As you know, primary directions refer to the applying aspect between two planets on the celestial sphere. The length of the direction arc is the number of degrees to the exact aspect, which determines the year when the event will occur.
This article will cover the method for calculating the direction arc in the Placidus house system. We will use a mundane position formula for the Placidus system that we derived earlier.
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Primary Direction Formula
Let's look at a familiar picture. The promittor $P$ approaches the significator $S$. When the mundane position of the promittor coincides with the mundane position of the significator (i.e., when the promittor reaches the green line of the significator's positions), the direction completes.
The path that point $P$ takes to intersect with the curve of the position of point $S$ is called the primary direction.
Let's return to formula $(2)$ of the mundane position. It is valid for both the promittor and the significator. In particular, when the promittor reaches the circle of positions of the significator, its mundane position coincides with the mundane position of the fixed significator $S$.
Therefore, we can write formula $(2)$ for the promittor, substituting the mundane position of the significator. Then, we will obtain the ecliptic coordinate of the point $P_\text{end}$, which denotes the end of the directional arc (see the figure above).
Here $MP_\text{S}$ is the mundane position of the significator, and $D_\text{P}$ is the declination of the promittor. Therefore, the right ascension of the end point of the directional arc is determined as follows:
The directional arc is the difference between the initial equatorial coordinate $RA_\text{P}$ of the promittor and the final equatorial coordinate of its end point $RA_\text{end}$.
It is the main formula for primary direction. It matches the formula for the Regiomontanus house system and is generally universal, as the reasoning is the same for any house system. Only the value of the mundane position changes depending on the chosen system.
In this formula:
- $(RA_\text{P}, D_\text{P})$ are the equatorial coordinates of the promittor,
- $MP_\text{S}$ is the mundane position of the significator, calculated using formulas $(2)$ and $(4)$ of the mundane position equations, and
- $\phi$ is the geographical latitude of the location.
Example
Let's consider Winston Churchill's horoscope in the case of primary directions in the Regiomontanus system.
Winston Churchill's horoscope
You can see that the Sun is the co-significator of his 10th house and simultaneously the natural ruler of fame and recognition. By its position, the Sun promises success in the native's social affairs, especially those related to Jupiter, as the Sun expresses itself through it, and Jupiter is responsible for high social status.
If we direct the Sun to the significator of the 10th house—Mercury—we should get the date of his remarkable social rise. Let's take the mundane position of Mercury in the Placidus system—233º 42', the coordinates of the Sun ($RA_\text{P}$ = 245º 56', $D_\text{P}$ = -21º 37'), and the birth latitude $\phi = +51.85º$ and substitute them into formula $(1)$ of this article.
We will get a directional arc of 24º 25'. It differs from the direction in the Regiomontanus system, which was 25º 37'. By multiplying this arc by the Naibod key (1.0147), we will get the number of years from birth to social rise. It is 24.78 years, or 24 years, nine months, and 12 days. If we add these years to the date of birth, we get September 1899. However, Churchill first became a Member of Parliament at the age of 25 in October 1900, and in the fall of 1899, he was captured in South Africa, which does not coincide with the indications of the directions.
At the same time, directions in the Regiomontanus system very accurately indicate the timing of actual events. It once again underlines the correctness of Morinus, who asserted that there is no more suitable house system for primary directions and predicting the timing of events than the Regiomontanus system.
