Léon GAMBETTA
This theme is the first that Paul Choisnard analyzes in his "Langage Astral". He uses Placidus' method of primary directions; this method has since been known under 'Fomalhaut-Choisnard'. Here we find the theme of Gambetta :
Gambetta Léon
02 Avr 1838 GREG CAL
monday GREG
| lat 44° 27' 0" | N 1°26' E
0
---------------------------------
natal (bt) 15 h 27 min
raas-rams :23h 56' 20"
reckoned bt Lat --> lmt 20 h 0 min
tu 19h 54' 16"
tsn 8h 42' 50"
---------------------------------
timezone : 0
DST : 0 (-)
Equation of time -0h 3' 39"
ΔT 0h 0' 6"
RADIX
TRAD, ALMUTEN OF NATIVITY (OMAR, IBN EZRA)
JU
term 3 tri 0 rul 0
exn 2 fac 3
su 0 mo 3 asc 0 syg
2 pof 3
DOM : JU
LILLY (PTOLEMAIC) ALMUTEN OF NATIVITY (with egyptian terms)
Lilly ALM : VE
ALGOL conj -
(zodiacal)
under sun bean’s :
ME
besieged : -- |
- nearby rays :--
chart NOCTURNAL | waxing (conjunctional) moon
HYLEG - ALCHOCODEN
KADHKHUDǠH |
♀ |
MUNDANE | REGIO |
dignity |
TERM |
E Occ |
power |
2 |
if the alcocoden is combust and so gives nothing, then venus and/or jupiter in the ascendant or midheaven can give their minor years |
retro |
- |
0 |
± 5° transition for zodiacal house |
- |
5,22° (*) |
IV |
ang |
(*) limit of Δ domitude is > 5° |
V |
succ |
|
± Δy (-) |
0,00 |
± |
trad Years |
45,00 |
3 / 45 Y |
|
* |
-0,75 [E] |
aspect |
JU 0 VE: -2,52 |
|
± Δ asp |
-2,52 |
(Σ Δasp :0 - ) |
— |
0 |
|
12° ju |
0 |
|
8° ve |
0 |
EQU ( 1,02 ) |
Σ Y |
43,23 |
43,92 |
1)-DIRECTION : □SU conj SA
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.
sin(DA) = -tan(φ)tan(δ)
φ = latitude 44,45 N
δ SA = -17,57 -
DA-SA = 18,1°
δ □SU =-23,35 -
DA-□SU =25,06°
We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the nocturnal point because the altitude of SA is -23,42°. important note: the SA and DM of the two points are always counted diurnal if the first point (here SA) is above the horizon even if the second is below. They are counted nightly if the first point (SA) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point SA is diurnal, and from the nocturnal meridian if it is nocturnal.
nocturnal meridian MC = 310,71°
AR SA = 236,57°
AR □SU = 275,94°
SA N (δ-) = 115,06°
DM N □SU = 34,78°
For the significator □SU altitude (h) =-54,68°. so :
SA D (δ-) = 108,1°
DM N SA = 34,78°
Then we compute Saf/DMf (so : SA f [ 115,06°] / DM f [ 34,78°])
Sa f / DM f =3,31
and the angle x = SAm x DM f/SA f, so : SA m [ 108,1°] x DM f [ 34,78°]/SA f [ 115,06°]
x = 32,68°
We find the direction by DMm - x, so : DM m [ 34,78°] ± x [32,68]
We must now have regard to the double ± sign of the last expression; in the case where f (SA) and m (□SU) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. This is not the case here, so sign = (+)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =41,46°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here □SU) and the f point is a planet or an axis, (here SA)
We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not conceivable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgement on this.
That time, we compute Sa m / DM m (so : SA m [71,9] / DM m [105,86])
Sa m / DM m =1,46
and the angle x = SA f x DM m/SA m, so : SA f [ 115,06°] x DM m [105,86] / SA m [71,9]
x = 78,91°
We find the direction by DM f - x, so : DM f [ 34,78°] ± x [78,91°]
We must now have regard to the double ± sign of the last expression; in the case where m (□SU) and f (SA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. This is not the case here, so sign = (-)
---------------------------------
arc C =44,13°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the 'Dictionnaire astrologique' of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his 'Horoscope annuel simplifié' (Dervy, 1973) p.181. Other formulas can be found in 'Les Moyens de pronostic en astrologie', Max Duval (editions traditionnelles, 1986) and 'Domification et transits' (Editions traditionnelles, 1985). We can also cite by André Boudineau : 'Les bases scientifiques de l’astrologie' (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.
First, compute the ascensional difference under f (SA) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, : cot (DAP f) = (Cot dec f[-17,57°] x Cot Lat [44,45°]) /sin DM f [74,14°] ± cot DM f [74,14°]
DAPf = 161,92°
We find the pole of f (SA) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [15,4°] x cot f [-17,57°]
pole SA regio =-39,99°
(1) We need now the DAP of m (□SU) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (SA) : sin (DAPm/f) = tan [39,98°] x tan [-23,35°]
DAP m/f = -21,22°
then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f SA = 251,98° and AO m = AR m ± DAP m ; idem for sign ; so AO m□SU = 297,16°
---------------------------------
arc D Regio = -45,19°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc f SA / p □SU
First, compute the ascensional difference under m (□SU) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, : Cot(DAP m) = (Cot decm[-23,35°] x Cot Lat [44,45°]) / Sin DM f [145,22°] ± Cot DM m [-34,78°]
DAP m = 20,32°
We find the pole of m (□SU) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [169,84°] x Cot m [-23,35°]
pole □SU regio =-22,23°
We need now the DAP of f (SA) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□SU) : Sin (DAP f/m) = Tan[22,23°] x Tan [-17,57°]
DAP f/m = -7,43°
then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m □SU = 286° and AO f = AR f ± DAP f ; idem for sign ; so AO f SA = 244,01°
---------------------------------
arc C Regio = -42,09°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.
For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.
So, initially, we have A => Tan f = tan dec f [-17,57°] / cos DM f [-74,14°]
A = -49,2°
Then : B = Lat [44,45°] + A [49,2°]
B = -4,75°
And, Tang C = Cot DM f [-74,14°] x Cos B [-4,75°] / Cos A [49,2°]
C = -23,43°
Then, we have Sin pole f = Cos C [-23,43°] x Sin LG [44,45°]
---------------------------------
So, pole SA regio = 39,98°
---------------------------------
Now go back to (1)
For m □SU; we have : A => Tan m = tan dec m [-23,35°] / cos DM m [-34,78°]
A = -27,73°
Then : B = Lat [44,45°] + A [27,73°]
B = 16,72°
And, Tang C = Cot DM m [-325,22°] x Cos B [16,72°] / Cos A [27,73°]
C = -57,31°
Then, we have Sin pole m = Cos C [-57,31°] x Sin LG [44,45°]
---------------------------------
So, pole □SU regio = 22,23°
---------------------------------
Now go back to (1)
MD = meridian distance (from MC if SA f [SA] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [SA] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [SA] and m □SU)
under bracket [] the fixed point, (here SA)
Arc regio-campa where SA = 275.71° and square SU = 275.45° of longitude. This arc represents a time of 3h, so that TU add to: 23h 06' (TU natal is 19h 54'). Here, the direction is converse in the sense of traditional astrology; the body gives the impression that it joins the square aspect emanating from the sun (this aspect is global at 275.45° of CAP, at a REGIO domitude of 65.38 for a pole of 22.22°).
2)-DIRECTION : □SA conj MO
converse direction |
Lat |
Dec |
AR |
MD |
SA |
HA |
MO |
5,21 N |
26,6 N |
116,04 |
12,99 D |
119,03 D |
106,04 W |
□SA |
0 S |
6,32 N |
165,21 |
34,49 D |
96,24 D |
61,75 E |
MD = meridian distance (from MC if SA f [MO] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [MO] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [MO] and m □SA)
under bracket [] the fixed point, (here MO)
This direction arc that interests us here is:
Arc regio-campa where MO = 114.12° and square SA= 163.94° of longitude. Here, the direction is converse in the sense of traditional astrology; the body gives the impression that it joins the square aspect emanating from Saturn. That's not all: we notice the proximity of the VE-JU opp in radix which is thus superimposed on this direction (JU being the dominant planet).
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.
sin(DA) = -tan(φ)tan(δ)
φ = latitude 44,45 N
δ MO = 26,32 +
DA-MO = 29,03°
δ □SA =6,32 +
DA-□SA =6,24°
We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the diurnal point because the altitude of MO is 69,07°. important note: the SA and DM of the two points are always counted diurnal if the first point (here MO) is above the horizon even if the second is below. They are counted nightly if the first point (MO) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point MO is diurnal, and from the nocturnal meridian if it is nocturnal.
 |
diurnal meridian MC = 130,71°
AR MO = 117,72°
AR □SA = 165,21°
=96,24°
DM D □SA=34,49°
For the significator □SA altitude (h) =41,45°. so :
SA D (d+) MO=119,03°
DM D MO=34,49°
Then we compute Saf/DMf (so : SA f [96,24°] / DM f [34,49°])
Sa f / DM f =2,79
and the angle x = SAm x DM f/SA f, so : SA m [119,03°] x DM f [34,49°]/SA f [96,24°]
x = 42,66°
We find the direction by DMm - x, so : DM m [34,49°] ± x [42,66]
We must now have regard to the double ± sign of the last expression; in the case where f (MO) and m (□SA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. this is the case here so sign = (-)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =55,65°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here □SA) and the f point is a planet or an axis, (here MO)
We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.
That time, we compute Sa m / DM m (so : SA m [60,97] / DM m [167,01])
Sa m / DM m =9,16
and the angle x = SA f x DM m/SA m, so : SA f [96,24°] x DM m [167,01] / SA m [60,97]
x = 10,5°
We find the direction by DM f - x, so : DM f [34,49°] ± x [10,5°]
We must now have regard to the double ± sign of the last expression; in the case where m (□SA) and f (MO) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. this is the case here : so, signe = (+)
---------------------------------
arc C =44,99°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the Dictionnaire astrologique of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his Horoscope annuel simplifié (Dervy, 1973) p.181. Other formulas can be found in Les moyens de pronostic en astrologie, Max Duval (editions traditionnelles, 1986) and Domification et transits (Editions traditionnelles, 1985). We can also cite by André Boudineau : Les bases scientifiques de l’astrologie (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.
First, compute the ascensional difference under f (MO) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, : cot (DAP f) = (Cot dec f[26,32°] x Cot Lat [44,45°]) /sin DM f [192,99°] ± cot DM f [192,99°]
DAPf = 168,31°
We find the pole of f (MO) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [4,24°] x cot f [26,32°]
pole MO regio =8,49°
(1) We need now the DAP of m (□SA) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (MO) : sin (DAPm/f) = tan [8,49°] x tan [6,32°]
DAP m/f = 0,95°
then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f MO = 120,28° and AO m = AR m ± DAP m ; idem for sign ; so AO m□SA = 166,15°
---------------------------------
arc D Regio = -44,2°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc f MO / p □SA
First, compute the ascensional difference under m (□SA) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, : Cot(DAP m) = (Cot decm[6,32°] x Cot Lat [44,45°]) / Sin DM f [34,49°] ± Cot DM m [34,49°]
DAP m = 3,23°
We find the pole of m (□SA) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [3,23°] x Cot m [6,32°]
pole □SA regio =26,99°
We need now the DAP of f (MO) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□SA) : Sin (DAP f/m) = Tan[26,98°] x Tan [26,32°]
DAP f/m = 14,58°
then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m □SA = 168° and AO f = AR f ± DAP f ; idem for sign ; so AO f MO = 132,31°
---------------------------------
arc C Regio = -58,83°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.
For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.
So, initially, we have A => Tan f = tan dec f [26,32°] / cos DM f [-12,99°]
A = 26,91°
Then : B = Lat [44,45°] + A [-26,91°]
B = 17,54°
And, Tang C = Cot DM f [-12,99°] x Cos B [17,54°] / Cos A [-26,91°]
C = -77,83°
Then, we have Sin pole f = Cos C [-77,83°] x Sin LG [44,45°]
---------------------------------
So, pole MO regio = 8,49°
---------------------------------
Now go back to (1)
For m □SA; we have : A => Tan m = tan dec m [6,32°] / cos DM m [34,49°]
A = 7,65°
Then : B = Lat [44,45°] + A [-7,65°]
B = 36,8°
And, Tang C = Cot DM m [34,49°] x Cos B [36,8°] / Cos A [-7,65°]
C = -49,62°
Then, we have Sin pole m = Cos C [-49,62°] x Sin LG [44,45°]
---------------------------------
So, pole □SA regio = 26,98°
---------------------------------
Now go back to (1)
3)-DIRECTION MO conj JU
this direction corresponds to the year 1879 when Gambetta was elected President of the Chamber of Deputies. It “resonates” the JU-VE radix opposition.
direct direction |
Lat |
Dec |
AR |
MD |
SA |
HA |
JU |
1,44 N |
9 N |
162,49 |
31,78 D |
98,94 D |
67,16 E |
CMO |
5,21 N |
26,6 N |
116,04 |
14,67 D |
119,42 D |
104,75 W |
MD = meridian distance (from MC if SA f [JU] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [JU] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [JU] and m CMO)
under bracket [] the fixed point, (here JU)
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.
sin(DA) = -tan(φ)tan(δ)
φ = latitude 44,45 N
δ JU = 9 +
DA-JU = 8,94°
δ CMO =26,6 +
DA-CMO =29,42°
We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the diurnal point because the altitude of JU is 45,15°. important note: the SA and DM of the two points are always counted diurnal if the first point (here JU) is above the horizon even if the second is below. They are counted nightly if the first point (JU) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point JU is diurnal, and from the nocturnal meridian if it is nocturnal.
diurnal meridian MC = 130,71°
AR JU = 162,49°
AR CMO = 116,04°
=119,42°
DM D CMO=14,67°
For the significator CMO altitude (h) =68,6°. so :
SA D (d+) JU=98,94°
DM D JU=14,67°
Then we compute Saf/DMf (so : SA f [119,42°] / DM f [14,67°])
Sa f / DM f =8,14
and the angle x = SAm x DM f/SA f, so : SA m [98,94°] x DM f [14,67°]/SA f [119,42°]
x = 12,15°
We find the direction by DMm - x, so : DM m [14,67°] ± x [12,15]
We must now have regard to the double ± sign of the last expression; in the case where f (JU) and m (CMO) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. this is the case here so sign = (-)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =43,93°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here CMO) and the f point is a planet or an axis, (here JU)
We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.
That time, we compute Sa m / DM m (so : SA m [81,06] / DM m [148,22])
Sa m / DM m =3,11
and the angle x = SA f x DM m/SA m, so : SA f [119,42°] x DM m [148,22] / SA m [81,06]
x = 38,36°
We find the direction by DM f - x, so : DM f [14,67°] ± x [38,36°]
We must now have regard to the double ± sign of the last expression; in the case where m (CMO) and f (JU) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. this is the case here : so, signe = (+)
---------------------------------
arc C =53,03°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the Dictionnaire astrologique of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his Horoscope annuel simplifié (Dervy, 1973) p.181. Other formulas can be found in Les moyens de pronostic en astrologie, Max Duval (editions traditionnelles, 1986) and Domification et transits (Editions traditionnelles, 1985). We can also cite by André Boudineau : Les bases scientifiques de l’astrologie (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.
First, compute the ascensional difference under f (JU) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, : cot (DAP f) = (Cot dec f[9°] x Cot Lat [44,45°]) /sin DM f [31,78°] ± cot DM f [31,78°]
DAPf = 4,13°
We find the pole of f (JU) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [4,13°] x cot f [9°]
pole JU regio =24,47°
(1) We need now the DAP of m (CMO) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (JU) : sin (DAPm/f) = tan [24,47°] x tan [26,6°]
DAP m/f = 13,18°
then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f JU = 166,62° and AO m = AR m ± DAP m ; idem for sign ; so AO mCMO = 129,22°
---------------------------------
arc D Regio = 55,49°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc f JU / p CMO
First, compute the ascensional difference under m (CMO) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, : Cot(DAP m) = (Cot decm[26,6°] x Cot Lat [44,45°]) / Sin DM f [14,67°] ± Cot DM m [14,67°]
DAP m = 4,82°
We find the pole of m (CMO) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [175,18°] x Cot m [26,6°]
pole CMO regio =9,53°
We need now the DAP of f (JU) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (CMO) : Sin (DAP f/m) = Tan[9,53°] x Tan [9°]
DAP f/m = 1,52°
then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m CMO = 121° and AO f = AR f ± DAP f ; idem for sign ; so AO f JU = 164,01°
---------------------------------
arc C Regio = 43,15°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.
For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.
So, initially, we have A => Tan f = tan dec f [9°] / cos DM f [31,78°]
A = 10,55°
Then : B = Lat [44,45°] + A [-10,55°]
B = 33,9°
And, Tang C = Cot DM f [31,78°] x Cos B [33,9°] / Cos A [-10,55°]
C = 53,73°
Then, we have Sin pole f = Cos C [53,73°] x Sin LG [44,45°]
---------------------------------
So, pole JU regio = 24,47°
---------------------------------
Now go back to (1)
For m CMO; we have : A => Tan m = tan dec m [26,6°] / cos DM m [14,67°]
A = 27,37°
Then : B = Lat [44,45°] + A [-27,37°]
B = 17,08°
And, Tang C = Cot DM m [14,67°] x Cos B [17,08°] / Cos A [-27,37°]
C = -76,33°
Then, we have Sin pole m = Cos C [-76,33°] x Sin LG [44,45°]
---------------------------------
So, pole CMO regio = 9,53°
---------------------------------
Now go back to (1)
--------------------------------------------------------------------------
Here a tab with values for Regiomontanus process :
|
|
|
DP REGIO-CAMPA D |
|
DP REGIO-CAMPA C |
|
METHOD SELVA |
A2 CMO |
A1 JU |
A1 JU |
A2 CMO |
A2 CMO |
A1 JU |
Tan A |
tan dec/cos dm |
|
-10,55 |
|
-27,37 |
|
B (1) |
+LG-A or -LG+A |
|
33,90 |
|
17,08 |
|
Tan C |
cot DM.cosB/cosA |
|
53,73 |
|
-76,33 |
|
Sin pole |
cos C.sinLG |
|
24,47 |
|
9,53 |
|
SinDA (2) |
TanA1.TanDecA2 |
[DAP (4)] |
4,13 |
13,18 |
4,82 |
1,52 |
AO (3) |
AO ±DA |
|
158,36 |
102,87 |
120,86 |
164,01 |
arc |
AO1-AO2 |
|
|
55,49 |
|
43,15 |
|
|
|
|
DIRECT |
|
CONVERS |
(1) B must be ≤ LG
(2)
to find AO of a star A2 under the pole of A1, we calculate the DA of
A2 under the pole A1
ex: tan pôleA1.tan DecA2=sin DA[A2/poleA1]
(3)
[+] sign if LG and Dec have the opposite sign; sign [-] if LG and Dec
have the same sign
(4) ascensional difference under pole
Always keep in mind that when we talk about converse direction, we are talking about arc in the traditional sense of the term (ie planet --> aspect).
