In the epoch of the whizz-machine one only needs to click a few buttons in a computer programme to generate a chart. This is tremendously convenient. It also has one side-effect. It is easy to forget the mathematics that underlie the chart.

A chart generally is a projection that simplifies navigation. In the case of an astrological chart it is a projection of a number of factors combined to give the best possible overview. It can in a sense be described as a planetary seal whose very 2-dimensionality provides a window to grasping both a complex astronomical as well as metaphysical reality. It is a navigation tool.

What is it a projection of? Here we need to look closer at the three-dimensional reality and must resort to spherical geometry. Have no fear! I am not going to present the theoretical geometry. Instead I will try to help you envision the geometry.

Place before your minds eye a transparent sphere. This sphere will represent the earth. Next imagine that this sphere is divided into two equal halves by a circular section. The section is the equator and the halves are the north and south hemisphere.

Next imagine another circular section that is perpendicular to the first. This section divides the sphere into an eastern and western hemisphere going thorough its north and south poles. Let us say that this particular section bisects a point that has been established, by convention, to be the starting point of 360 sections that equally bisect our imagined equator. This is the meridian that passes through Greenwich, England. All 360 equal sections are also called degrees of longitude. You still awake? Yes? See, it’s easy!

But what if we want to exactly pinpoint the position of Greenwich, which is a little more than halfway the distance from the equator to the North Pole? Here we have to imagine 90 increasingly smaller sections that are parallel to the equator. These are degrees of latitude. And so we can exactly define the position of any place on earth, not only Greenwich, (51N28 latitude, 0E00 longitude), with two coordinates. I won’t go into detail here, but the parallel of latitude also helps define the horizon.

But we are not finished yet. Let us take another position east of Greenwich, say Berlin which is roughly 13 degrees east of Greenwich and 52 degrees north of the equator. But why do we used the term degrees? Well, the distance from Berlin, let us call it point B, along the same meridian, to a point on the equator, let us call it E, is the arm of an angle that runs from B to the centre point of the earth and from there to point E. (Point E can be said to be a projection of point B onto the equator) This is a 52 degree angle. The 13 degrees of ~~latitude~~ longitude are also an angle between the projection of B on the equator and the projection of Greenwich to the equator. You can see here that our reference is always to the equator. This is important because this same principle is used elsewhere. We’ll get to that later.

Now these 360 degrees are special because they can also be converted to time. How’s that possible? Well if we imagine that our imaginary sphere rotates around its axis in one day then we can divide the 24 hours for one revolution into equal divisions of time. There is just one tiny catch, when applied to the earth the revolution is 4 minutes shorter than clock time. We speak of a sidereal time to make just that distinction. If you are calculating a chart the old-fashioned way, this will be one of the first conversions you will make. From clock time to sidereal time. This revolution of the earth around its axis in one day is also called primary movement and it is reflected in our chart by the houses, whose movement is also clockwise. Primary movement is also what underlies what is known as primary directions. (I’ll discuss these in a followup article). Up to here, with the aid of a Table of Houses we have the first set of calculations needed for our chart. We have an empty chart with the house divisions.

Now there are two other spheres that we consider in our calculations. These are the celestial sphere and also a sphere whose “equator” is formed by the path of the Sun in its yearly revolution around the earth. This is the ecliptic. The ecliptic is not divided into 24 hours but into 12 Celestial Signs of 30 degrees each. The beginning point for both the ecliptic and the celestial sphere is where the ecliptic crosses the celestial equator at 0 degrees Aries.

The celestial sphere shares the same equator as the terrestrial sphere. But instead of describing the position of a planet on the celestial sphere in terms of longitude and latitude we speak of right ascension and declination. The angle of projection of a planetary body to the celestial equator is the Declination. The angle on the celestial equator formed by this projected point to 0 degrees Aries is known as Right Ascension.

And now to the ecliptic. This can be considered as the equator of a sphere that is tilted roughly 23 degrees away from the terrestrial and celestial spheres. Now a planet’s position can also be defined in terms of the ecliptic. Here again we speak of a planet’s longitude and latitude. This is the second set of calculations needed to cast a chart. This is done with the aid of an ephemeris. This second set of calculations are for the secondary movement of the planets which is counter clockwise. Secondary Progressions are based on this movement of the planets. That is in fact the origin of the names for Primary Directions and Secondary Progressions.

There is just one last point to be made. When we calculate our planetary positions and place them in the chart, we reduce their three dimensional position to two dimensions. When I say a planet or a fixed star is at 29 degrees Leo I have projected its real position to the ecliptic. For example we read in our ephemeris that Mars and Jupiter are conjunct at 27 Gemini. If the sky is clear, and both planets do not have the same degree of latitude we will see that one is above the other. Astrologically we say that the planet with the higher latitude is stronger. What we are saying is that when we project their position in the celestial sphere to the ecliptic they both share the same ecliptic point.

Dear reader. If you could follow all of this then you should have no difficulty in understanding primary directions in particular and I haven’t mentioned such creatures as sin., cos., tan., cot., semi- diurnal or nocturnal arcs until now”! 🙂 You have been primed! You see the general confusion about directions is such that even most programmer’s of astrological software get them wrong and should the rare programmer get them right they are presented in an unusable form!*

*If you are a purveyor of astrological software please **do not** solicit your software here. You may of course send me a message in the “Reply” section provided at the bottom of the home page. If you are convinced that you have **the** primary directions programme then you may certainly send me a usuable demo version! 🙂 or :-(?

Good Morning Thomas,

great article, as usual 🙂

You seem to have an ability to explain difficult concepts plainly and simply. That is a rare gift these days. Much appreciated.

Have you seen this one, on a similar subject:

http://www.skyscript.co.uk/polar_oblique.html

I particularly liked the one called “It’s the Oblique Sphere, stupid!”

best wishes

Peter

Hello Peter!

Thank you. Yes I am familiar with the series. I also liked the “Oblique Sphere” article.

best wishes,

Thomas

Hi Thomas,

Very clean , , , surgical even.

Thanks for unbending these concepts and setting them

straight.

Sir Arthyr

Hi Arthyr!

You’re welcome. You see Dame Detrimentia mentioned a recent letter in which two Promissors’ stood at the door… And so I thought it might be a good idea to write something on primary directions so that Dame Detrimentia’s delectable prose would be understood – directly.

yours,

Thomas

Hi thomas,

I’m four years late to the party here. Noticing that in 7th paragraph the following sentence,…. The 13 degrees of latitude are also an angle between the projection of B on the equator and the projection of Greenwich to the equator,….. shouldn’t that be longitude as you are referring to Berlin as roughly 15 d east and 52 d n.

Just recently found your site and am devouring it. Thanks for your great work and mentoring.

Best

Francis Xavier

Hello Francis

Attentive readers are such a blessing. The correction has been made!

Thank you. 🙂