Sunday, 1 March 2015

The Ascendant in Polar Latitudes - Reverse and Direct

The ascendant seems to behave unpredictably in polar regions, i.e., in areas above the arctic circle and below the antarctic circle. The ascendant seems to leap around, from one edge of the horizon to the other, and is sometimes direct and sometimes 'retrograde'. Some degrees never rise, and consequently can never set; some degrees never set, and consequently can never rise. However, the behaviour of the ascendant in polar latitudes is quite predictable and follows an understandable course.

The following description applies to all polar latitudes. However, as one travels north (in the northern arctic circle) fewer and fewer degrees rise and set in the conventional sense (i.e., in the manner that is observable in sub-polar latitudes). I will look at the situation at 70 North, which is around 3 1/2 degrees north of the arctic circle. At this latitude the two signs around the summer and winter solstices don't rise and set. The summer signs, Gemini and Cancer, remain above the horizon (i.e. are circumpolar and never set). The winter signs, Sagittarius and Capricorn, remain below the horizon and never rise.

It is worth bearing in mind that the phenomena associated with circumpolar and sub-horizon signs in the polar regions are related to the astrological concept of antiscia. Antiscia are pairs of degrees that fall equidistant from the winter and summer solstices. So the first circumpolar degree at any particular latitude (i.e., the first degree that doesn't set at the latitude), is the antiscion of the final circumpolar degree at that latitude. Degrees between the two antisicia are ones that remain above the horizon. A similar explanation may be given for sub-horizon signs in polar regions.

The following data is taken from a table of RAMC (right ascension of the MC) in Alan Leo's Casting the Horoscope. This book forms one part of Alan Leo's classic instructional textbooks for astrologers. Leo's tables give the RAMC for every latitude from the equator to 70 North. The ascendant for each latitude and RAMC can be read from the table. The RAMC for a given latitude also shows the MC.

The tables show that when the RAMC is 237 degs 03 mins (15 hours 48 mins and 12 secs) 29 Scorpio 15 is on the midheaven. This degree in Scorpio is the last degree to join the meridian before the phenomenon of sub-horizon midheavens occurs. At this time 29 Scorpio 15 also forms the ascendant. At polar latitudes, twice a day, the ascendant and MC will conjunct on the horizon due south of the observer. This is the first instance of the ascendant and MC conjoining. (See 1. in the image below.)

Leo's tables also show that the last degree to rise at 70 North (i.e., before the circumpolar zone of the zodiac) is 29 Taurus 15 - at RAMC 237 degs 03 mins (sidereal - 15 hours 48 mins and 12 secs). What is to be made of this? What the tables are illustrating is that at the moment the ascendant conjoins the MC due south at RAMC 237 degs 03 mins, the opposite degree in Taurus immediately begins to rise due north. At the same time the last degree of Scorpio becomes the descendant and begins to set. It is often said that the ascendant has 'flipped'. However, it is more accurate to say that the rising degree has passed from the final degree of Scorpio to the final degree of Taurus. This 'handover' occurs because of the way that the ecliptic moves in relation to the horizon in polar latitudes. (See 2. in the image below.)

What happens now is even more unusual, at least when compared to the principles of astrology in tropical and temperate regions. The ascendant degree begins to move along the eastern half of the horizon in a 'retrograde' fashion, with the later degrees in a sign rising before the earlier degrees. So, for example, 25 Taurus, in polar latitudes above 70 north, will rise before 20 Taurus, and this degree rises before 10 Taurus and so on. However, the degrees will rise in an orderly fashion, with each degree rising in sequence, but in reverse order to that observed in sub-polar latitudes. Notice that signs will also follow each other over the horizon in reverse order, with Taurus rising before Aries, Aries before Pisces and so on. To clarify this point, consider that in tropical and temperate zones the degree to rise after 29 Taurus would be 00 Gemini. However, in this example from the polar zone, 28 Taurus rises after 29 Taurus, and this is followed by 27 Taurus.

This phenomenon occurs because the ecliptic lies close to the plane of the horizon in polar latitudes. This means that rather than rising at a large angle to the horizon, the ecliptic appears to be 'peeled away' from the horizon, from the north point of the horizon to its south point. This is most noticeable when the ascendant is in reverse in the sense that I have described it here. The other notable feature of this retrograde ascendant is that the 'twelfth house' is below the horizon and the 'first house' is above the horizon. This is quite different to most astrological house systems in tropical and temperate regions where the twelfth house is above the horizon and the first is yet to rise (in the sense that is it has appeared above the horizon). The implications of this will be considered in a later article, looking at house systems in polar regions.

The ascendant now moves rapidly along the eastern half of the horizon towards the point due south of the observer. At times, around ten degrees of the ecliptic can rise in less than eight minutes (the first decan of Aries at 70 North). When the rising degree reaches the antisicion of 29 Scorpio 15 - 00 Aquarius 45 - the ascendant is again conjunct the MC. The midheaven, in the time that it has taken the ascendant to travel backwards from 29 Taurus 15 to 00 Aquarius 45, has travelled from 29 Scorpio 15 to 00 Aquarius 45. (See 3. in the image below.) This occurs at RAMC 302 degs 57 mins (sidereal - 20 hours 11 mins and 48 secs). In total the ascendant has been rising in reverse for 4 hours 23 mins 36 secs and has covered nearly half the zodiac.

At this point, the rising degree is immediately handed to 00 Leo 45 - due north of the observer. (See 4. in the image below.) From this point, until 29 Scorpio 15 again becomes the ascendant and MC conjointly due south of the observer, the ascendant will rise in the way that it does in sub-polar regions, with earlier degrees in a sign rising before later degrees. The order of the signs will also be preserved, with Leo rising before Virgo, etc. During the time that the ascendant moves from 00 Leo 45 to 29 Scorpio 15 the midheaven moves methodically (at the rate of one degree every four minutes) through the rest of the zodiac from 00 Aquarius 45 to 29 Scorpio 15. It 'chases' the slowly rising ascendant, eventually 'catching' the rising degree in the last degree of Scorpio. The movement of the ascendant from 00 Leo 45 to 29 Scorpio 15 takes 19 hours 36 mins 24 secs. The polar ascendant cycle then repeats during the next diurnal phase. All midheavens between 00 Aquarius 45 and 29 Scorpio 15 will be formed above the horizon, in the way that the MC is observed in tropical and temperate latitudes.

The following diagram summaries the movement of the ascendant and midheaven at the polar latitude of 70 degrees north. The cycle begins at 1. and concludes at 4. before returning to 1. for a further diurnal cycle.



Figure 1. The Ascendant and Midheaven at 70 Degrees North

In short, the minimum zenith distances of midheavens formed in Sagittarius and Capricorn at this latitude will be greater than ninety degrees (sub-horizon), whilst the minimum zenith distances of midheavens formed in the rest of the zodiac will be less than ninety degrees (above horizon). There are two midheavens at this latitude - 29 Scorpio 15 and 00 Aquarius 45 - where the zenith distance will be precisely ninety degrees (on the horizon) when the ascendant conjoins the MC at the sidereal times identified above.

Please note that the combined rising times for the retrograde and direct ascendants at 70 north is 24 hours, even though around 120 degrees of the zodiac (Sagittarius, Capricorn, Gemini and Cancer) will not rise (i.e., have a zenith distance of precisely ninety degrees) during the course of a day. A midheaven will be formed at all 360 degrees of the zodiac over the course of 24 hours. However, just over sixty degrees of the zodiac (Sagittarius, Capricorn) will form an MC below the horizon.

This article is the third part of a series of pieces exploring the ascendant, midheaven and houses in polar regions. Readers are directed to preliminary blog entries on the definition of the midheaven and ascendant using the concept of zenith distance.

The Definition of the Midheaven

The Definition of the Ascendant


Tuesday, 17 February 2015

February 2015 New Moon

The February 2015 new moon is an interesting one. It falls in the very last few minutes of tropical Aquarius. The new moon is at the midpoint of transiting Uranus and Pluto, which are in the final throes of their seven-time square.

One of the most interesting aspects of this new moon is its opposition to the fixed star Regulus. This star made a sign change in late 2011, moving from its two thousand year journey through tropical Leo to begin a two thousand year passage through tropical Virgo.

Dane Rudhyar and others have speculated that this sign change for the star associated with the Heart of the Lion (Leo) marks the beginning of the Age of Aquarius. This is because the star falls exactly 150 degrees from the Vernal Equinox.

Therefore when Regulus changes sign in the tropical zodiac, the vernal equinox (the First Point of Aries) changes sign in the sidereal zodiac, in this case from sidereal Pisces to sidereal Aquarius (assuming a sidereal zodiac of twelve signs of thirty degrees each).

Regulus is the stellar king, being one of the brightest stars in the sky, but also the brightest star lying closest to the ecliptic. This makes it a natural fiducial star, one that might be used to measure the passage of ages.

The following chart shows the new moon for 18 February 2015, set for Exeter. Interestingly, the opposition Sun-Regulus occurs more or less exactly as the star culminates at this longitude.


Figure 1: February 2015 New Moon (opposite Regulus)

In the latter part of 2015, Jupiter will conjunct Regulus as it enters Virgo. This may mark a major turning point in some of the issues that currently beset the world, including conflicts in Ukraine, the Middle East, and North Africa.

One interpretation of the movement of Regulus into Virgo is that much of the world's current attachment to monotheistic religion may wane. It will be worth watching the transit of Jupiter to Regulus to see if this bears out.

Sunday, 15 February 2015

The Definition of the Ascendant

The ascendant is the fundamental angle of the horoscope. It is one of the features of the horoscope that has endured over millenia and has been central to astrological practice since classical times. The ascendant first appeared as an astrological feature in classical Greek horoscopes around 200 BCE (Avelar and Ribeiro, p. 5).

Astrologers will often define the ascendant as the point of the ecliptic on the eastern horizon at the time and place of birth. This is a reasonably good definition and is found in reliable textbooks. For example, in The Revised Waite's Compendium of Natal Astrology, the ascendant is defined as the point of the ecliptic which cuts the eastern horizon (Candlish, p. 20). In this textbook it is noted that the ascendant varies according to the time and place (i.e., latitude) of birth.

Robert Hand provides two useful and more precise definitions of the point in his essay on the ascendant, midheaven and vertex in extreme latitudes (for reference see below). Hand's first definition is that the ascendant may be the point of intersection of the rational horizon and ecliptic in the east (i.e., the eastern node). His second definition is that the ascendant may be the ascending node of the ecliptic upon the rational horizon. (Hand, p. 132)

Hand introduces an important refinement in both definitions. He makes it clear that the horizon used by astrologers when identifying the ascendant is the rational horizon rather than the visible or apparent horizon. The visible horizon is the horizon available to the observer at the time and place for which the chart is cast. This is a small circle engirding the place lying parallel to the rational horizon. (Mayo, p. 15-16) The rational horizon is a great circle defined by points at a distance of ninety degrees from the zenith, the point immediately above the observer on the celestial sphere. (Mitton, p. 191)

This definition of the rational horizon uses the concept of zenith distance. The definition of zenith distance is taken from Mitton's Dictionary of Astronomy. Zenith distance is "the angular distance from the zenith to a point on the celestial sphere, measured along a great circle." (Mitton, p. 416) The great circles in the example of the rational horizon will run through the zenith and nadir.

In the following image, the horizontal frame of reference is shown, with the rational horizon being the green plane running through the east, north, west and south points. The red arrows running from the zenith to the rational horizon illustrate the zenith distance of ninety degrees that defines this plane.


Figure 1: The Celestial Sphere (Horizontal Frame of Reference)

In a previous blog entry I used the concept of zenith distance to define the midheaven. The midheaven or MC is the degree of the ecliptic that has attained its minimum zenith distance during a diurnal cycle, irrespective of its direction in relation to an observer or its height in relation to the horizon. (http://www.exeterastrologygroup.org.uk/2015/01/the-definition-of-midheaven_18.html) In this second article, I would like to explore the possibility of defining the ascendant in astrology using the same terms and conditions as that adduced for the midheaven.

In this case, the ascendant ought to be defined without reference to direction (east) or according to above and below (the ascending node option). In this second instance, the ascendant would be defined as the point of intersection between the ecliptic and the rational horizon where the ecliptic moves above the reference plane (the rational horizon).

To define the ascendant using the same terms and conditions as that used for the midheaven, we have to limit ourselves to reference to zenith distance. I wish to suggest that a definition of the ascendant using this concept is that it is the point on the ecliptic that has a zenith distance of ninety degrees but has not yet attained its minimum zenith distance during the diurnal cycle. The two criteria - zenith distance, not yet attained its MZD - are necessary to distinguish the ascendant from the descendant. The latter also has a zenith distance of ninety degrees. The distinguishing feature of the descendant is that it is the point on the ecliptic with this zenith distance that has already attained its minimum zenith distance during the diurnal cycle.

How does this definition work. Firstly, the specification of the zenith distance ensures that the ecliptic degree coincides with a point on rational horizon, i.e., both points have a zenith distance of ninety degrees. This is in fact what the ascendant is - the intersection or coincidence of the two planes: the ecliptic and rational horizon. Secondly, the rising degree - or ascendant - is moving from its intersection with the rational horizon towards its intersection with the meridian when it will attain its minimum zenith distance during the day (it will be at is closest approach to the zenith).

The descendant is the point opposite the ascendant, exactly fulfilling the condition of having a zenith distance of ninety degrees (again coincident with a point on the horizon) but having attained its MZD earlier in the day, i.e., it is now setting.

In this definition of the ascendant, the application of direction (east) or concepts of above and below are not required to make a precise meaning of the term. In fact, the ascendant so defined will always be in the eastern half of the rational horizon and the descendant will always be in the western half of the same plane. However, the application of direction is neither a necessary nor sufficient condition for the definition of the concept. Likewise, the recourse to above and below is not required and can be dispensed with, as we did for the definition of the midheaven.

In the following image, the definition of the ascendant offered above is illustrated. Note that the coincidence of the plane of the ecliptic and the plane of the rational horizon occurs at zenith distance of ninety degrees. The rising degree will move from its position on the horizon to the MC during the course of one diurnal cycle and set later at a zenith distance of ninety degrees.


Figure 2: The Ascendant Definition Illustrated

We now have precise definitions for the angles of the horoscope using the minimum number of concepts. In fact, in both cases, the concept of zenith distance is the only term that needs to be formally employed. Both definitions work at all latitudes and for any time during a diurnal cycle. That is, they are universally applicable, unlike, in particular, alternative definitions of the midheaven that have been offered using the concepts of direction and above/below.

The midheaven is defined as the ecliptic degree that is at its minimum zenith distance during its diurnal cycle. This degree will always be coincident with the meridian of the place but the zenith distance of any particular degree on the MC will vary with the latitude of the place. When a degree is on the midheaven it is at its closest approach to the zenith during its diurnal cycle. The degree may, in some circumstances in the polar circles, be below the horizon.

The ascendant is defined as the ecliptic degree that has a zenith distance of ninety degrees but is yet to attain its minimum zenith distance during its diurnal cycle. It will, in due course, become the midheaven, but will not do so until it coincides with the meridian of the place and attains its MZD. The descendant is the ecliptic degree that has a zenith distance of ninety degrees and has already attained its minimum zenith distance.

The IC (Imum Coeli) is the ecliptic degree that is at is maximum zenith distance during its diurnal cycle. This degree will always be coincident with the meridian of the place but the zenith distance of any particular degree on the IC will vary with the latitude of the place. When a degree is on the IC it is at its furthest distance from the zenith during its diurnal cycle. The degree may, in some circumstances in the polar circles, be above the horizon.

The nonagesimal degree is the point on the ecliptic that is closest to the zenith at the time and place for which the chart is cast - that is, it is the point on the ecliptic that has the minimum zenith distance measured on any great circle running through the zenith and nadir at this time and place.This point is different from the MC; the degree associated with the nonagesimal will have been, or will be, closer to the zenith when it had, or has, its MZD on the meridian. The MC and the nonagesimal will only coincide when the first degree of Aries or the first degree of Libra rises, that is, when the equinoctial axis has a zenith distance of exactly ninety degrees.

In a later blog, I will explore some of the implications of these definitions, particularly for house systems generally employed by astrologers.

REFERENCES

Helena Avelar and Luis Ribeiro (2010) On the Heavenly Spheres: A Treatise on Traditional Astrology. AFA Press.
Alan Candlish (1990) The Revised Waite's Compendium of Natal Astrology. Arkana Penguin.
Robert Hand (1982) Essays on Astrology: The Ascendant, Midheaven and Vertex in Extreme Latitudes. Whitford Press.
Jeff Mayo (1976) The Astrologer's Astronomical Handbook. L N Fowler and Co.
Jaqueline Mitton (1993) The Penguin Dictionary of Astronomy. Penguin Books.

Friday, 30 January 2015

Phaethon Ephemeris - 2015

Phaethon is a hypothetical point used in astrology. For more information see:

Interview with Bernard Eccles

Bernard was one of the authors of the classic astrology book called Dark Stars. He co-authored it with Eric Morse. They described it as the remnants of an exploded planet or second sun. It is associated with the asteroid belt.

The following positions are determined using the more precise method of calculating planetary positions outlined in Peter Duffett- Smith's book Practical Astronomy With Your Calculator. The routine was converted into a simple program written in BASIC.

I have checked the output against the ephemeris provided by Raymond Henry (Eric Morse) and Bernard Fitzwalter (Bernard Eccles) in Dark Stars, the book where they discuss Phaethon. The positions correlate with those in Dark Stars, for the period 1900-2003, within about 15 minutes of longitude, and generally no more than 30 minutes of longitude.


2015 - Phaethon Positions for midnight

All positions are direct, unless followed by S - stationary or R - retrograde

1 Jan 2015, 1 AQ 2
2 Jan 2015, 1 AQ 27
3 Jan 2015, 1 AQ 52
4 Jan 2015, 2 AQ 17
5 Jan 2015, 2 AQ 43
6 Jan 2015, 3 AQ 8
7 Jan 2015, 3 AQ 33
8 Jan 2015, 3 AQ 58
9 Jan 2015, 4 AQ 24
10 Jan 2015, 4 AQ 49
11 Jan 2015, 5 AQ 14
12 Jan 2015, 5 AQ 40
13 Jan 2015, 6 AQ 5
14 Jan 2015, 6 AQ 31
15 Jan 2015, 6 AQ 56
16 Jan 2015, 7 AQ 22
17 Jan 2015, 7 AQ 47
18 Jan 2015, 8 AQ 13
19 Jan 2015, 8 AQ 38
20 Jan 2015, 9 AQ 4
21 Jan 2015, 9 AQ 29
22 Jan 2015, 9 AQ 55
23 Jan 2015, 10 AQ 20
24 Jan 2015, 10 AQ 46
25 Jan 2015, 11 AQ 12
26 Jan 2015, 11 AQ 37
27 Jan 2015, 12 AQ 3
28 Jan 2015, 12 AQ 29
29 Jan 2015, 12 AQ 54
30 Jan 2015, 13 AQ 20
31 Jan 2015, 13 AQ 46
1 Feb 2015, 14 AQ 11
2 Feb 2015, 14 AQ 37
3 Feb 2015, 15 AQ 3
4 Feb 2015, 15 AQ 28
5 Feb 2015, 15 AQ 54
6 Feb 2015, 16 AQ 20
7 Feb 2015, 16 AQ 45
8 Feb 2015, 17 AQ 11
9 Feb 2015, 17 AQ 37
10 Feb 2015, 18 AQ 2
11 Feb 2015, 18 AQ 28
12 Feb 2015, 18 AQ 54
13 Feb 2015, 19 AQ 19
14 Feb 2015, 19 AQ 45
15 Feb 2015, 20 AQ 11
16 Feb 2015, 20 AQ 36
17 Feb 2015, 21 AQ 2
18 Feb 2015, 21 AQ 28
19 Feb 2015, 21 AQ 53
20 Feb 2015, 22 AQ 19
21 Feb 2015, 22 AQ 45
22 Feb 2015, 23 AQ 10
23 Feb 2015, 23 AQ 36
24 Feb 2015, 24 AQ 1
25 Feb 2015, 24 AQ 27
26 Feb 2015, 24 AQ 52
27 Feb 2015, 25 AQ 18
28 Feb 2015, 25 AQ 43
1 Mar 2015, 26 AQ 9
2 Mar 2015, 26 AQ 34
3 Mar 2015, 27 AQ 0
4 Mar 2015, 27 AQ 25
5 Mar 2015, 27 AQ 51
6 Mar 2015, 28 AQ 16
7 Mar 2015, 28 AQ 41
8 Mar 2015, 29 AQ 7
9 Mar 2015, 29 AQ 32
10 Mar 2015, 29 AQ 57
11 Mar 2015, 0 PI 23
12 Mar 2015, 0 PI 48
13 Mar 2015, 1 PI 13
14 Mar 2015, 1 PI 38
15 Mar 2015, 2 PI 3
16 Mar 2015, 2 PI 28
17 Mar 2015, 2 PI 53
18 Mar 2015, 3 PI 18
19 Mar 2015, 3 PI 43
20 Mar 2015, 4 PI 8
21 Mar 2015, 4 PI 33
22 Mar 2015, 4 PI 58
23 Mar 2015, 5 PI 23
24 Mar 2015, 5 PI 48
25 Mar 2015, 6 PI 13
26 Mar 2015, 6 PI 38
27 Mar 2015, 7 PI 2
28 Mar 2015, 7 PI 27
29 Mar 2015, 7 PI 51
30 Mar 2015, 8 PI 16
31 Mar 2015, 8 PI 41
1 Apr 2015, 9 PI 5
2 Apr 2015, 9 PI 30
3 Apr 2015, 9 PI 54
4 Apr 2015, 10 PI 18
5 Apr 2015, 10 PI 43
6 Apr 2015, 11 PI 7
7 Apr 2015, 11 PI 31
8 Apr 2015, 11 PI 55
9 Apr 2015, 12 PI 19
10 Apr 2015, 12 PI 43
11 Apr 2015, 13 PI 7
12 Apr 2015, 13 PI 31
13 Apr 2015, 13 PI 55
14 Apr 2015, 14 PI 19
15 Apr 2015, 14 PI 42
16 Apr 2015, 15 PI 6
17 Apr 2015, 15 PI 30
18 Apr 2015, 15 PI 53
19 Apr 2015, 16 PI 17
20 Apr 2015, 16 PI 40
21 Apr 2015, 17 PI 3
22 Apr 2015, 17 PI 27
23 Apr 2015, 17 PI 50
24 Apr 2015, 18 PI 13
25 Apr 2015, 18 PI 36
26 Apr 2015, 18 PI 59
27 Apr 2015, 19 PI 22
28 Apr 2015, 19 PI 45
29 Apr 2015, 20 PI 7
30 Apr 2015, 20 PI 30
1 May 2015, 20 PI 53
2 May 2015, 21 PI 15
3 May 2015, 21 PI 38
4 May 2015, 22 PI 0
5 May 2015, 22 PI 22
6 May 2015, 22 PI 44
7 May 2015, 23 PI 7
8 May 2015, 23 PI 29
9 May 2015, 23 PI 50
10 May 2015, 24 PI 12
11 May 2015, 24 PI 34
12 May 2015, 24 PI 56
13 May 2015, 25 PI 17
14 May 2015, 25 PI 38
15 May 2015, 26 PI 0
16 May 2015, 26 PI 21
17 May 2015, 26 PI 42
18 May 2015, 27 PI 3
19 May 2015, 27 PI 24
20 May 2015, 27 PI 45
21 May 2015, 28 PI 5
22 May 2015, 28 PI 26
23 May 2015, 28 PI 46
24 May 2015, 29 PI 7
25 May 2015, 29 PI 27
26 May 2015, 29 PI 47
27 May 2015, 0 AR 7
28 May 2015, 0 AR 27
29 May 2015, 0 AR 47
30 May 2015, 1 AR 6
31 May 2015, 1 AR 26
1 Jun 2015, 1 AR 45
2 Jun 2015, 2 AR 4
3 Jun 2015, 2 AR 23
4 Jun 2015, 2 AR 42
5 Jun 2015, 3 AR 1
6 Jun 2015, 3 AR 20
7 Jun 2015, 3 AR 38
8 Jun 2015, 3 AR 56
9 Jun 2015, 4 AR 15
10 Jun 2015, 4 AR 33
11 Jun 2015, 4 AR 51
12 Jun 2015, 5 AR 8
13 Jun 2015, 5 AR 26
14 Jun 2015, 5 AR 43
15 Jun 2015, 6 AR 1
16 Jun 2015, 6 AR 18
17 Jun 2015, 6 AR 35
18 Jun 2015, 6 AR 51
19 Jun 2015, 7 AR 8
20 Jun 2015, 7 AR 24
21 Jun 2015, 7 AR 40
22 Jun 2015, 7 AR 56
23 Jun 2015, 8 AR 12
24 Jun 2015, 8 AR 28
25 Jun 2015, 8 AR 43
26 Jun 2015, 8 AR 58
27 Jun 2015, 9 AR 13
28 Jun 2015, 9 AR 28
29 Jun 2015, 9 AR 43
30 Jun 2015, 9 AR 57
1 Jul 2015, 10 AR 12
2 Jul 2015, 10 AR 26
3 Jul 2015, 10 AR 39
4 Jul 2015, 10 AR 53
5 Jul 2015, 11 AR 6
6 Jul 2015, 11 AR 19
7 Jul 2015, 11 AR 32
8 Jul 2015, 11 AR 45
9 Jul 2015, 11 AR 57
10 Jul 2015, 12 AR 9
11 Jul 2015, 12 AR 21
12 Jul 2015, 12 AR 33
13 Jul 2015, 12 AR 44
14 Jul 2015, 12 AR 55
15 Jul 2015, 13 AR 6
16 Jul 2015, 13 AR 16
17 Jul 2015, 13 AR 27
18 Jul 2015, 13 AR 37
19 Jul 2015, 13 AR 47
20 Jul 2015, 13 AR 56
21 Jul 2015, 14 AR 5
22 Jul 2015, 14 AR 14
23 Jul 2015, 14 AR 23
24 Jul 2015, 14 AR 31
25 Jul 2015, 14 AR 39
26 Jul 2015, 14 AR 47
27 Jul 2015, 14 AR 54
28 Jul 2015, 15 AR 1
29 Jul 2015, 15 AR 8
30 Jul 2015, 15 AR 14
31 Jul 2015, 15 AR 20
1 Aug 2015, 15 AR 26
2 Aug 2015, 15 AR 31
3 Aug 2015, 15 AR 36
4 Aug 2015, 15 AR 41
5 Aug 2015, 15 AR 45
6 Aug 2015, 15 AR 49
7 Aug 2015, 15 AR 53
8 Aug 2015, 15 AR 56
9 Aug 2015, 15 AR 59
10 Aug 2015, 16 AR 2
11 Aug 2015, 16 AR 4
12 Aug 2015, 16 AR 6
13 Aug 2015, 16 AR 8
14 Aug 2015, 16 AR 9
15 Aug 2015, 16 AR 9
16 Aug 2015, 16 AR 10 S
17 Aug 2015, 16 AR 10 S
18 Aug 2015, 16 AR 9 S
19 Aug 2015, 16 AR 8 R
20 Aug 2015, 16 AR 7 R
21 Aug 2015, 16 AR 6 R
22 Aug 2015, 16 AR 4 R
23 Aug 2015, 16 AR 1 R
24 Aug 2015, 15 AR 59 R
25 Aug 2015, 15 AR 56 R
26 Aug 2015, 15 AR 52 R
27 Aug 2015, 15 AR 48 R
28 Aug 2015, 15 AR 44 R
29 Aug 2015, 15 AR 39 R
30 Aug 2015, 15 AR 34 R
31 Aug 2015, 15 AR 29 R
1 Sep 2015, 15 AR 23 R
2 Sep 2015, 15 AR 17 R
3 Sep 2015, 15 AR 10 R
4 Sep 2015, 15 AR 4 R
5 Sep 2015, 14 AR 56 R
6 Sep 2015, 14 AR 49 R
7 Sep 2015, 14 AR 41 R
8 Sep 2015, 14 AR 32 R
9 Sep 2015, 14 AR 24 R
10 Sep 2015, 14 AR 15 R
11 Sep 2015, 14 AR 6 R
12 Sep 2015, 13 AR 56 R
13 Sep 2015, 13 AR 46 R
14 Sep 2015, 13 AR 36 R
15 Sep 2015, 13 AR 25 R
16 Sep 2015, 13 AR 15 R
17 Sep 2015, 13 AR 4 R
18 Sep 2015, 12 AR 52 R
19 Sep 2015, 12 AR 41 R
20 Sep 2015, 12 AR 29 R
21 Sep 2015, 12 AR 17 R
22 Sep 2015, 12 AR 5 R
23 Sep 2015, 11 AR 53 R
24 Sep 2015, 11 AR 40 R
25 Sep 2015, 11 AR 27 R
26 Sep 2015, 11 AR 14 R
27 Sep 2015, 11 AR 1 R
28 Sep 2015, 10 AR 48 R
29 Sep 2015, 10 AR 35 R
30 Sep 2015, 10 AR 22 R
1 Oct 2015, 10 AR 8 R
2 Oct 2015, 9 AR 55 R
3 Oct 2015, 9 AR 41 R
4 Oct 2015, 9 AR 28 R
5 Oct 2015, 9 AR 14 R
6 Oct 2015, 9 AR 1 R
7 Oct 2015, 8 AR 47 R
8 Oct 2015, 8 AR 34 R
9 Oct 2015, 8 AR 20 R
10 Oct 2015, 8 AR 7 R
11 Oct 2015, 7 AR 53 R
12 Oct 2015, 7 AR 40 R
13 Oct 2015, 7 AR 27 R
14 Oct 2015, 7 AR 14 R
15 Oct 2015, 7 AR 1 R
16 Oct 2015, 6 AR 49 R
17 Oct 2015, 6 AR 36 R
18 Oct 2015, 6 AR 24 R
19 Oct 2015, 6 AR 12 R
20 Oct 2015, 6 AR 0 R
21 Oct 2015, 5 AR 49 R
22 Oct 2015, 5 AR 37 R
23 Oct 2015, 5 AR 26 R
24 Oct 2015, 5 AR 15 R
25 Oct 2015, 5 AR 5 R
26 Oct 2015, 4 AR 54 R
27 Oct 2015, 4 AR 44 R
28 Oct 2015, 4 AR 35 R
29 Oct 2015, 4 AR 25 R
30 Oct 2015, 4 AR 16 R
31 Oct 2015, 4 AR 8 R
1 Nov 2015, 3 AR 59 R
2 Nov 2015, 3 AR 51 R
3 Nov 2015, 3 AR 44 R
4 Nov 2015, 3 AR 37 R
5 Nov 2015, 3 AR 30 R
6 Nov 2015, 3 AR 23 R
7 Nov 2015, 3 AR 17 R
8 Nov 2015, 3 AR 11 R
9 Nov 2015, 3 AR 6 R
10 Nov 2015, 3 AR 1 R
11 Nov 2015, 2 AR 56 R
12 Nov 2015, 2 AR 52 R
13 Nov 2015, 2 AR 48 R
14 Nov 2015, 2 AR 45 R
15 Nov 2015, 2 AR 42 R
16 Nov 2015, 2 AR 39 R
17 Nov 2015, 2 AR 37 R
18 Nov 2015, 2 AR 35 R
19 Nov 2015, 2 AR 34 R
20 Nov 2015, 2 AR 33 R
21 Nov 2015, 2 AR 32 R
22 Nov 2015, 2 AR 32 S
23 Nov 2015, 2 AR 32 S
24 Nov 2015, 2 AR 33
25 Nov 2015, 2 AR 34
26 Nov 2015, 2 AR 35
27 Nov 2015, 2 AR 37
28 Nov 2015, 2 AR 39
29 Nov 2015, 2 AR 41
30 Nov 2015, 2 AR 44
1 Dec 2015, 2 AR 48
2 Dec 2015, 2 AR 51
3 Dec 2015, 2 AR 55
4 Dec 2015, 3 AR 0
5 Dec 2015, 3 AR 4
6 Dec 2015, 3 AR 10
7 Dec 2015, 3 AR 15
8 Dec 2015, 3 AR 21
9 Dec 2015, 3 AR 27
10 Dec 2015, 3 AR 34
11 Dec 2015, 3 AR 41
12 Dec 2015, 3 AR 48
13 Dec 2015, 3 AR 55
14 Dec 2015, 4 AR 3
15 Dec 2015, 4 AR 11
16 Dec 2015, 4 AR 20
17 Dec 2015, 4 AR 29
18 Dec 2015, 4 AR 38
19 Dec 2015, 4 AR 47
20 Dec 2015, 4 AR 57
21 Dec 2015, 5 AR 7
22 Dec 2015, 5 AR 18
23 Dec 2015, 5 AR 28
24 Dec 2015, 5 AR 39
25 Dec 2015, 5 AR 50
26 Dec 2015, 6 AR 2
27 Dec 2015, 6 AR 14
28 Dec 2015, 6 AR 26
29 Dec 2015, 6 AR 38
30 Dec 2015, 6 AR 51
31 Dec 2015, 7 AR 4

References

Bernard Fitzwalter and Raymond Henry (1988) Dark Stars: Invisible Focal Points in Astrology. Wellingborough: The Aquarian Press. The authors adopted these pseudonyms for the publication of Dark Stars. The authors' actual names were Bernard Eccles (Fitzwalter) and Eric Morse (Henry).

Peter Duffett-Smith (1988) Practical Astronomy with your Calculator (3rd ed.). Cambridge: Cambridge University Press. Bernard and Eric's original programming in the 1980's used the methods outlined by Duffett-Smith in his book.

Monday, 26 January 2015

Greek General Election - follow up

Syriza did indeed win the Greek General Election and Alexis Tsipras has been sworn in as prime minister. It occurred to me that the size of Syriza's victory – just a couple of seats short of an outright majority – mirrored that of Angela Merkel in 2013. I decided to have a look at Germany's re-unification chart to see if there were any similarities with Greece's national chart. To my utter amazement, I discovered that Germany has 4 Leo 22 rising – almost exactly the same degree as Alexis Tsipras' Sun (4 Leo 57 at noon – birth time unknown). His Sun is also conjunct Germany's South Node, which suggests unfinished business.

(Click to enlarge)

I can't see anything else of great significance between the two charts. There's a close Saturn-Neptune opposition between Greece's (remember – the Greek national chart is almost the same as Tsipras') and Germany's, but you'd expect it to involve Germany's Saturn and Greece's Neptune – not the other way round. Or does this suggest that Tsipras will force Germany to be more realistic about its dream of a United States of Europe?

In turn, transiting Saturn will be making its presence felt in Greece later this year as it will contact Greece's and Tsipras' Neptune in November. So it's possible that both parties are going to have to take reality checks and disappointment. No strong personal interaction between Merkel's and Tsipras' charts leaps out at me. However, his North Node is conjunct her Ascendant and his Uranus is stirring things up for her as it's conjunct her natal Neptune (those dreams again) and square her natal Sun (he's threatening the stability of the project she holds so dear).

(Click to enlarge)


It looks like it's going to be an interesting year in Europe. I also came across another left-wing radical party with a charismatic young leader today. This is the Spanish Podemos ('We Can') led by Pablo Iglesias. Formed at the beginning of 2014, the party is now the second largest in Spain. Iglesias was elected to the European Parliament in 2014. He has much in common with Alexis Tsipras and visited Greece to help with Syriza's election campaign.

(Click to enlarge)

The similarities between Iglesias' and the post-Franco national chart for Spain are not as striking as those between Tsipras' and Greece's, but note that the two Suns are once again within a few degrees of each other. I can't find a birth time for him, so this is a noon chart, but if he were born some time after 9:30pm Iglesias' Moon would be conjunct Spain's Mars. Also of note is that transiting Saturn will be contacting Iglesias' Mars and Spain's Neptune at the end of this year and the beginning of 2016. Spain is another country that's struggling with debt. Curiously, it has 3 Aquarius 43 rising – almost exactly opposite Germany's Ascendant and Tsipras' Sun. Perhaps now that Greece has led the way, Spain will follow by demanding an end to austerity. (Spain is due to hold a General Election towards the end of 2015). Interesting times indeed ...



Notes

(1) Bi-wheels have the countries on the inside as we know the times and therefore the Ascendants

(2) Information for all national charts was taken from The Book of World Horoscopes, full details in previous post

Saturday, 24 January 2015

Some thoughts on the Greek General Election

Belatedly, I decided to take a look at the chart for Greece as the people prepare to vote in what could be a ground-shifting election tomorrow. I've used the chart drawn up for the swearing-in of Constantine Karamanlis as prime minister following the collapse of the military dictatorship in 1974.1 One of the interesting things about this election is that the man who's widely tipped to become the next prime minister of Greece – Alexis Tsipras – was born only four days after the republic was formed. Therefore apart from the position of his Moon (of which we can't be sure as we don't have a birth time for him), he has almost the same horoscope as Greece itself. And there are very significant transits to these charts on election day.

Traditionally, voting takes place between sunrise and sunset in Greece2 so I've erected a chart for election day based on sunrise in Athens, which is both the capital and Tsipras' place of birth.

(Click to enlarge)
One of the first things I noticed was that Uranus (13 Aries 04) on election day is almost exactly square the Ascendant in the chart for Greece (13 Cancer 08). Also, Mercury is retrograde in the election chart. It's being drawn back to the Sun, having turned retrograde just a few days ago. In terms of Mercury's synodic cycle (a subject dear to my heart at the moment), the cycle is drawing to a close so Mercury is being pulled toward the future with its eye firmly fixed on the past. Greece has been in economic melt-down for years and I freely admit to being biased because I love the Greeks, but I feel they've been very cruelly treated by the EU. Many Greeks have suffered terribly during this period – you can 'listen again' to some of the interviews John Humphrys made in Greece this week for the BBC Today programme3. Many Greeks are saying that all the other politicians have failed them so this time they're going to give Syriza (the radical left coalition that Tsipras heads) a chance. They're looking for change, and this shows in the transiting Uranus, which is also squaring the Greek Saturn (just risen in the national chart) and Mercury.

There are, in fact, many significant transits to the Greek Ascendant-Saturn-Mercury. Transiting Pluto is also exactly opposite this trio and the nodes are square. Interestingly, the North Node is in Libra, a sign that's concerned with social justice but whose shadow side is totalitarianism. The South Node in Aries suggests the root of Greece's problem was selfishness and rampant individualism during the Good Times – or the 'snout in the trough' sort of behaviour that came to light here in the UK during the MPs' expenses scandal. The shadow side of this – a bright shadow – is that people were forced to find other ways to survive once the money ran out. Some didn't make it, but in other cases it built strong networks and communities based more on what people are than on what they have.

Coming back to the retrograde Mercury in the election chart, this can also be seen as either a people who have turned in on themselves and their problems or who are turning against the tide. They've had enough of the 'business as usual' approach of mainstream politicians and they're willing to give Syriza a chance. Of course, we can't be certain that Syriza will win and we certainly can't be sure that Syriza will be any better for them than what has gone before. They could be lured onto the rocks by a siren's song, or they could find that their dreams of a better life come true. Note that transiting Neptune is square the natal Neptune of Greece and Tsipras – though transiting Saturn is approaching their Neptune. When Saturn reaches that point could be when they get a reality check.

(Click to enlarge)
Those seem to be the most important things to me, but I'd just like to mention Alexis Tsipras' chart in relation to the opening and closing of polls in Athens. The Sun on election day is exactly opposite his natal Sun, and at dawn his Sun has just sunk below the horizon of the election chart. When the polls close ten hours later, his Sun has just risen above the Ascendant in the close of poll chart. That, together with the fact that the Moon is riding high at the top of the election chart suggests to me that he'll be the people's choice. Moon is conjunct Uranus and South Node and all three are in the ninth house, a sign that people want change and they have faith in him to deliver it.

(Click to enlarge)



References

(1) Campion, Nicholas The Book of World Horoscopes Wessex Astrologer, Bournemouth (2004) pp 146-7




Sunday, 18 January 2015

The Definition of the Midheaven


The midheaven, or MC (from Medium Coeli), is one of the angles of the horoscope. The other principal angle is the ascendant. The identification of the angles seems unproblematic, and astrologers are often able to cite some sort of definition for each one. However, a technically correct definition for the ascendant or midheaven can be elusive.

For example astrologers will often say that the midheaven is the highest point in the chart. This is a disarmingly simple statement, but once considered in detail, turns out be a crude and problematic definition of the MC. Firstly, which point in the chart is being identified. To say the midheaven is the highest point in the chart doesn't really clarify the issue of what, exactly, this point is in the horoscope. Secondly, and most problematically, 'highest' in relation to what? Terms like 'highest' and 'higher' are relative and need to be defined in terms of some sort of absolute position.

Robert Hand provides two useful and more precise definitions in his essay on the ascendant, midheaven and vertex in extreme latitudes (for reference see below). Hand's first definition is that the midheaven may be the point of intersection of the meridian and ecliptic in the south. His second definition is that the midheaven may be the point of intersection of the ecliptic and meridian above the horizon. (p. 132)

These definitions do advance our understanding because we now know that the midheaven or MC is the point where the ecliptic meets the meridian. The meridian is the great circle through the running north and south points of the observer's horizon, and through the zenith, the point exactly overhead on the celestial sphere, and the nadir, the point on the celestial sphere opposite the zenith. 

The following diagram illustrates the points made in the previous paragraph. Note that the midheaven is shown crossing the ecliptic above the horizon and due south. This is a fair representation of the midheaven for a northern hemisphere observer at mid-latitudes. The diagram is for illustrative purposes and the situation will vary for observers at other latitudes.




Figure 1: The Celestial Sphere (Horizontal Frame of Reference)

But how do we decide between the definitions of the midheaven that Hand has offered? By direction? Or by altitude above the horizon? This is critical because in polar regions and at the equator both definitions become ambiguous for different reasons.

Let's consider the definition by direction. Firstly, to be accurate, the definition by direction must be made relative to the hemisphere of the observer. For those in the southern hemisphere, the midheaven is generally to the north. So for more precision, the definition of the midheaven must be extended to refer to the hemisphere of the observer. However, a problem immediately arises for observers in the tropics (those living close to the equator). For an observer who lives just north of the equator, the midheaven will be to their north when signs of northern declination (those north of the equator) are culminating.

So our definition by direction and hemisphere has already broken down. To correct this problem, we have had to qualify the directional definition further, by reference to the latitude of the observer. What seemed to be a straightforward description of the midheaven has now become complex and unwieldy.

What about the definition with relation to the horizon. In this definition the midheaven is always above the horizon, irrespective of its direction. This, on the face of it, seems quite reasonable. After all, it is true for anybody living in the tropics and temperate regions. However, when we get to the polar regions (beyond on the arctic or antarctic circles), we find that the midheaven so defined may again be to the north for northern observers. Others also claim that the MC is always to the south in polar regions even when it is below the horizon.

I think there are good reasons why we should be critical of both definitions of the midheaven - by direction (south/north) and by position relative to the horizon (above/below). Neither seems to have offered an unambiguous definition of the concept we are examining.

The definition of above and below the horizon refers to altitude above the horizontal plane. So, in the case of Hand's second definition of the midheaven, the point of intersection of the ecliptic and meridian will have an altitude above the horizon. But let's consider the phenomenon of the midnight sun. In northern polar regions, the sun in summer (at its most northerly declination) will spend 24 hours above the horizon - it neither rises nor sets in the sense of being above or below the horizon.

Now when the northern winter solstice (00 Capricorn 00 in the tropical zodiac), the point on the ecliptic with the most southerly declination, is due south of the observer in polar regions it will be below the horizon. At this time, the Sun at the northern summer solstice will be due north of a northern polar observer but above the horizon.

If we accept the definition of the midheaven as being the point of intersection between the ecliptic and the meridian above the horizon, then the Sun at 00 Cancer 00, the northern summer solstice (in the tropical zodiac), will be on the MC. However, consider the situation twelve hours later: the Sun at the summer solstice will be on the meridian again, this time in the south, but at a point much higher in the sky with relation to the horizon. The winter solstice will still be below the horizon, but also on the meridian due north.

What should we make of this? The summer solstice Sun seems to be on the MC again. It is crossing the meridian and clearly above the horizon. The other point of the ecliptic crossing the meridian, the northern winter solstice, is still below the horizon in the north. So the sun seems to have been on the MC twice in one day if we use the above/below definition of the midheaven in polar regions.

It's my view that it is the second instance of the Sun crossing the meridian that we want to call Sun-MC. This is because it is both on the meridian and at its highest point in the sky in a single diurnal cycle. In short the Sun is at its closest approach to the zenith, the point immediately above the observer. Of course, in polar regions it won't actually be immediately above the observer, but it has attained its minimum zenith distance. It is this observation that finally provides us with an unambiguous definition of the midheaven or MC.

The midheaven or MC is the degree of the ecliptic which, at the time and place of casting the horoscope, has its minimum zenith distance (MZD) measured on the meridian; that is, it is the point at which that particular degree makes its closest approach to the zenith in any single diurnal (24 hour) cycle. This definition does not mess up in the tropics, where directional definitions become unclear, and it means that being above or below the horizon is not relevant, which has been shown to be a problem in polar regions.

The definition of zenith distance is taken from Mitton's Dictionary of Astronomy. Zenith distance is "the angular distance from the zenith to a point on the celestial sphere, measured along a great circle." (p. 416) In our case the great circle of interest is the meridian because in any one diurnal cycle, the minimum zenith distance for any particular point on the ecliptic will occur along this circle.

What about the tropical northern winter solstice? This point never comes above the horizon in northern polar regions. It will still be on the MC according to this definition because when it is due south of a northern observer the particular degree associated with the northern winter solstice – 00 Capricorn 00 in the tropical zodiac - will have reached its minimum zenith distance (MZD) in that diurnal cycle. That is, at that particular time and place, it will be at its closest approach to the zenith despite being below the horizon.

This may seem quite counter-intuitive at first. After all the Sun will still be higher in relation to the horizon in the north than the winter solstice degree below the horizon in the south. But the critical point is that the Sun at this time is not at the closest point to the zenith that it can be during the course of the day. This point will come when it attains its MZD on the meridian twelve hours later.

And consider the midwinter Sun at these latitudes - say, just above the arctic circle. It will rise to a point just below the southern horizon at  noon when it attains its MZD. Although the Sun in midwinter will be below the horizon, a glimmer of noon-day light will come over the horizon. Is this not what we would want for a Sun-MC conjunction, even one below the horizon. It's as light as it is going to get for a midwinter Sun on or just above the arctic circle. Twelve hours later, with the Sun on the IC defined by MZD, it will be midnight and deep dark. 

The following diagram illustrates these points. The summer solstice Sun (identified by CN for Cancer) is shown just above the northern horizon (the midnight sun). In the course of 12 hours it will move along the dashed orange line to the point on the meridian due south of the observer. It is moved there by the rotation of the earth on its pole (marked NCP-SCP). The purple line from the zenith to the highpoint of the Sun shows the MZD (minimum zenith distance) at noon - the Sun-MC. Note that the Sun in the course of those 12 hours has moved to a position much higher in the sky than the midnight Sun - the Sun-IC.

The winter solstice Sun (identified by CP for Capricorn) is shown deep below the northern horizon at midnight. In the course of 12 hours it will move along its dashed orange line to the point on the meridian due south of the observer, just below the horizon. However, note that it has still moved towards the zenith, the point at the top of the sphere. The MC defined by MZD is marked. The difference in zenith distances at both points is shown by the light blue line.



  Figure 2: Illustrating the Concept of Minimum Zenith Distance Marking the Midheaven

At any particular time in the day there may be points on the ecliptic that have less zenith distance (i.e. are closer to the zenith) than the point on the MC. An example is the nonagesimal point, the degree on the ecliptic with the maximum altitude above the horizon at a particular time and place. In general the nonagesimal degree won't be the MC at the time for which the horoscope is cast because it will have had its minimum zenith distance (it's closest approach to the zenith) at some other time during the diurnal cycle.

For example, a nonagesimal degree west of the meridian will have attained its MZD (i.e. been on the midheaven) at some time earlier in the day. A nonagesimal degree east of the meridian it will attain its MZD some time later in the day when it will be the degree of the ecliptic on the meridian.

In fact, the nonagesimal can be precisely defined as the degree on the ecliptic with the minimum zenith distance measured on any great circle running through the zenith and nadir at a particular time and place. 

It is worth noting that exactly at the poles all definitions of the MC become problematic, partly because all directions from the north pole lead south (towards the southern pole) and vice versa in the southern hemisphere. This makes the definition of the meridian itself difficult. However, this is not really a serious issue because as soon as one moves away from the pole, the definition of the meridian becomes possible once again.

So: the MC cannot be defined by direction (fails at the tropics) nor by its being above the horizon (problematic in the polar circles - the 'double midheaven' issue). The definition is unambiguously made using the concept of minimum zenith distance. The midheaven or MC is the point of intersection between the ecliptic and the meridian where that particular degree attains its minimum zenith distance during its diurnal cycle, irrespective of its direction in relation to an observer or its height in relation to the horizon.

Perhaps we should rename the MC the MMZD - minimum meridional zenith distance!

Postscript

Since posting this blog the author has discovered an article in the Astrological Association Journal by Norman Blunsdon that covers this issue. Members of the Astrological Association may wish to explore this piece online (as a benefit of their membership) or at the AA Library. 

The reference is:

N Blunsdon (1967) Low Thoughts on High Latitudes. Astrological Association Journal: Vol. 8, No. 3, p. 30.


It is reprinted in the AA's compendium of early classic articles from the Journal - An Astrological Anthology: Vol. 1 (1959-1970). Selected and arranged by Zach Matthews.

In this piece, Blunsdon points out that the midheaven is the same at all latitudes, and changing the midheaven to conform to a definition (always above the horizon) transgresses this principle. 

Blunsdon writes: "Let us first consider the MC and its derivation. As this is formed by the Meridian for the subject's birthtime, it is both personal and constant. We use the Local Sidereal Time and usually find the corresponding MC in our house tables: this is the same for all latitudes."

References:

Robert Hand (1982) Essays on Astrology: The Ascendant, Midheaven and Vertex in Extreme Latitudes. Whitford Press.

Jaqueline Mitton (1993) The Penguin Dictionary of Astronomy. Penguin Books.