets and asteroids in your wheel, you have a pretty complete (even crowded) chart.