Algebra of Aspects
In the following pages, I have introduced a new technique of prediction (Algebra of
Aspects). It is based on the well-known principles of astrology and some new
theories. I have indicated a pattern of planets, which exists in all the charts
belonging to persons engaged in any particular profession. The horoscopes can be
divided into three types:
1. Those in which Moon signifies the X house.
2. Those in which Moon gains significance when a planet (other than the Ruling
Planet) is in unison with the luminary.
3. Those in which the Moon is not a Significator of the X house.
As our aim in this article is to prove that the vibrations of planets have a
bearing on man's destiny, we have taken for our discussion the first two types only.
Note: 1. The horoscopes have been cast according to the Nirayana system (fixed or
Sidereal Zodiac). Precision of the equinoxes (Ayanamsa) corresponds to the base
year 291 A.D and Newcomb's rate of precision is used.
2. Porphyry's method of House Division is adopted, taking the Cusp as the
midpoint of a house. The ascendant and the mid-heaven are determined and the arc
is trisected to get the other cusps.
3. The charts are displayed in the South Indian style. The house- cusps are marked
I, II, III, etc.
In the case of bank employees, Jupiter, the governor of finances, among other
things, bears positive relationship to the luminary, Moon.
1
In the case of teachers, Mercury will be related to the Moon
positively.
POLARITY OF PLANETS
A planet becomes positive with respect to the X house when
a) it rules the Sign on the X cusp, or
b) it rules the sign on the Ascendant, or
c) it is close to and above the X cusp (more in longitude than the cusp),
d) it is close to and above the ascendant cusp.
A planet becomes negative with respect to the X house when
a) it rules the sign on the IX cusp, or
b) it rules the sign on the XII cusp, or
c) it lies close to and below the X cusp (less in longitude than the cusp), or
d) it lies close to and below the ascendant cusp, or
e) it lies close to and above the XII cusp.
Note: If a planet has different polarities by rulership and occupation,
ignore rulership.
JUP 16-52 XII 8-24 MOO 1-40
I 10-50 II III
In this Chart Saturn rules Capricorn, the sign on the x cusp. Hence positive. Venus lies close to and above the X cusp. So the planet is positive. Mercury is very close to, but less in longitude than the X cusp (below the cusp). Jupiter is also negative as it rules the sign Sagittarius on the IX cusp. Note that the planet gains negative polarity by being above the XII cusp too.
IV
SAT 26-21 VE 6-14 X 3-32
V
ME 26-43 MAR 20-31SUN 7-34
VIII VII VI
2
IX I5-58
SIGNIFICATION:
Significator of a house is the planet which governs the matters of
the house. A planet signifies the houses it rules or occupies.
Occupation is significant only if the planet is close to the cusp. In
other words the planet must be in conjunction with the cusp. The
orb of conjunction is 11 degrees in the case of the luminaries and
the biggest of planets, Jupiter. For the other planets the orb is 10
degrees.
ME ® 26-01
X 22-44
SU 17-26
JUP 0--3 XII 22-07 MOO 24-27 I 22-49
VE 25-01 XII 24-26 Here Mercury and Jupiter are
positive. Saturn, Moon and Venus are negative.
II
VIII III
VII VI MAR (R) 25-11 SAT 18-38
3
Study the following chart.
The signs Sagittarius and Pisces are ruled by Jupiter, which are on
the ascendant and the X cusps. Hence Jupiter signifies the
ascendant and the X. Saturn signifies the XI and XII houses, by
ruling Capricorn and Aquarius respectively. Being very close to the
X cusp, it also signifies the X. Venus signifies III and VIII houses by
ruling the signs Taurus and Libra. It also signifies VI by being close
to the cusp within 10°. Mercury signifies VI house in addition to IV
and VII houses.
I 19-52 II III IV
XII
V
XIME 9-38VE 11-40SU 20-05
X 16-56 SA 7-12
JU 2-16 IX 15-55 MOO 5-58
MA 6-14 VII 19-52
4
Note: In Vedic astrology, the cusp is taken as the midpoint of the
house, which extends to 15° on either side. In Western astrology,
the cusp is the beginning point of the house.
But we have found, in our research, that the planets exhibit their
influence only if they are very close to the cusp. The cusp is taken
as the midpoint and the house extends on either side of the cusp.
A planet becomes a Significator with respect to the X house when
a) It rules the sign on the X cusp (positive), or
b) It rules the sign on the IX cusp (negative), or
c) Occupies the X house and is close to the X cusp above it, (more in
longitude than the cusp) (positive), or
d) Lies close to the X cusp and is below it (less in longitude) (negative).
ASPECTS - POSITIVE AND NEGATIVE
The vibrations of planets are said to focus at certain angular distances
called Aspects.
The orb of an aspect is the angular distance at which the influence of the
aspect begins or ends before or after the focal point. The longitude of
planets may be measured clockwise or anti clockwise.
MAJOR ASPECTS
5
Angular distances ORB POLARITY
Conjunction(Same
longitude)9° -
Opposition(180°) 7° -
Trine (120°) 6° +
Square(90°) 5° -
Sextile (60°) 4° +
Semi square (45°) 4° -
Semi sextile (30°) 3° +
MINOR ASPECTS
Angular distances ORB POLARITY
15° 2° +
72° 2° +
108° 2° +
162° 2° +
144° 2° +
22½° 2° -
135° 2° -
150° 2° -
6
Note: Whenever the luminaries and the biggest of planets, Jupiter, are in
aspect to another planet, a liberal orb of 2° more for major aspects, and 1°
for minor aspects should be allowed. The same holds for separating
aspects.
Study the following chart.
IV V VI VII
III
VIII
MOO 19-53
VE 19-37
JU 11-30
SA 26-21
ME 24-4 I 16-25 SU 7-51
XII XI
MA 5-41
X 23-13
7
The following table shows the aspects between planets in the above
chart.
SUN MOON MARS MERCURY
JUPITER VENUS SATURN
SUN ___SEMISQUARE 45 (--)
SQUARE 90 (--) ____
SEMISEXTILE 60 (+)
SEMISQUARE 45 (--)
_____
MOON
SEMISQUARE
45 (--)
_____
SESQUI-QADRATE 135 (--)
____CONJUNCTION (--)
CONJUNCTION (--)
BIQUINTILE 144 (+)
MARS
SQUARE
90 (--)
SESQUI-QADRATE
135 (--)
______
TREDECILE 108 (+)
TRINE 120 (+)
SESQUI-QUADRATE 135 (--)
CONJUNCTION (--)
MERCURY
____
___
TREDECILE
108 (+)
____ _____ TRINE 120 (+)
JUPITER
SEMISEXTILE
60 (+)
CONJUNCTION
(--)
TRINE
120 (+)
____ ______CONJUNCTION (--)
SESQUI-QUADRATE 135 (--)
VENUS SEMISQUARE
CONJUNCTION
SESQUI-
QUADRATE
____ CONJUNCTION
____ BIQUINTILE 144 (+)
8
45 (--)
(--)
135 (--)
(--)
SATURN
_____
BIQUINTILE
144 (+)
CONJUNCTION
(--)
TRINE
120 (+)
SESQUI-QADRATE
135 (--)
______
BIQUINTILE
144 (+)
COMBUSTION (ASTHANGAM)
Whenever a planet (other than the Moon) is very close to the Sun (within
8°), it becomes combust. The aspect on and by the luminary is to be taken
into account.
III
MO 0-28
SA 17-19
JU 18-29
V VI
SU 18-02 ME 10-59 VE 5-5
It appears as though there is no aspect on Mercury by Jupiter and Saturn. But note that Mercury is combust and the Sun is in aspect by the two planets. Hence Mercury receives the rays of Jupiter and Saturn. And vice versa, Jupiter and Saturn get the rays of Mercury.
VII
I 12-55 VIII
XII 15-11 MA 15-18
XI
X 21-32
IX
9
UNISON (SAMAGAMAM)
When Moon transits very close to the planets, (other than the Ruling
planet) including the Sun, they attain "Samagama". It is no more a
conjunction. Moon gains the polarity of the associated planet. Unlike in
combustion, the aspect on the planet, not the luminary, should be
considered.
II III IV JUP 6-28 MOO 14-36
SAT19-34 I 10- 20
There is no direct aspect by the Sun on the Moon. But note that Jupiter is in Samagama with Moon and Sun in square to Jupiter.
Hence Sun .............>Square ....> Moon (Jupiter)
VI
XII ME 23-11
XI X VE 13-18 IX 8-10 MA 26-20
SU 2-41
MULTIPLICATION THEORY OF POLARITIES
When a planet A is in aspect to B, it can be represented symbolically as A -
> B and we say that A is related to B. We can say that "A is in aspect to B"
10
or "B is in aspect by A". When A is in aspect to B, B need not necessarily be
in aspect to A. This occurs because the luminaries and Jupiter have a
greater orb than the other planets.
In the above chart, consider Mercury and Jupiter. The angular
distance between the planets is 82°-38" =83°.
Jupiter aspects Mercury. The orb is 7°. The orb of square aspect is
5°.Jupiter being the biggest of planets, has a greater orb of 2°
more.So, Jupiter ----Square (90) ----> Mercury.
But Mercury does not aspect Jupiter, as the prescribed orb is only
5°. Jupiter is in square to Mercury is not in aspect to
Jupiter.
I 19-52 II III IV
XII 6-9-1959, 7-55 AM
11-06 N, 79-22 E
V
XI
Me 9-38
Ve(r)11-40
Su20-05
X 16-56
Sa 7-17 Ju 2-16 Mo 5-58 Ma 6-14
11
Whether the relation is positive or not is to be judged by multiplying the
polarities of the planets and the aspect.
In the above chart, consider the relationship between Jupiter and Saturn
with respect to the ascendant.
Jupiter rules the sign Sagittarius on the XII cusp. Hence negative. Saturn
owns the sign Capricorn on the ascendant and so the planet is positive. The
angular distance is 152-03.
Jup (-) ......... 150 (-)........... > Sat (+) = +
By multiplying the polarities of the planets and the aspect, the product is
positive! So Jupiter bears positive relationship to Saturn with respect to the
ascendant.
Let us consider the relation ship between Mercury and Saturn w.r.t. the VI
house. Saturn rules the sign on the I cusp and hence positive. Mercury is
the lord of Gemini on the VI cusp and gains negative polarity. The angular
distance is 123-14 ~ 120.
Me (-) .........120 (+) ..........> Sa (+) = -. So Mercury is negatively related to
Saturn w.r.t. VI house.
.................................................................
III IV V VI
MO 11-35
JUP 21-48
I 27-27 ME 20-37
SA 23-51 XI X MA 12-00SU 7-37 VE 12-01
12
Bank Employees
Ju 29-12
Bank Employee
7-12-1953 6-56 hrs
79-09 E 12-56 N
I 26-27
Mo 28-43
Su 21-34
Ve 8-38
Me 2-09
XI 0-37
Sa 12-08
XII 28-32
X 2-43
Ma 28-46
It appears as though Moon is not a Significator of the X house, as it is in no
way connected to the X or IX house. But, it may be noted that the Sun,
which rules Leo, the sign on the IX cusp is in Samagama (Unison) with
Moon, being close to it (within 8º). So Moon gains significance and is
negative in character. Jupiter is in opposition to Sun. Jup --180°--> Sun
Jupiter is neutral since it is not connected to the Ascendant, XII, X or IX,
either by rulership or by occupation. Moon is negative because, it attains
the polarity of the planet transiting very close to it.
Ju(N) --180°(-)--> Su(-) (Mo)= +
Moon is positively related to Jupiter.
13
---------------------------------------------
Bank Employee
29-11-1959 11-10 hrs
77-00E 11-00 N
I 20-14
XII 22-59 Sa 12-31
Ju 18-14 Su 13-03 Ma 3-37 Me (r) 2-35
X 28-30 Mo 27-00
Moon is just below the X cusp and hence signifies the house. Jupiter is
combust by being very close to the Sun (within 8º). Sun is 15º away from
the Moon. Sun (Jup)--15º--> Mo. Moon is negative. Jupiter is also negative
as it rules the XII house. Sun (-)--15º (+) -->Mo (-) = + Jupiter bears
positive relationship to Moon!
--------------------------------------------------------------
Ma 20-19 Ve 6-16 Su 11-12 Me 20-17
Bank Employee
26-06-1958 16-45 I.S.T
11-39N 78-12 E
IX
X 16-13
I 14-52 Sa 28-20
Mo 8-27 Ju 28-40
Moon signifies IX house by ruling the sign Cancer. Hence negative in
character. Jupiter is neutral. Jupiter is in conjunction with Moon.
Jup (N) ----- conjunction (-) ------> Moon (-) = +. The relationship is positive.
--------------------------------------------------------------
14
Moon occupies the X house. It is close to the cusp within its orb of
conjunction (10°). The angular distance between Moon and Jupiter
is approximately 64°. So, Jupiter is in sextile to Moon. Jup --60°--> Moon.
Jupiter rules Sagittarius, the sign on the XII cusp. Moreover, it is close to
and above the XII cusp. Hence, it is negative in polarity.
Moon is below (less in longitude) the X cusp. So moon is negative. The
aspect is positive. Jup (-) --60° (+) -->Mo (-) = + It is a positive relationship!
------------------------------------------------------------------
Ma 5-37Me16-44 SU 25-55
Bank Employee 09-05-1960 23-32Hrs. 78-10 E 9-58 N
I 6-54
Sa(R)25-06 XII 16-20 Jup(R) 9-49
Mo 5-39 X 15-11
15
Here, Moon rules Cancer, the sign on the X cusp. So Moon is the significator
w.r.t. the X, the house of profession. The angular distance of Moon from
Jupiter is 61°-05' = 61°. So, Jupiter is in sextile aspect to Moon.
Jup (N) --60° (+) -->Moon (+) = + It is a positive relationship.
-------------------------------------------------------------------------
VII VIII IX
Ju (R) 6-29
Bank Employee
19-09-1950
08-35Hrs. 11-39 N 78-12 E
X 6-37
IV
Ve 18-09 Me 29-00(R)
Mo 5-24 Ma 2-20 I 8-26Sa 0-01 Su2-34
16
Moon rules the sign Cancer on the IX cusp. So it is a Significator. Jupiter
bears semi-square aspect to Moon (43°-17' = 45°). Jupiter is not associated
with IX, X, XII or I. So, it is neutral with respect to the X house. Moon is
negative by ruling IX. Jup (N) --45° (-) -->Moon (-) = + It is a positive
relationship!
---------------------------------------------------------------------------
Mo 19-45
Bank Employee
28-11-1949
07-15 Hrs 78-12 E 11-39 N
Ma 24-11
Sa 25-28
X 27-09
Jup 6-27
Ve 29-26Su 12-28 Me 15-55 I 24-05
17
Moon rules the sign on the X cusp. So, Moon becomes a Significator with respect to
the X house. The luminary is 151°-39' away from Jupiter. The nearest aspect is 150°
(orb allowed is 2°). Though Moon rules X, it is very close to the Ascendant cusp and
is below the cusp (less in longitude). So, it is negative in character (Occupation is
more powerful than rulership).
Jupiter is neutral. The aspect is negative. Jup (N) --150° (-) -->Moon (-) = +
It is a positive relationship!
-------------------------------------------------------------------------
Jup 15-27 VII VIII IX
Su 6-39
Bank Employee 20/21-01-
1952 01-30 Hrs 11-39 N78-12 E
X 21-57
IV
Me 17-07 Ve 28-38
Ma 7-16
Mo13-48
I 23-13
Sa 21-53
18
Moon is within 10° from the X cusp and hence signifies the house of profession. The
luminary is 108° away from Jupiter, which is an aspect.
Jup--108°-->Mo. Moon is transiting above the X cusp at the moment of birth.
Hence positive in quality with respect to the X house, though it rules the sign on
the II cusp as occupation is stronger than rulership. Jupiter is neutral.
Jup (N) ---- 108° (+) ---> Moon (+) = + the relationship is positive with respect
to the X house.
----------------------------------------------------------------
VIII IX X 21-13 Mo 0-50
Jup 12-37Bank Employee
11-12-1962 23-50 Hrs
11-39 N 78-12 E
Sa 14-40
Ma 0-16 I 19-48
Me 5-00 Su 26-00 Ve 20-18II
Ma 3-27 Ve 8-25 Me 0-31 Su 18-20
X 17-20
Sa (R) 0-05I 16-03 Mo 27-04
Ju(R) 28-59
19
The sign Cancer is on the IX cusp. Hence, Moon becomes a Significator with respect
to the X house. Moon is approximately 60° away from Jupiter.
Jup --60°--> Moon.
Moon is negative by rulership of IX. But being close to the Ascendant cusp and
above it (more in longitude), it gains positive polarity. As occupation is more
powerful than rulership, Moon is considered positive. Jupiter is neutral. Jup(N) --
60°(+)-->Moon(+) = +
It is a positive relationship! So the native has become a bank employee!
-----------------------------------------------------------------
20
This horoscope belongs to a teacher. Mercury is Trine to Moon. Mercury,
the indicator of Education is negative by being close to and above the
XII cusp. Moon is also negative by ruling Cancer.
Me (-) -- 120º (+) --> Moon (-) = +
So, Mercury is positively related to Moon with respect to the X house.
------------------------------------------------------------------------------
Ma 23-05 Sa (r) 4-42 Ju (r) 28-30 Mo 22-03
Teacher
13-10-1941
9-00 AM
82-14 E 16-57 N
X 11-43
I 19-04 Ve 9-47
XII 9-57 Me 18-54
Su 26-28
21
Ve 23-56 XII 11-04 Me (r) 11-17 Su 25-38
I 14-00 Ju 23-27
X 5-12 Mo 1-31
Teacher 10-05-1931 7-10 AM 78-12 E 11-39 N
Ma 21-38
Sa (r) 0-26
Moon is just below the X cusp signifying the house, negative in character.
Mercury is in Quintile aspect to the Moon (72º). Mercury just above the XII
cusp; the planet is negative in polarity.
Mercury (-) ----72º (+) ----> Moon (-) = +
-----------------------------------------------------------
22
Ma (r) 22-21 Sa (r) 1-32
Teacher 29-11-1943
7-10 AM
78-12 E 11-39 N
IX
X 26-25Jup 3-44
Mo 1-40 I 23-29 Me 23-21 Su 13-01
Ve 26-50
Moon rules the sign Cancer on the IX cusp.
But it is very close to and above the ascendant.
(More in longitude than the cusp). Occupation is stronger than rulership.
Hence Moon is positive. The luminary is in conjunction with Mercury (8
degrees). Mercury is in rapt conjunction with the ascendant, but below it.
Hence negative.
Mer (-) ----conjunction (-) -----> Mo (+) = +
Mercury bears positive relationship to Moon with respect to the X house.
-------------------------------------------------------------------
Mo 15-40 Ju (r) 28-24
Sa 21-51 Ma 6-20
Teacher
30-01-1966
12-30 AM
78-12 E 11-39 N
X 16-00
Su 16-10 Me 11-20 Ve (r) 10-37
I 17-40
23
Moon signifies X house by ruling the sign on the X cusp.
Mercury rules Virgo the sign on the XII cusp and so negative in polarity.
It is combust by being very close within 8 degrees to Sun.
So consider the aspect by Sun to Moon. Moon is in square (90) by Sun.
Mer (Sun) (-) ---- Square (-) -> Mo (+) = +
-----------------------------------------------------------------
Ju 15-27
Su 6-39 Teacher
21-01-1952
1-30 AM
78-12 E 11-39 N
X 21-57
Me 17-07 Ve 28-38 I 23-13 Mo 13-48 Ma 7-16
24
Moon is positive by rulership but negative by occupation. Note that
the luminary is very close (within 10 degrees below) to the ascendant.
Hence negative in polarity.
Mercury rules Virgo the sign on the XII cusp. Hence negative.
Mercury is in sextile aspect to Moon (The orb is nearly 4 degrees)
Mercury (-) ---- 60 (+) ---- -> Moon (-) = +
The relationship is positive.
---------------------------------------------------------------------
25
Ju (r0 6-29Teacher
19-091950
8-35 AM
78-12 E 11-39 N
X 6-36
Ve 18-09 Me (r) 29-00
Mo 5-54 Ma 2-20 I 8-25 Sa 0-01 Su 2-34
Here Moon is positive. Mercury is combust by being very close to Sun.
Mercury is negative by ruling Virgo the sign on the XII cusp.
Sun is in Square aspect to Moon (90 degrees).
Sun (Mercury) (-) ------90 (-) ----> Moon (+) = +
By multiplying the polarities of the planets and the aspect, the product is
positive.
Mercury bears positive relationship to Moon w. r. t. the X house.
Ma 17-06 IX
Teacher
26-12-56
2-25 AM
77-37 E 12-56 N
X 10-15
Me 0-44
Su 10-56 Sa 15-29 Ve 14-25
I 11-45 Ju 7-56 Mo 29-02
26
Moon rules Cancer, the sign on the X cusp. Hence, positive. Mercury gains
negative polarity by ruling Gemini on the XII cusp. Mercury is exact square
to Moon. Mercury (-)..... Square (-) .......> Moon (+) = +
CONCLUSION
It is now clear that man’s destiny is already predetermined at the moment
of birth.
From the discussion of the example charts, it will be clear that we have
proved two things.
a) The ruling planet is invariably related to Moon by aspect.
b) The relationship is always positive with respect to the X house.
An interesting point to be noted is that Jupiter or Mercury does not rule
any one profession. For example Jupiter has law, priesthood etc in his
domain. Mercury rules communication, statistics etc in addition to
teaching.
"All crows are black birds" but "All black birds are not crows". The converse
is not always true. Mercury should be positively related to the Moon in a
teacher's chart. But if the planet is positively related to the Moon in a
27
chart, the native need not be a teacher! He can be an ambassador, auditor
or a journalist.
Hence the need for research to find out which planets bear positive
relationship to the Moon in the chart for any particular profession (In case
the luminary gains significance to the X house).
Any point of the zodiac moves very fast over the cusps (at the rate of one
degree approximately for every four minutes). The planets gain or lose
their significance of houses and their polarities are also altered within a
very short time. This explains why twins born with a few minutes'
difference have different characteristics.
Algebra of Aspects is a technique, which can be employed successfully for
rectification of unknown birth times.
.............................................................................................
28