Current Pattern Math
In our Pisces and Gemini 1978 issues I presented the math necessary to erect a natal chart. I feel it is about time I presented the next step.
“Current patterns” is a general term covering a number of techniques. Transits, the simplest, require essentially no math—just look up where the planets are in a current ephemeris. Progressions and returns both involve calculations to determine what date and time to construct a chart for, followed by normal natal chart erection procedures. Directions are a completely different technique. In this issue I will only present a few basics of progressions and returns.
Progressions are systems for equating one cycle to another. The most widespread system, called Day-for-a-year or Major or Secondary, equates one day of motion of the planets and angles to one year of the life. Tertiary progressions equate one day of motion to one lunar month of life. Minor progressions equate one lunar month of motion to one year of life.
Return charts are charts erected for the exact moment some body returns to its natal position or returns to the position of some other body.
To begin with secondary progressions, a popular tool is something called the Calculated Date or Limiting Date or Adjusted Calculated Date (ACD). The ACD is that date in the current year on which progressed planetary positions read directly from an ephemeris without interpolation will be exact. Since we are equating a day in the ephemeris to a year of life, any time during the day must equate to a date in the year. Our starting point is our birth time on our birth day. One full day in the ephemeris and one full year of life will bring us to our time of birth on the next day in the ephemeris and our date of birth in the ongoing year. Interpolating planetary positions to the birth time will always get us progressed planetary positions for the birth day. If we read the planetary positions from the ephemeris without interpolation they will fall on some other calendar date (the same date every year)—that date is the ACD!
To get the ACD, remember the basic equation we are using (1 day = 1 year). From this we get: 24 hours = 12 months, 2 hours = 1 month, 120 minutes = 30 days (assuming standardized months), 4 minutes = 1 day. This series of correspondences allows us to convert time in the ephemeris to days and months elapsed in the life and vice versa. Since the ACD is the date corresponding to 0 or 12 hours UT (or ET for sticklers—it doesn’t matter for this technique), we need to convert the time difference between our Greenwich time of birth (Universal Time: UT) and 0 or 12 to a number of months and days. I will assume a midnight (0 hour) ephemeris for the rest of this article—the noon ACD will always be 6 months later. Since a midnight ephemeris is for 0 hours, the difference between that time and our UT of birth is the same as the UT of birth (time - 0 = time). Using the above equalities, every 2 hours becomes 1 month, and every 4 minutes of any time left over becomes one day. For me, 10:23 UT becomes 5 months and 6 days (rounding). This is the difference in months and days between the ACD and the birthday. To get the ACD subtract this from the Greenwich date of birth. For me, February 9 - 5 months 6 days = September 3 preceding my birthday. Because of the uneven lengths of the months and the idealization employed in this method, the ACD can occasionally be in error by 1 or 2 days. If you feel you must have it exactly right, convert the time entirely into days and use a table of days between dates to get the correct day (or count the days).
The ACD is very useful. You only have to calculate it once per chart, no matter how many years of progressions you do. It is the same day every year. If you are doing progressions for a long time period you can save yourself a lot of planetary interpolation by working from the ACD and reading positions straight from the ephemeris. If you are progressing for a specific date, the ACD is a better starting point than the birthday.
To do secondary progressions for a specific date, you need to interpolate the planetary positions to a specific time on the day you are looking at in the ephemeris. There is less chance for error working from the 0 hour base of the ACD than from the birth time base of your birthday. To get the time for interpolation, figure out how many months and days the date you want is after the most recent ACD (always go after the ACD to avoid confusion). Convert this into time using the equations given above, and the result is the UT to interpolate to. For me, December 25 is 3 months and 22 days after my ACD which equates to a UT of 7 hours and 28 minutes—progressions for Christmas will involve interpolating to 7:28 UT.
The above principles apply to any year. To know what day to look at in the ephemeris, just count VERY carefully. Positions for your time of birth on the day after birth are progressions for your first birthday, one day later for your second birthday, etc. Positions from the ephemeris for 0 hours on your day of birth are for the ACD before you were born, 0 hours on the day after birth gives the first ACD after birth, 0 hours the next day gives the ACD of the next year, etc. Just count day by day and year by year. For me, born February 9, 1955 at 10:23 UT with an ACD of September 3 preceding my birthday (for a midnight ephemeris), 0 UT February 9 = September 3, 1954, 0 UT February 10 = September 3, 1955, ..., 0 UT March 7, 1955 = September 3, 1980, etc.
Secondary progressions for any date are just a matter of counting days in the ephemeris to match years elapsed since birth and determining the time to interpolate to if you don’t want to read for the ACD. The date and time you use in the ephemeris are called the “derived” date and time (derived by equating a day to a year). Progressed angles are a more complicated problem than progressed planets, and I will discuss them in a later issue.
Returns are a simpler principle than progressions, but are often harder to do simply because they require a higher precision in calculations. To do a return, scan the current ephemeris for the most recent date the body was at the desired position. Using a reversal of standard planetary interpolation techniques, determine the time on that day the position was exact. For a solar return, you know you can look in the ephemeris around the birthday and be on target. For lunar and planetary returns, you have to scan the ephemeris. In fact, planetary returns are essentially wasted effort if done by hand, because positions are not printed to anywhere near the necessary precision in any ephemeris. High precision is needed in returns to get accurate angles. The average motion of the sun is 2.4 seconds of arc per minute of time, so an error of 1 minute of arc would produce an error of 24 minutes in the time of a solar return. Lunar returns are not quite as bad since the moon moves about 32 seconds of arc in a minute of time, but for both solar and lunar returns positions to the second of arc are preferred. Planetary returns are difficult because they require precision to thousandths of a second of arc.
To actually do the return after finding the day it occurs in the ephemeris, write down the positions on that day and the day after. Subtract the “this day” position from the desired position to get the “part of day” motion. Subtract the “this day” from the “next day” position to get the daily motion. Divide the part of day motion by the daily motion to get the fraction of a day elapsed up to the time of the return. Multiply this fraction by 24 to convert it to hours. This is the UT of the return. (I no longer make even token gestures to log tables—there is no excuse nowadays for not using a calculator.) For me, with a natal sun of 19 Aquarius 53 56, I can see in the 20th Century Ephemeris that next year’s return will be February 8, 1981. The this-day position is 19:8:33 and the next-day position is 20:9:19. This gives a partial motion of 19:53:56 - 19:8:33 = 0:45:23, a daily motion of 20:9:19 - 19:8:33 = 1:0:46, and a fraction of 0:45:23 / 1:0:46 = .7468459 which multiplied by 24 gives a UT of 17.9243 or 17:55:27. IMPORTANT NOTE: I have gone directly from position to UT in this example because I was using The American Ephemeris for the 20th Century. If you use an ephemeris in which positions are given for Ephemeris Time instead of Universal Time (almost all other ephemerides) you must correct the resulting time. Subtract the Delta T correction from the calculated time to get the UT.
There is a long standing argument by many proponents that returns should be corrected for precession. I will not go into that issue here, but suggest that anyone concerned read Jim Eshelman’s book on solar returns.
I have tried to keep the above discussion general enough for it to be clear that the return of a planet to its natal position is not the only kind of return. You can have “returns” of planets to the positions of other planets or other points (a 0 Aries “return” is another name for an Aries ingress). Sun on Moon and Moon on Sun are both used. You can also have a return of a planet to its own progressed position—a technique called a “kinetic return”. Kinetic solar and lunar returns are both possible by hand, but tedious—I suggest getting a computer to do it if at all possible (I don’t know if Neil Michelsen offers them yet).
The only way to correctly determine a kinetic return involves iterative or repetitious calculations. I will describe here how to do a kinetic solar return. First, determine what the derived date for a current progression will be. Calculate the UT that will get you a progression for THAT date in the current year. Using that date and UT, calculate the sun exactly. Calculate the moment in the current year that the sun returns to the progressed position you just calculated. Using the date and time of the return you just calculated, re-calculate your derived time and get a new progressed sun. Calculate the return for the new progressed sun. Keep calculating new progressions and returns until they stop changing each other. The progressions involved in kinetic returns are being carried to a very high precision, so the ACD and derived UTs should be calculated using exact counts of days rather than the easier months and days approximate method.
The same method is used to do kinetic lunar returns, except more iterations will usually be needed. Start by getting the current progressed moon. Find the most recent return to that position. Recalculate the progressed moon for that date and repeat to convergence.
You see why I prefer to let a computer do it?