This article will manually calculate a primary direction from the horoscope provided in the example of thematic forecasts. We will use only the formulas in this blog and a simple engineering calculator or Excel formulas.
[toc]
Which Direction We Will Calculate
We will calculate the direction of tR in s to the cusp of the 5th house. This direction, as we have seen, promises the native their firstborn.
Clarifying Venus' Coordinates
First, we will determine Venus's celestial latitude, which is its deviation up or down from the ecliptic. Not all computer programs display this information, so we will go to the astro.com website, in the "20th century" section, and choose the year 1926 in the "with declination and latitude" tables.
In the selected table, we find the row corresponding to April 21, the native's birthday. There, we will see that the celestial latitude of Venus is $\text{lat} = 0\text{n}5$. It means that Venus deviated by $0°5'$ to the northern part of the celestial sphere on that day.
Five arcminutes are $5/60$ or approximately $0.08$ degrees. Thus, the celestial latitude of Venus at the time of birth was $+0.08°$.
Celestial longitude is the zodiacal degree of Venus starting from 0° Aries. Venus is at 13°57' Pisces, which means it is almost 14 degrees from the beginning of Pisces, which is at 330° relative to 0° Aries. In other words, Venus is at 343°57' of the zodiac circle. Fifty-seven arcminutes is 57/60 or 0.95 degrees. Thus, Venus's longitude is 343.95° relative to 0° Aries.
Thus, Venus has the following equatorial coordinates:
Coordinates of Venus' Sextile
Our promittor is not Venus itself, but its sextile. Therefore, we need to find the coordinates of Venus's sextile on the Morinus aspect circle.
For the calculation, we will use the formula $(1)$ from the aspect circle. We know the coordinates $(\lambda_P, \delta_P)$ of Venus itself and the magnitude of the aspect—plus 60°. The only unknowns are the maximum deviation of Venus from the ecliptic on its current path $\delta_\text{max}$, and whether it is moving away from or towards its point of maximum deviation.
First, we find the maximum deviation of Venus $\delta_\text{max}$ on its path from the past to the nearest node. We will return to the ephemeris table for 1926, which we used earlier. This time, we will move forward from April 21 and observe Venus's latitude until we find the point where it crosses the ecliptic.
On the next day, April 22, Venus moves into the southern hemisphere. This is evident from its latitude on the next day—0s1, meaning 0 degrees 1 minute south. Thus, somewhere between April 21 and 22, Venus crosses the ecliptic, i.e., conjuncts its south node.
Great, we have found the end of Venus's path of interest. Now, we need to find its beginning. For this, we will return in time to see the moment Venus last crossed the ecliptic. This moment was on the night of December 31 to January 1 of the current year.
Now we scan Venus's entire path along the northern hemisphere—from January 1 to April 21—to find where Venus deviated most from the ecliptic to the north. The maximum elevation of Venus occurred on February 14, when its latitude was 8 degrees 21 minutes north. Since 21 minutes is 21/60 degrees, the maximum deviation of Venus can be recorded as $\delta_\text{max} = 8.35°.$
We also noted that Venus was at its elevation in the past, meaning it was moving away from its point of maximum elevation above the zodiac circle at the time of birth. Thus, we will use the coefficient $k = -1$ in formula $(1)$ of the aspect circle. The first line of the formula looks as follows:
N.B.: Please note that calculators typically work with radians instead of degrees.
Converting degrees to radians is straightforward. You divide the degrees by 180 and multiply by $\pi$. Here is an example of such a conversion:
To convert radians to degrees, we do the reverse—divide the number of radians by $\pi$ and multiply by 180. For example,
Therefore, when calculating $\sin 8.35°$ using a calculator, you need to input the number in radians, which is 0.1457 instead of 8.35.
I will use degrees for convenience in this article, as it is a more straightforward form of notation. However, when working with the calculator, you must input radians.
So, returning to our formula, we see that,
The result of calculating $\arcsin(0.00928)$ on the calculator is also presented in radians—this is $0.00928^\text{rad}$, which, when converted to degrees, means $0.53°$. Thus, $\lambda' = -59.47°$. Since our celestial latitude turned out to be negative, we need to add 360 degrees to it to make it positive.
Rule: If you get a negative value that should be within the interval from 0 to 360 degrees, add 360° to it.
So, we found that $\lambda' = 300.53°.$
Now, let's move on to the other two lines of formula $(1)$ from the circle of aspects:
Now we can calculate the ecliptic coordinates of Venus' aspect, namely:
We obtained a celestial latitude greater than 360 degrees.
Rule: if you get a value greater than 360 degrees, but it should be from 0 to 360 degrees, subtract 360° from it.
As a result, we get the ecliptic coordinates of Venus' sextile in Taurus in the Morinus aspect circle:
To calculate the further direction of Venus' sextile to the 5th house cusp, we need to express the coordinates of this sextile in the equatorial coordinate system.
Equatorial Coordinates of Venus' Sextile
To convert the ecliptic coordinates of Venus' sextile to equatorial, we will use formula $(1)$ from the transformation of spherical coordinates.
We already know the values of $\lambda$ and $\delta$ of our promittor; we only need the Earth's axial tilt angle, $\epsilon$, which is 23.45°.
Substituting $\lambda=43.68°$, $\delta=-7.19°$, and $\epsilon=23.45°$ into equation $(1)$, we get:
or
Rule: When dealing with the arctangent of the division of two numbers, you should use the ATAN2 function in the calculator or the Excel formula and substitute the numerator and denominator separately.
Now, we can express the obtained values in degrees.
These are the equatorial coordinates of Venus sextile—its right ascension $RA$ and declination $D$.
Oblique Ascension of the Ascendant
To calculate the mundane position of the significator, we will need the degree of the oblique ascension of the ascendant. The ascendant in this chart has a celestial latitude of 21°v24'. Since Capricorn starts at 270 degrees of the ecliptic, we can write that the celestial latitude of the ascendant is equal to 270° + 21° + 24/60° = 291.4°. By definition, the celestial longitude of the ascendant is zero since the cusp of the house is always in the ecliptic plane.
We need to convert the ecliptic coordinates of the ascendant—celestial latitude $\lambda=291.4°$ and celestial longitude $\delta=0°$—into equatorial coordinates. To do this, we will again use the familiar equation $(1)$ of the conversion of spherical coordinates.
or
Converting radians to degrees, we obtain $RA = -66.86°$ and $D = -21.745°$. To eliminate the negative value of the right ascension, as usual, we will add 360 degrees:
These are the ascendant's equatorial coordinates. Knowing these coordinates, one can easily find the ascendant's oblique ascension. To do this, we will use the formula $(2)$ to calculate the oblique ascension. In this formula, we only need to consider the geographical coordinates of the city where the native was born.
The geographical coordinate of birth is 51° N 30'—the native was born 51 degrees and 30 minutes north of the equator. For northern latitudes, we traditionally use the "plus" sign. Therefore, the geographical latitude $\phi$ is (51 + 30/60)° with the "plus" sign, or $+51.5°$.
Now we can use the mentioned formula $(2)$ of calculating the oblique ascension:
or
We have found the oblique ascension of the ascendant. Now, we can calculate the mundane position of the significator.
Mundane Position of the Significator
The significator is the cusp of the 5th house. Therefore, we will use the formula $(4)$ of mundane positions calculation.
We obtain a value of 443.23°, which exceeds 360°. Therefore, we subtract 360 from the obtained value. As a result, the mundane position of the 5th house cusp is 83.23°.
Arc Length of the Primary Direction
Now, we can move on to calculating the arc length of the primary direction. To do this, we will use formula (1) of the arc of the direction calculations.
We will substitute the following values into this formula:
Then we obtain the following arc length:
As usual, we add 360° to the arc to eliminate the negative value. As a result, we obtain a direction arc of 325.93°. However, there's a problem—this direction arc is greater than 180 degrees, and each degree roughly corresponds to one year of life. People don't live that long. We must find the shorter distance between the Venus sextile and the 5th house cusp.
As some ancient astrologers did, we cannot rotate the sphere in the opposite direction to obtain a +34.06° arc. This approach is meaningless—the sphere only rotates forward.
We will use the converse direction method as Morinus transmitted it. Specifically, we will temporarily consider the Venus sextile as a fixed point and direct the moving degree of the 5th house cusp towards the Venus sextile. Then, we will find a shorter path between the significator and the promittor.
Converse Direction
To use reverse direction, we need to change the promittor to the significator in formula (1) of the direction arc calculations, namely, substitute the following values:
- $(RA_P, D_P)$—equatorial coordinates of the 5th house cusp
- $MP_S$—mundane position of the Venus sextile
These values will need to be recalculated.
Equatorial Coordinates of the Vertex of the 5th House
The 5th house cusp has the following ecliptic coordinates:
- Celestial longitude $\lambda$: 10°d09' or 10° + 60° + 9/60° = 70.15°.
- Celestial latitude $\delta$: 0°.
Substituting them into formula $(1)$ of conversion of spherical coordinates, we obtain the equatorial coordinates of the 5th house cusp:
Mundane Position of the Venus Sextile
Now we will calculate the mundane position of the fixed Venus sextile using formula $(2)$ of calculation of the mundane position, substituting into it the equatorial coordinates of the Venus sextile:
Arc of the Converse Direction
Now we can substitute the found values into formula $(1)$ of calculation of the arc of direction:
This time, we obtained a positive arc length in the reverse direction without turning the celestial sphere backward. One degree of the arc of primary direction corresponds to approximately one year of life. Let's examine the difference we obtained:
- If we had rotated the celestial sphere backward to solve the issue of reverse direction, we would have obtained an arc length of 34 degrees, corresponding to approximately 34 years of life.
- However, following Morinus's method and simply exchanging the promittor and significator, we get a completely different arc—21 degrees. The difference is a whole decade.
Let's verify the accuracy of the calculations according to Morinus's method in practice.
Verification of Obtained Results
To convert the arc of direction into years of life, we need to use the Naibod key, which is to multiply the arc of direction by 1.0147.
We find that 21.38° corresponds to 21.69 years of life or 21 years, eight months, and approximately eight days. Adding this period to the date of birth, we get the year 1947, December 30th.
As I've already noted, the direction of the promittor to the 5th house cusp (at least in female charts) more often indicates the time of conception rather than the birth of the child. Therefore, we can confidently add another nine months to this date. Then, we get the expected time of the child's birth in the autumn of 1948, around September-October. Indeed, the firstborn was born that autumn, November 14, 1948.
If we had followed the old method and rotated the sphere in the reverse direction when calculating converse directions, we would have arrived at a different date—August 1961. But in that year, the native did not have any children.
This example again underscores the genius of Morinus, who significantly improved the apparatus of primary directions in astrology.
