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Ken Ward's Astrology PagesAstrology: Calculating the Ascendant. 

The ascendant is the sign on the Eastern horizon when the
birth occurred. On this page, we will use Mary as an example. Mary was born 7 May 1982 at 11 hours 17 minutes AM, New Berlin, New York, USA. The longitude is 75 degrees, 20 minutes west of Greenwich. And the latitude is 42 degrees 37 minutes North of the equator. We have already calculated Mary's sidereal time of birth, so all we have to do is to look in the tables of houses to find the ascendant. Mary's sidereal time of birth is:
The tables depend of the latitude of birth, so we need to look at the tables for the nearest latitude to Mary's place of birth. The American Ephemeris 1931 to 1980 contains tables of houses which we can use. There are, of course, many other sources. The tables are organized in terms of time, each time 4 minutes different from the previous, and in terms of latitude, each latitude 1 degree different from the previous. You can look at the tables and pick the nearest ascendant. As the time is nearer 1 hours 16, you can choose to look at the table for 1 hours 16. As the latitude is nearer to 43 than to 42, you can choose to take the value from the tables for latitude 43. The result from the tables is 5le19. The correct answer (5le9) can be computed. Accurate Computation of the Ascendant (Advanced)To explain the principle here, I am using the table below, which has simple numbers to illustrate the procedure. Remember these are not real ascendants, etc. Let us also imagine that the native was born at 1 hour 18 minutes sidereal time, and at a latitude of 42.5 degrees. These are some imaginary figures:
First the native was born at 42.5 degrees, which is half way between the two values we have above. That is half way between 4 and 6. So the mean ascendant at 42.5 latitude and at 1 hour 16 minutes is 5. Similarly, the mean latitude at 1 hour 20 minutes is the mean value of 8 and 10, which is 9. So we have the two mean ascendants at the two times These ascendants are 5 and 9. These are the ascendants at 42.5 for the two times above. To find the actual ascendant we need to find the average of these two values, which is 7. So our imaginary ascendant is 7. Let's look at the real example of Mary.
As before we want to find the mean ascendant at 1 hour 16 minutes to begin with. In this case, Mary was born 37 arcminutes after the first latitude of 42 degress. The two latitudes above differ by 60 arcminutes. So the factor for Mary is 37/60 or 0.6167. The difference between the two ascendants (4le47 and 5le19) is 32 arcminutes. We multiply this by the factor by the difference:
We add this to the lower latitude's ascendant (4le47) so:
We do the same for the second time. In this case we have 5le34 and 6le5. The difference is:
Multiplying this by the same factor as before (0.6167) we get
So we get the ascendant at the higher time as:
Mary was born (sidereal time) 1 hour 16 minutes 13 seconds. The difference in the two times is 4 minutes or 240 seconds. The proportion is 13/240, or 0.05417. The difference between the two mean ascendants (5le7 and 5le53) is 46 arcminutes. The amount to add to the lower value is:
So we add this to the lower value:
The table below is just my notes on computing these values on a spreadsheet.
