In a previous post, I introduced midpoints, the geometric bisection of a pair of planets or points in a horoscope. In the horoscope of Einstein, we studied the significance of the presence of Mercury at the Jupiter-Neptune midpoint, i.e. Mer=Jup/Nep. The midpoint is measured along the shorter arc between a pair of planets or points, and is called the **direct midpoint**. This same midpoint however is “reflected” at several other places in a horoscope, where it carries equal significance. These other places that carry the reflection of the direct mipoint are called **indirect midpoints**.

## Indirect midpoint by opposition

In Einstein’s chart, Ura=Mar/Sat, but Uranus is not on the direct Mars/Saturn midpoint:

You can see that the direct midpoint between Mars and Saturn is at 00 Pis 41. The **opposite** of that midpoint is a reflection, falling at 00 Vir 41. This is the indirect point that Uranus occupies with an orb of 35 minutes of arc. The effect of the reflected energy at this indirect midpoint is no different than at the direct midpoint, and should be considered equally valid. For Ura=Mar/Sat, Ebertin writes: “*Extraordinary and unusual powers of resistance, the ability to give as well as to take under provocation, the inclination to apply brute force*.”

## Indirect midpoint by square

The following chart shows Nep=Ura/Asc:

The direct midpoint Ura/Asc falls at 06 Leo 14. Its reflection, by **square**, falls at 06 Tau 14. Neptune is at this indirect midpoint within an orb of 1^{o}39′. Again, this indirect midpoint is not less effective than the direct midpoint, and should be treated with equal importance. Of Nep=Ura/Asc, Ebertin has this to say: “*The stage of suffering emotionally from the contact with restless people.*”

## Indirect midpoint by semisquare

Here’s another indirect midpoint picture, Plu=Nep/Mid:

The direct Nep/Mid midpoint falls at 09 Ari 58. If you add 45 degrees to it, you get 24 Tau 58. In the previous post, I wrote that for midpoints (and as it turns out also for transits of the outer planets, and solar arcs of all planets), the 45 degree semisquare aspect and the 135 degree sesquadrate aspects are as important as the major Ptolemaic aspects. So this reflection 45 degrees away is as important as the direct midpoint, and is occupied by Pluto to within 12 minutes of arc, an extremely tight orb. For Plu=Nep/Mid Ebertin says, “*The pursuit of peculiar objectives, supernatural experiences.*“

## Midpoint sort

Spotting midpoints by gazing at a chart is extremely tedious and error prone. Even just finding direct midpoints requires careful arithmetic, and when you think of all possible pairs, plus indirect midpoints, you know that you need help from the computer. Fortunately, all western astrological programs come with an option to show midpoints, through what is known as a midpoint sort. The following table, generated by my Lifespan program, shows what is called the **360-degree sort** on Einstein’s horoscope:

(In the header of the table, ignore the “Event” label. This is filled in if there is an event that is being overlaid on the midpoints sort, but in this case we are not looking to analyze an event.)

The 360-degree sort lists the direct midpoints between all pairs of planets and points, in ascending order of position around the zodiac from 0 degrees Aries to 30 degrees of Pisces. The bold entries are for the planets and points. If a planet or point lies within 2 degrees of orb before or after a midpoint, then you have a hit! In the first midpoint illustration on Einstein’s chart, we saw Mer=Jup/Nep. You can see it here at the very top of the sorted list which starts with Jup/Nep at 02 Ari 41, immediately followed by Mer at 03 Ari 09.

The second illustration showed Ura=Mar/Sat, an indirect midpoint by opposition. If you look for Ura in the 360-degree sort, you will find it at its natal position of 01 Vir 16. Of course, the Mar/Sat midpoint is nowhere near it. However, if you use what’s called the **180-degree sort**, you can spot the Ura=Mar/Sat midpoint right away:

The 180-degree sort folds the zodiac in two so the span is cut down to 0-180 degrees, from 0 Aries to 30 Virgo. Anything that was in Libra through Pisces of the natal chart will now be at its opposite point. Since the direct Mar/Sat was at 00 Pis 33, in the 180-degree sort it would show up as 00 Vir 33.

To see indirect midpoints by square, you will need to use the **90-degree sort**. The indirect midpoint by square configuration of Nep=Ura/Asc can be easily see in this sort:

This sort folds the zodiac, then folds it over again so in the end you only have a quarter of the original left, spanning 0 Aries through 30 Gemini. All natal positions that are in Taurus through Pisces are quartered. So for instance, the direct midpoint of Ura/Asc falls at 06 Leo 14, beyond Gemini. Folding it once (to get to the Aries-Virgo span) will keep it at Leo, but folding it again would place it 90 degrees earlier, at 06 Tau 14.

Lastly, for the indirect midpoints by semiquare, you will need to use the **45-degree sort**:

The 45-degree sort spans only 1/8 of the zodiac, going from 0 Aries to 15 Taurus. The direct midpoint Nep/Mid falls at 09 Ari 46. Pluto, which is at 24 Tau 46 natally, is folded down to 09 Ari 46 in the 45-degree sort, which brings it to within 12 minutes of arc of the Nep/Mid midpoint.

Since the direct and indirect midpoints are equally important, we would want to see all of them in the same table. And it turns out that the 45-degree sort by itself would give you all of them. This is because every time you fold, you preserve all the original midpoints, except some of them will be reflected to their indirect positions. And every time you fold, you add potentially new indirect midpoints that otherwise wouldn’t be seen.

In the next post, we will explore the midpoint tree, which gives us all the midpoints within orb of a chosen planet or point.