a book on mathematical astrology

A BOOK ON

MATHEMATICAL !C,';

ASTROLOGY

Y.K. BANSAL

Publisher

• Bharatiya Prachya Evam Sanatan Vigyan Sansthan

•

CONTENTS

Prayer to Ganesh, Goddess Saraswati and the

Nav Graha (i)-(ilU

Preface (v)

1. Chapter 1

Astrological terminology I

Solar System, The earth, Equator, North & South

Hemisphere, Geographical longitude and Latitude

1-15

2. Chapter 2'

Astrological Terminology II

Celestial Sphere, Celestial Poles, Celestial Equator,

Ecliptic, Zodiac, Celestial Longitude, Celestial Latitude,

Declination, Right Ascension, Oblique Ascension

16-22

3. Chapter 3

Astronomical Terminology III

Equinoctial points, Precession of Equinoxes, Movable

& fixed Zodiac, Ayanamsha, Sayana & Nirayana

System, Determination of Approximate. Ayanamsha,

nakshatra, Ascendant, Tenth house (Me) Table of

Ascendants, Tables of houses and Ephemeris 23-31

4. Chapter 4

Time Measure

Siderial day, Siderial year, Apparent Solar day, Mean

Solar day, Months, Lunar Month, Solar Month, Years,

Tropical Year, Anomalistic year. 32-35

5. Chapter 5

Time Differences

Local time, Standard time, Greenwich Mean time,Conversion of time, Time Zone, LMT Correction

36-47

6. Chapter 6

Sidereal Time

Necessary to have the Sidereal time system, SiderealTime of a given moment. 48-56

7. Chapter 7

Sun Rise & Sun Set

Sunrise, Sunset, Apparent Noon, Ahas & Ratri,Calculation of Time of Sunrise & Sunset. Calculationof time of Sunrise and Sunset by method 'ofinterpolation 57-61

+;:a4*4

8. Chapter 8

Casting of Horoscope I

Forms of horoscope. Modem and Traditional

Method of casting Horoscope.

9. Chapter 9

Casting of Horoscope II

Calculation of Ascendant for placessituated in Southern Hemisphere

10. Chapter 10

Casting of Horoscope m(Modern Method)

Graha SpastaILongitudes of planets

62-68

69-73

74-82

11. Chapter 11

Casting of Horoscope IV

Using Condensed Ephemeris 1941-1981. 83-88

12. Chapter 12

Casting of Horoscope V

Condensed Ephemeris 1900-1941 89-93

13. Chapter 13

Casting of Horoscope VI

Vimshottari Dasha System, Janma Rashi, JanmaNakshatra, Basis for Vimshottari Dasha System.Calculation of Vimshottari Dasha Balance at

Birth 94-98

14. Chapter 14

Casting of Horoscope VII

Major and sub-periods, Vimshottari Dasha, AntarDasha 99-102

15. Chapter 15

Casting of Horoscope VIII

Traditional Method, Rashiman, Calculation of lagna atDelhi, Calculation of planetary position (Longitudesof planets), Calculation of Dasha Balance 103-109

16. Chapter 16

Bhavas

Bhavas X Cusp, MC etc. 110-119,17. Chapter 17

Shadvargas 120-127

18. Saptavarga Calculation 128-130

19. Index 131-132

(0

Offering Prayer to the Lord Ganesha,Goddess Saraswati and the Nav Grahas

Dear Students,

1.1 We, the members of the Indian Council ofAstrological Sciences (Regd.) Chennai, welcome you to thecourse for NOTISHA PRAVEEN. Before we take you tothe study of the subject namely 'Mathematical Astrology'through a series of specially designed course material tomeet your requirements; it is important to invoke the blessingsof the Almighty God. Astrology, as you may be aware, is adivine science and therefore is very sacred.

1.2 The beginning of any auspicious deed is always'preceded by offering prayets to lord Ganesha, who is alsothe lord of intelligence:

.~ '!('MJIIRaf4a .,.;if:l<'!l\if,\~~ I~ ~~ f<t;m~ ~ ~CR qIGq~\ifo:t I I

Gajaananam BhootganaadisewitamKapittha Jamboo phal saarbhakshanam.Umaasutam ShokavinaashakaaranamNamaami Vighneishwara Paadapankajam

Which means :I prostrate before the lotus-feet of lord Vighneshwara,

the offspring of Uma, the cause of destruction of sorrow,worshipped by bhutaganas (the five great elements of theuniverse viz. fire, earth, air, water and sky) etc., who has theface of a tusker and who consumes the essence of kapitthaand jambu fruits.

2 Mathematical Astrology

12. Zodiac

13. Celestial longitude (Sphuta)

! 14. Celestial latitude (Vikshepa)

15. Declination (Kranti)

I 16. Right ascen'sion (Dhruva)

17. Oblique ascension or Rashimaan

18. Equinoctial points

19. Precession of the equinoxes and Ayanamsha

20. Moveable and fixed zodiacs

21. The Sayana and Nirayana system

22. The table of Ascendants

23. The Table of Houses

24. The Ephemeris

1.3 We will now take the above mentioned terms and. discuss these one by one so as to make these terms clear tothe students. It may however be mentioned here that a largenumber of the above mentioned terms are quite simple andself explanatory. Most of the students, particularly thosewho have studied the geography as a subject during theirschool education, would be familiar with the terms mentionedabove. Nevertheless we.will discuss and explain all the abovementioned terms in a systematic manner so that the veryconcept of these terms is understood by the students.

1.4 The Solar System

• Our Solar System is centered round the Sun. Nineplanets viz. Mercury, Venus, Earth, Mars, Jupiter,

, Saturn, Uranus (or Herschel), Neptune and Pluto

·CHAPTER 1ASTROLOGICAL TERMINOLOGY I

1.1 Under this topic 'Astrological Terminology' wepropose to discuss and acquaint our students with variousterms and their meaning, definition, etc. commonly used inastrology, particularly those used in mathematical Astrology.In addition, certain astronomical terminology will also bediscussed in these lessons, to the extent these are used inmathematical astrology. A more detailed exposition of theseastronomical terminology is available to the students in thebook'Astronomy Relevant to Astrology' by VP. Jain.

1.2 The various terminology with which the studentsare expected to be familiar are as follows :

1. The solar system.

~. The earth

3. The equator of the earth

4. Northern hemisphere, and southern hemisphere.

5. Geographical longitudes (Rekhansha)

6. Geographical latitudes (Akshansha)

7. Meridian of Greenwich as reference point at theearth's equator

8. Celestial sphere or the cosmic sphere

9. Celestial poles \'J' .\

>.~ i,~

10. Celestial Equator

11. Ecliptic or the Ravi Marga(1)

Mathematical Astrology J

alongwith belt of Asteroids revolves in elliptical orbitsaround the Sun.

In Hindu Astrology, the last three planet i.e. Uranus(or Herschel), Neptune and Pluto have no place. On theother hand the classical Hindu Astrology recognises the Moonand the two shadowy planets i.e. Rahu and Ketu (or theMoon's Nodes) as equivalent to planets. Rahu and Ketuare not physical bodies but are mathematically calculatedsensitive points of intersection of the orbits of the Moonand the Sun (or in fact that of the Earth but which appearsto be that of the Sun).

1.4.1 The planets Mercury and Venus are situated inthe space between the Sun and the Earth. These planets aretherefore known as 'Inner Planets'. These are also known as'Inferior Planets'.

SOLAR SYSTEM

------------------ ---__. 0 --------- _- -. - - - - - - - - - - - - - - P':u~o D NEPTUNE

- - - - - - URANUS-0 -- --.., ------~- --~-------- ~-~

._-------~- ----~-------- ------ ~-~---- --~ ~---- --.... -....... -- ..... .... ........

.- -~ ~ ~ ~ ~ ~ o , ' 'OJ,UP,I~R' , , 0,...,- MARS',

, .... ...., SATURN

~---------~', , '... ----... ',' \ '

.. , , .... ' ~AR';;;cJ \ \ \

'\ I \\ '" IMERCURY 0 'YVENU,' \

I I \" I I I ,

,/ I

Figure 11.4.2 The other three planets namely Mars, Jupiter and

Saturn are so situated in the space that their orbits are on

6

CENTRE OF THE.EARTH

IMAGINARY PLANEPASSING THROUGHTHE CENTRE OFTHE EARTH ANDPERPENDICULARTO EARTH'S AXIS

N

5

Mathematical Astrology

EARTH'S SURFACE

Figure 3

1.7 Northern and Southern Hemisphere

We know that the globe of the earth is not a perfectsphere like a ball. In fact the earth's diameter along theequator is larger than its diameter along the axis due to thefact that the earth is slightly flattened at the poles where asit is slightly bulging out at the equator. The shape of theEarth is comparatively more similar to that of an orange ora melon rather than that of a perfect sphere. Even then, foreasy comprehension/calculations and understanding thevarious phenomenon, we consider the earth's globe to be aperfect sphere, though it is actually not so. In Para 1.6above we have seen that the imaginary plane cuts the earth'ssurface in a great circle known as earth's equator. However,if the same plane was to cut the earth's globe (or the sphere)

" into two parts, each part will be exactly half of the sphere. and will therefore be known as the Hemisphere. The

hemisphere towards the North end of the axis of the earthis known as Northern Hemisphere. Similarly the hemisphere

Malhcmattcal Astrology 7

towards the south end of the axis of the earth is known as'Southern Hemisphere. Figure 4 illustrates the abovephenomenon clearly where in the two halves of the earth'sglobe have been shown separated at the plane of the earth'sequator.

N

AXIS OFTHE EARTH

s

EARTH·SEQUATOR

Figure 4

1.8 Geographical Longitudes iRekhanshasAnd Geographical Latitudes (Aksltansha)

In order to fix the position of an object or a point ona plane, we have to divide the plane by drawing two sets ofparallel lines at equal intervals perpendicular to each other.A graph paper which all of us would have used in ourschool days, is a good example to understand thisphenomenon. In the adjacent figure 5 we have two sets ofparallel lines which are at equal intervals and at the sametime are perpendicular to each other, i.e. to say that all linesin N-S direction are perpendicular to all the Lines in W-Edirection. Similarly all lines in W-E direction are parallel to


each other but perpendicular to the lines in N-S direction.'With the help of these equidistant parallel and perpendicularlines, we can correctly find the coordinates of any givenpoint viz. A, B, C or D with reference to any given pointof reference (say '0'). For example:

For 'J>; we can say 7 units in E direction and 7 units in N

direction.

For 'B' we can say 6 units in W direction and 5 units in

N direction.

For 'C' we can say 8 units in W direction and 8 units in

S direction.

and similarly

For 'D' we can say 4 units in E direction and 5 units in S

direction.N

w

- ."6.1

,Il

C

E

s• Figure 5

Alternatively, if the coordinates of any point are known,we can locate the point exactly on the plane by counting thenumber of units indicted by the coordinates, in the appropriate

Mllthcmatical Astrology 9

direction. The same concept is applied to the earth's surfacealso with slight modifications as the surface of the earth isnot a perfect plane but is having curvature, the earth's globebeing a sphere for all practical purposes.

1.8.1 The surface of the earth's sphere is imagined tobe cut by several planes each one of them passing throughthe centre of the earth and perpendicular to the plane ofEarth's equator. These planes will describe imaginary circleson the surface of the earth so that each one of these imaginarycircles will be passing through the North as well as theSouth pole of the earth and will have the same centre as thatof the earth. The distance measured along the surface of theearth between any two such consecutive circles will be zeroat both the poles (as all the circles will be passing throughthe poles) and will be maximum at the equator. These circlesare known as the 'Meridians of Longitude'. These havebeen explained in the figure 6.

MERIDIANS OFLONGITUDE

~NORTHPOLE

EARTH'SeQUATOR

'r"

; , s' SOUTH POLE

Figure 6

10

,.


1.8.2 Again let us imagine the surface of the earth tobe cut by imaginary planes which are all parallel to the planeof earth's equator. These planes will also describe circles onthe surface of the earth and the centres of all such circleswill be falling on the axis of the earth and each one of thesecircles will be parallel to each other as well as parallel to theearth's e.quator. These circles are known as parallels ofLatitude. These have been explained in the figure 7.

It may be seen from the figure that all these circles(parallel of latitudes) have their centres on the axis of theearth just like equator also has its centre on the axis of theearth. These are shown as 0, 01, 02 and so on upto 06 inthe figure.

1.8.3 Students will recall that the 'meridians oflongitudes' are nothing but concentric circles on the surface.of the earth whose planes are all perpendicular to the planeof equator. Similarly, the 'parallels of latitudes' are againcircles on the earth's surface but with their planes parallel tothe plane of earth's equator. It is therefore self evident thatat any given point on the surface of earth, the meridian oflongitude and the parallel of latitude will be mutuallyperpendicular to each other and will therefore intersect eachother at right angles or 900

•

1.8.4 Students are advised to re-read Para 1.8.1 to1.8.3 above so that the application of the concept of 2 setsof equidistant parallel lines, each set being mutuallyperpendicular to the other set (Para 1.8) could be properly

, understood by them to locate or identify any place or cityon the surface of the earth.


EARTH'SEQUATOR

.'j

l"WI~'~:·i'_\'p""~r. (""";I·":'V'ln"~·rr-,,~..,~~, .~

11

N

s

Figure 7

1.8.5 We have already seen that the earth's equator isa circle. As any circle comprises of 360° of arc so the earth'sequator will also have 360°, For easy comprehension, wemay imagine that there are 180 numbers ofconcentric circlesdrawn on the surface of earth in such a way that their planesare perpendicular to the plane of earth's equator, These 180circles will describe 360 lines on the surface of earth (eachcircle will give two lines i.e. one in the front and the otherat the back) which as we already know (Para 1.8.1) areknown as meridians of longitudes. Each of these 360meridians of longitude will pass from both the poles of theearth and at equator will be 1° apart. The distance betweenany two consecutive lines measured along the surface ofearth will be maximum at earth's equator which will go ondecreasing as we proceed along these lines either towardsNorth. Pole or towards the South Pole where it willbecome'Zero' .


1.8.6 We may also consider for easy comprehension

that the circles which are known as the Parallels of Latitude

are also 180 in numbers i.e. 90 circles in the Northern

Hemisphere and the remaining 90 circles in the southe~n

Hemisphere so that the angular distance (angle substanded

at the centre of earth) between any two consecutive circle

is 10 again as in the case of Meridians of the longitudes. We

will therefore, have a set of parallel lines at 10 angular distance

apart running from E to W or W to E around the earth's

globe all of which will be perpendicular to the Meridians of

longitude (para 1.8.3).

1.8.7 We can now super-impose the figures 6 and 7

and see that the new figure formed by merging or super

imposing the two figures will have a graph like appearance

drawn on the surface of the earth which by and large will be

somewhat similar to figure 5. The only exception will be

that the lines in N-S direction or the Meridians of longitudes

will not be eactIy parallel to each other in the true sense..However as the students may be aware that earth's globe

has a circumference of about 40,232 kms or 25,000 miles

(approx.), the space of earth's surface covered beween two

consecutive lines of 1° angular distance in N-S as well as E

W directions will be roughly of the order of 110 kmsIx 110

kms or 69 miles x 69 miles. Hence we may consider them

Co be parallel for the place or city under consideration.

\

II

Mathematical Astrology 13

N

80 90"

110' 90'

S

-"t:'r-t--+--+~-+--+-+-+-r)-- PARALLELSI OFLAnruDEs

MERIDIANS OF--:T--ll----it---'~~~~-+-+_ilLONGITUDES

Figure 81.8.8 From the figure 8 above though it is clear that

the meridians of longitudes are never exactly parallel in thestrict sense, but as explained in para 1.8.7 for the limitedspaces marked as 'N, 'B', and 'C' on the earth's surfacethese meridians (shown by dotted arrows in the figure) areconsidered as parallel. Therefore the conditions of figure 5in para 1.8 above are considered to have been fulfilled.

1.8.9 Having drawn 2 sets of parallel lines at equaldistance which are mutually perpendicular also, we are nowset to locate any place on the surface of earth. We now onlyneed to know its coordinates from a given reference point.In the context of earth's globe these coordinates are knownas 'geographical longitudes' which are measured along theearth's equator either towards 'East' or 'West' from thereference point/line. The other coordinate being thegeographical latitudes which are measured in perpendiculardirection from earth's equator either towards 'North' or'South' from the reference point or line. For the purpose of

1-1- Mathematical Astrology

•

longitudes, the reference line or the reference meridianhas been chosen as the meridian passing throughGreenwich near" London. This meridian i.e. the meridianpassing through Greenwich is considered as 0° longitudeand the longitudes of all other places on earth is measuredwith reference to this meridian only either towards Eastor towards West. Hence all places, cities etc. on the surfaceof earth are located within either OOE to 1800E longitude orOOW to 1800W longitude. Similarly for the purposes of

I~ latitudes the reference line or parallel of latitude is theequator itself. The latitudes of all places, cities etc.situated on the surface of the earth are measured fromthe equator whose latitude is 0°, either towards Northor South depending on whether the place is in Northernor Southern Hemisphere. Hence the latitudes vary fromOON t0900N for places in Northern Hemisphere and fromOOS to 900S for places situated in Southern Hemisphere.Thus the point ofintersection of 0° longitude i.e. the Meridianof Greenwich with the Earth's Equator is considered as thereference point '0' shown in fig. 5.

1.8.10 Students would have seen that the explanationfor Geographical longitudes and latitudes have been dealtwith in much greater detail and is quite exhaustive in itscontent. If the phenomenon is clear with reference to theearth's globe, studens will find it easy to understand whenthe same is applied to the space and the planets, which is ofour primary concern while talking about the Astrology.

EXERCISE - 1

Question 1 : Write short notes on .:

(a) Terrestrial Equator (c) Meridians oflongitudes


(h) Northern and Southern (d) Parahels of latitudesHemisphere

Question 2 : Describe briefly our solar system indicatingthe inner and outher planets.

Question 3 : Find out with the help of an Atlas, theGeographical longitudes and latitudes of the places givenbelow:

(a) Allahabad (b) Anantnag (c) Calcutta

(d) Bangkok (e) Vetican city (j) Sitka

(g) Yokohama (h) Iceland (k) Hanoi

(l) Kanazawa (m)Mokameh (n) Manila

CHAPTER·2

ASTROLOGICAL TERMINOLOGY II2.1 In the previous chapter we have seen how to locate

or define a place on the earth's surface. We will now apply thesimilar principles to the space and see how to locate or definethe position of various planets situated in the space. For thispurpose, we will have to imagine that the entire space aroundour planet earth is a huge sphere with infinite diameter whichextends far beyond the farthest of the planets with which weare concerned in Astrology. So living on this planet earth, theother planets in the space including the sun and the Moonwould appear to us to be situated on the imaginary surface ofthis imaginary sphere.

2.2 Celestial Sphere or the Cosmic Sphere

The imaginary sphere in the space surrounding our entireSolar system, mentioned in Para 2.1 above, is known as thecelestial sphere or the cosmic sphere.

2.3 Celestial Poles

If the Earth's axis is extended infinitely towards Northand South, it will meet the imaginary surface of the cosmicsphere or the celestial sphere at some point. These points onthe surface ofcosmic sphere are known as the CelestialPoles

. and the extended axis becomes the imaginary axis of the

• celestial sphere.

2.4 Celestial Equator

The projection of earth's equator or the terrestrialequator on the imaginary surface of the celestial sphere is

(16)


known as the Celestial Equator.

2.4.1 As the earth's equator divides the earth's globe intotwo halves, similarly the celestial equator divides celestial orcosmic sphee into two equal halves or hemispheres. Theseare known as Northern celestial hemisphere and the Southerncelestial hemisphere.

2.5 Ecliptic (Ravi Marg)

The apparent path ofthe Sun in the space along whichit seems to move around the earth is known as Ecliptic.This is also known as Ravi Marg. The Ecliptic or the RaviMarg, like the orbits of other planets is not a circle but iselliptical or oval in shape. Ecliptic can also be defined as aprojection of Earth's orbit around the Sun on to the surfaceof cosmic sphere. The plane ofEcliptic is inclined to the planeofcelestial equator at an angle of about 23YzO due to the slant!inclination of the earth's axis to the vertical. Figure 9 givenbelow will clarify the position.

PLANE OFECLIPTIC

s

N. POLE OFN CELESTIAl

_---.....:S~PHERE

---.;,>---~ ~

S. POLE OFTHE ECUPTIC

CELESTIALSPHERE

PLANE OFCELESTIALEaUATOR

CELESTIAL"'I/EQUATOR

--+--.

ii... Figure 9 '.: ,


2.6 Zodiac

If one observes the movement of planets, it is seen that

they also move in their own orbits along with the Sun's path,but their path deflects north-south also. However the planetsnever proceed more than 9° either north or south ofthe ecliptic.Hence if a parallel line on either side ofthe ecliptic is drawn atan angular distance of about 9° then the ecliptic will come inthe middle and either side will be a broad band/path way inwhich all planets can be located. This imaginary belt/bandstretching about 9° north and 9° south of the ecliptic withinwhich the planets and the Moon remain in course of theirmovement in the heavens, is known as Zodiac. In astrologywe refer to this broad band of 18° instead of referring to theentire sky.

2.7 Celestial Longitude (Spltuta)

This is the arc of the ecliptic intercepted between thefirst point of Aries (Nirayana) and a perpendicular arc to theecliptic drawn through the body (planet) and the poles of theecliptic. In other words it can also be defined as the angulardistance of any heavenly body (viz. planets etc.) measured indegrees along the ecliptic, in one direction from the origin (orthe reference point - first point ofAries of the zodiacal signor the vernal Equinox). The first point ofAries is different inSayana and Nirayana system. Students will recall that in thecase ofGeographical longitudes, the measurement was along

he terrestrial equator and it was either towards east or westfrom the Greenwich or the reference point or 0° longitude sothat the maximum longitude of any place on the surface of• earth could be either 1800E or 1800W. However in the case ofZodiac or to say the celestial sphere, the measurement ofcelestial longitude of any planet is in one direction onlyfrom the origin or the reference point. As such the celestial

,~"Jrr'" '''l!It' '",,' liA!",' ,..Marhcmatical Astrology 27

S,No, Name of E:'I.1~nt Extent Lord of No, of

tNakshatra (Longitude) Sign Rashi Nakshatra years in

Star Virnshottari

Dasha

7. Mithuna 20° to nJPITERt,_

Punarvasu 80° to 93°20' 16 l~

Karka3°20',,~

8. Pushya 93°20' to 106°40' Kafka 3°20' to SATURN 19

Karka 16°40'

9. Ashlesha 106°40'to 120° Karka 16°40' to MERCURY 17

Karka30° or

SimhaO°

"Iii: TOTAL 120--10. Magha 120° to 133°20' SimhaOOto KETU 7

Simha 13°20'

11. Poorva 13302O'to 146°40' Sirnha 13°20' to VENUS 20Pha1guni Simha 26°40'

12. Uttra 146°40' to 160° Simha 26°40' to SUN 6Phalguni Kanya 10°

13. Hasta 1600to 173°20' Kanya 10° to MOON 10Kanya 23°20'

14. Chitra 173°20'to 186°40' Kanya 23°20' to MARS 7Tula6°40'

15. Swati 186°40' to 200° Tula 6°40' to RAHU 18Tula20°

16. Vishakha 200° to 213°20' Tula 20° to ruPITER 16Vishchika 3°20'

17. Anuradha 213020'to 226°40' vrisldUka 3020'to SATURN 19 J"';'

Vrishchika 16°40'

18. Jyeshtha 226°40' to 240° Vrishchika 16°40' MERCURY 17

to Vrishchika 30°orDhanUO°

TOTAL 120.......-19. Moola 240° to 253°20' DhanuOOto KETU 7

Dhanu 13°20'

20. PoorvashadJa 253°20'to 266°40' Dhanu 13°20'to VENUS 20Dhanu 26°40'

21. Uttrashadha 266°40' to 280° Dhanu 26°40' to SUN 6Makara 10°

22. Shravana 280° to 293°20' Makara 10° to MOON 10Makara 23°20'

28

S.No. Name ofNakshatra

Star

Extern(Longitude)

Extent

Sign Rashi


Lord of No. of

Nakshatra years in

Vimshottari

Dasha

23. Dhanishtha 293°20' to 306°40' Makara 23°20' to MARS ·7Kurnbha 6°40'

r.:24. Shatahhisha 306°40' to 320° Kumbha 6°40' to RAHU 18

Kumbha 20°

25. Poorva 320° to 333°20' Kumbha 20° to JUPITER 16

Bhadra Meena3°20'

-7.':'2'6. Uttra Bhadra 333°20' to 346°40' Meena 3°20'to SATURN 19Meena 16°40'

27. Revati 346°40' to 360° Meena 16°40' to MERCURY ~7

Meena 30° or

MeshaO°

TOTAL 120

3.9 Ascendant or Lagna

The ascendant or thelagna point is the point of

intersection of the ecliptic at the given time with the horizonofthe place. In astrology it is the first house ofthe horoscope.

This point of intersection is very important as it is considered

to be the commencing point ofthe horoscope. The earth rotates

on its axis from West to East in about 24 hours. Due to this

rotatory motion the whole sky (Zodiac) appears to come up

from below the horizon gradually. The Ascendant or the Lagna

is the 'Rising sign' in the eastern horizon. The period of each

lagna is not equal like the rashi or the sign division. As all the

12 rashis or signs must rise one after the other in a day (due to

rotation ofearth on its axis once a day) each rashi/sign becomes

the lagna one after the other consecutively, with the passage

• of time. The names of the lagnas or the Ascendants are the

same as that of the rashi/sign rising at any given time.

3.10 The Tenth House or M.e.

The point ofintersection ofthe ecliptic with the meridian


Question 2 : Write short notes on :

(a) Precession of Equinoxes (b) Moveable and Fixedzodiacs (c) Ayanamsha

Question 3 : What do you understand by Sayana andNirayana sytem ? which system do you prefer and why?

Question 4 : What is the yearly rate of precession ofVE. ? Do you consider the year 285 AD or 397 AD as theyear of coincidence of both the Zodiacs i.e. Nirayana andsayana ? Work out the approximate Ayanamsha for the year2003 considering the year of coincidence as 285 AD as wellas 397 AD.

Note: Students are advised to have with them the Bookentitled "A Manual of Hindu Astrology" by Dr. B.V Ramanfor a fuller treatment and understanding of MathematicalAstrology.


(a) Lunar Month or Chandra Maan : It has 30 lunardays or Tithis and is measured from New Moon to next newMoon. At some other places it is measured from Full Moon to

next Full Moon.

(h) Solar Month or Saur Maan : It is the time the 'Suntakes to move in one sign and is measured from one Sankrantito the next Sankranti.

4.9 Years

In Hindus there are three types ofdifferent years in voguewhich are as follows.

(a) The Savanayear : It has 360 mean solar days

(b) The Lunar year: It has 354 mean solar days

(c) The Nakshatra year : It has 324 mean solar days

4.10 Tropical Year

The Tropical Year or the year of seasons, is the time ofthe passage of the sun from one Vernal Equinox to the next

,Vernal Equinox. The VE. point slips to the west at the rate of

50.x" per year.

4.11 Anomalistic Year

The anomilistic year is the mean interval beweensuccessive passages ofthe earth through perihelion. Perihelionis the point on a planetary orbit (in this case earth) when it isat the least distance from the Sun.

4.12 The lengths of different years mentioned in para4.5,4.10 and 4.11 above, according to modem calculation (as

• given by Dr. B.V Raman in his book A Manual of HinduAstrology) are as follows:


"'-Year

D

The Tropical year 365

The Sidereal year 365

The Anomalistic year365

EXERCISE-4

35

Length

H M S

5 48 45.6

6 9 9.7

6 13 48

(i) 55 Ghati 23 pal (ii) 2 Ghati 56 Pal(iii) 32 ghatis

Question 3 : Convert the following into Ghati, Pal andVipal

(i) 6 Hrs 45 Min 30 Sees (ii) 13 Hrs 49 Min 36 Sec

(iii) 21 Hrs 3 Min 45 Sees (iv) 17Hrs21 Min 12 Sec

•

CHAPTERS

TIME DIFFERENCES

5.1 Students are aware that the Sun is the creator oftime,day and night and the seasons. A Hindu day commences fromthe sunrise and remains in force till the next sunrise, when thenext day commences. When the sun is exactly overhead it iscalled Mid day or Local noon. At the moment of sunrise forany place, the local time for that place is Zero hour (or Ghati)as per traditional Hindu systemofreckoning the time.Howeveras the earth is not a flat body but spherical and also rotatingon its axis, the Sun rises at different times at different places.As the rotation of the earth on its own axis is from west toeast, it is evident that the eastern part ofthe earth will seethe Sun first, and due to the rotation of the earth, furtherwestern parts of the earth moves towards east gradually andsee the Sun. This process goes on and.on. In other words, aswe live on this planet earth we do not see or feel the rotationofthe earth from west to east, but we see that the Sun rises inthe east and gradually comes over head and then sets in thewest.

5.2 Local Time

We have seen above that the eastern parts of the earthwill see the Sun first and subsequently as more and morewestern parts move to east due to rotation of earth, thoseparts will also gradually see the Sun. In other words it meansthat the Sun will rise later at a particular place as compared toa place towards east of the earlier place. It therefore implies

(36)


that Zero hour of the day will commence earlier at a placewhich is in the east of another place where the Zero hour ofthe day will commence later. Similarly the Noon time or theMid day will occur earlier in the eastern part of the earth ascompared to any place towards west of the earlier place. We

, know that earth complete one full rotation (360°) on its axisin about 24 hours or 24 x 60 = 1440 minutes. It simply meansthat Earth will take about 1440/360 = 4 min. to rotate by I o

on its axis. We can therefore conclude that Zero hour at aplace 'B' which is I° towards west ofplace '~, will commencelater by 4 minutes as compared to place 'X. So the local timediffers from place to place. Strictly speaking as neither theearth is a perfect sphere nor its orbit around the Sun is a perfectcircle and as also the axis ofearth is inclined by about 23~° tothe perpendicular to the plane ofearth's orbit, even the durationof time or the rate of elapsing oflocal time is not unifrom forthe same place. In order to have a uniform rate of time lapseand also to avoid complex mathematical computations, a moreconvenient term has been adopted for Astrological purposeswhich is known as 'Local Mean Time' for a particular place.The local time or more accurately the local mean time (LMT)which is created by the gradual rising of the Sun and theroundness and rotation of the earth is the real or natural timeof a place. This differs from place to place and is dependenton the longitude and latitude of the place. In Astrology wereduce every given time into Local Mean Time first and thenproceed further.

5.3 Standard time

As explained above, the local time differs from place toplace. This becomes quite inconvenient when we have to referto time at a broader perspective say National or Internationallevel. With the advent of the postal department and later therailways etc., this difficulty increased in india as well as

Mathematical Astrology ~l)

observer's meridian (which is the great circle on the celestialsphere, passing through the zenith and both the celestialpoles).

6.2 Necessity to have the Sidereal Time Systemr\~

Students may be aware that for any astrologicaldelineation, the horoscope prepared for a particular epoch(moment) is not only a necessity but the only astrologicalequipment available to the astrologer based on which heanalyses the shape of things to come in the future. Thehoroscope which is a map of heavens at the given moment,contains 12 houses and the commencement of thehoroscope is the 'first house' or the 'lagna' or the'ascendant'. It is therefore most important to calculatethe correct lagna or the ascendant without which nohoroscope can be prepared. Students may now recall thatwhile discussing about the ascendant or lagna vide Para 3.9of Lesson 3 it was stated that due to the rotatory motionof the earth from west to east on its axis, the whole ofsky (or the zodiac with which an astrologer is concerned)appears to come up (or rsing) from below the horizongradually and the sign or rashi (and more particularly theexact degree of the zodiac or that sign) rising in the easternhorizon, is known as the 'lagna' or 'ascendant'. As thelagna or ascendant or the sign of zodiac rising on theeastern horizon of a place at any time, is dependent onthe rotation of earth on its axis due to which the timesystem known as the 'Sidereal Time' is also created, so

. it becomes evident that the rising sign or the lagna, inturn, is dependent on the sidereal time of the place atthe given moment or epoch. It therefore transpires that inorder to know the lagna or the rising sign for a particularmoment or epoch (be it a birth of a child or birth of a

.~'


question, incident or accident etc.) it is necessary to firstcalculate the sidereal time of the moment at that placewhere the birth of a child or a question or incident has takenplace. Students may please refer to the Tables of Ascendantsby N.C. lahiri and see themselves that the Ascendants forthe different latitudes are given with reference to the siderealtime only. We therefore now proceed to discuss the methodto calculate the sidereal time of a given moment or epoch.

6.3 How to calculate the Sidereal Time of a givenmoment or Epoch

Students are advised to refer to the Tables of Ascendantsby N.C. Lahiri (all references in this lesson pertain to theseventh edition of the book published in 1985) and proceedas follows:

Step 1 :

Step 2

Step 3

Step 4 :

Note down the sidereal time at 12h noon localmean time for 82°30'E longitude for 1900 ADfor the day and month of the given moment fromTable I at page 2.

Note the correction for the given year from TableII given on pages 3 and 4 of the book and applyto sidereal time in step 1.

Note the correction for the different localitiesfrom Table III given on page 5. A detailed listof principal cities of India has been given onpages 100 to 107. The last column of the tableindicates the correction to the 'Indian SiderealTime'. Similarly the table for the foreign citieshas been given on page 109 to III of the bookand the last column of the table again indicatesthe correction to the Indian Sidereal Time.

The correction for the year (step 2) and the


correction for the place (step 3) should be appliedto the sidereal time noted in step 1 according tothe sign (+) or (-) prefixed to the correction asshown in the respective table. Having appliedthese corrections, the result obtained (let us callit' A') will represent the Sidereal time for thegiven date, year and place but will be for thelocal noon i.e. 12 hrs, as we have not yet appliedthe correction for the hour and minutes beforeor after the local noon, as the case may be, forthe give moment.

Step 5 Convert the given time of epoch into LMT byapplying the LMT correction. This has beendiscussed elaborately in great detail and explainedwith the help of examples also vide para 5.8 ofthe preceding chapter. However the quantum andthe sign (+, -) of the correction to be applied tothe 1ST or ZST, as the case may be, has alsobeen indicated in the tables at pages 100 to 107for principal cities of India under column LMTfrom 1ST and, at pages 109 to 111 for foreigncities under column LMT from ZST.

Step 6: As the Sidereal time noted in the step 1 pertainsto the local noon, we have to find out as to howmany hours before or after the local noon, is thegiven time of the moment or Epoch. In otherwords we have to find out the "Time Interval"between the Local Mean Noon (LMN) and theLMT of the given moment. So, in case the LMTof the given moment is before noon, subtract itfrom 12:00 hours. In case the LMT of the givenmoment is in the afternoon, the LMT itself


(+) 1m : 11'

(+) om : 03'=

=

=

=

becomes the Time Interval (T.I.) also because

after 12 noon our watches show 1:00 PM and

not 13:00 which means that 12 hours have already

been deducted.

Step 7: The Time Interval (T.I.) worked out in step 6

above is to be increased by applying the

correction given in table IV which gives the

correction for hours and minutes of the T.1. By

. applying this correction we get the IncreasedT.!. Let us call it (B).

Step 8: The 'Increased T.I.' (B) is added to the corrected

Sidereal Time (A) in step 4 above in the case of

PM (afternoon) births or epoch and, subtracted

from the (A) in the case of AM (before noon)

births or epoch, as the case may be. The result

thus obtained is the Sidereal Time of the birth or

epoch or the given monment. The above

mentioned eight steps can be explained with the

help of a practical example or illustration.

Example 1 : Find out the Sidereal Time of birth of anative born at Delhi on Sunday the 25th October 2002 at09:30 AM (1ST) lFP40 'N 11.0 (') t:Solution: Use Tables ofAscendants by N.C. Lahiri

Step 1: Sidereal Time at 12h noon

on 25 October 1900 (page 3)

Step 2: Correction for the year 2002

(from page 4)

Step.3: Correction for Place (Delhi)

(page 5 as well as page 102)

Step 4: Sid. Time on 25th Oct. 2002

at Delhi, at noon (A)

•

Mathematical Astrology ·53

Step 5 : 1ST of birth (given)LMT correction (page 102)

Therefore LMT of Birth

==

09 : 30 : 00(-) 21 : 08

09 : 08 : 52

02 : 51 : 08

00 : 2000 : 09

02 : 51 : 37

14 : 13 : 59(-) 02 : 51 : 37

Sidereal Time of birth = 11 : 22 : 22

Example 2 : Find out the Sidereal Time of birth of anative born at New York on 25th October 2002 at 09:30AM (ZST)

= 14: 15 : 39

= 09 : 30 : 00= (+) 04 : 00

=09 : 34 : 00

(+) 1 : 11

(+) 1: 43

h m s14 : 12 : 45

=

=

Solution: Use Tables ofAscendants by N.C. Lahiri

Step 1: Sidereal Time for 25 Oct 1900at 12 noon LMT at 82°301£ long. (page3) =

Step 2: Correction for the year 2002(page 4)

Step 3: Correction for place of birth(New York) page III

Step 4: Sidreal Time on 25th October, 2002at noon at New York (A)

Step 5 : ZST of birth (given)LMT correction (page-Ill)

Therefore LMT of Birth


Step 6: T.I. from noon(12 hrs - 9 hrs 34 mts) ;:: 02: 26 : 00

Step 7: Correction to increase TIfor 2 hrsfor 26 min

(B)

(A)-(B)

Therefore Increased II

Step 8: Being AM Birth

=+ 20;::+ '04

;:: 02: 26 : 24

;:: 14: 15 : 39(-) 02 : 26 : 24

Sidereal Time of Birth ;:: 11: 49 : 15

Example 3 : Find out the Sidereal Time ofbirth ofa nativeborn at Sydney (Australia) at 3:25PM (ZST) on 17th August 2002.

Solution: Use Tables ofAscendants by N.C. Lahiri

Step 1: Sidereal Time on 17 August 1900at 12 noon LMT at 82°30'E (page3)

Step 2: Correction for the year 2002 (page 4)

Step 3: Correction for place of birth(Sydney) page 111

Step 4: Sid. Time on l Zth August, 2002 atnoon at Sydney (A)

Step 5 : ZST of birth (given)LMT correction (page 111)Therefore LMT of Birth

Step 6 :

• Step 7 :

T.I. from noon, being PMbirth, the LMT itselfbecomes the II

Increase in II (Table IV page 5)for 3 hrsfor 29 min 48 sec

Therefore Increased II (B)

h 111 S

;:: 09 : 40 : 43

;:: (+) 01 : 11;:: (-) 00 : 45

;:: 09 : 41 : 09;:: 03 : 25 : 00

(+) 04 : 48;:: 03 : 29 : 48

= 03 : 29 : 48

;:: 30

05

;:: 03 : 30 : 23


09 : 41 : 09(+) 03 : 30 :23

13 : 11 : 32Sidereal Time of Birth

6.4 Caution

We hope that by now the students would haveunderstood the methodology to work out the Sidereal Timevery clearly. However before we end this topic, we will liketo caution our students to note carefully the few pointsmentioned below :

Step 8: Being PM Birth (A)+(B)

6.4.1 Unlike the civil time (LMT or GMT or 1ST orZST) the Sidereal Time is never expressed in terms of AMor PM. It is always starting at '0' hour and goes upto 24hour after which it again starts as OhOUf.

6.4.2 WAR TIME: From 1st Sept. 1942 to 14th Oct.1945, the Indian Standard Time (1ST) was advanced byone hour all over India including modern Bangia Desh andPakistan for purposes of daylight saving during the war periodand was thus ahead of GMT by 6H 30 min. Therefore anyrecorded time during this period (Both days inclusive) mustbe reduced by 1 hour to get the corrected 1ST before LMTcorrection is applied to obtain the LMT of birth. (Providedthe same correction is not made while noting down the timeon the record.)

6.4.3 SUMMER TIME : Students are advised to referto page 112 of their Tables ofAscendants and read carefullyeach and every word thereof in order to acquaint themselveswith the summer timings being observed in Britain, USA,Canada, Mexico, USSR and other European countriesmentioned therein. The recorded time falling on the dates/period of summer timings indicated in page 112, must


therefore be corrected first as applicable, before it isconverted to local Mean time of epoch.

EXERCISE 6

Question: Find out the sidereal time of Birth inrespectof under mentioned particulars/details of Birth :

Place of Birth(POB)

Time of Birth(TOB)

5:25 AM (lST)10:30 PM (lST)6:24 PM (ZST)4:40 PM (LMT)2:20 PM (ZST)11:30 PM (ZST)00:29 AM (lST)12:00 Noon (LMT)

Date of Birth(DOB)

21-2-200211-7-200217-8-200223-4-200210-12-20025-6-200225-12-200201-01-2002

(a)(b)

(c)

(d)(e)

if)(g)(h)

S. No.

Meerut (UP, India)Bangalore (India)Tokyo (Japan)Seoul (S.Korea)Greenwich (England)Rangoon (Burma)Jaipur (Rajasthan, India)Kakinanda (AndhraPradesh, India)

(i) 23-9-2002 12:21:08 PM (1ST) New Delhi (lndia)(j) 25-4-2002 5:30 PM (ZST) New York (USA)

Note : For the facility of the students, the Questionsfor calculating of the sidereal time of birth for current yearare given. The student can try for the years 1821, 1816,1911, 1923 or any other year to have practice.

CHAPTER 7SUNRISE AND SUNSET

7.1 In the previous lesson we have seen the methodologyfor working out the Sidereal Time of birth or of an epoch.With this Sidereal Time we enter the relevant Table ofAscendants for the latitude of the place of birth to find outthe Ascendant. However, before we proceed on to find theascendant or lagna or the rising sign, we deal with the subjectof sunrise and sunset in this lesson. The time of sunrise,sunset etc is very useful in astrological calculation to findout the dinmaan, ratrimaan (i.e. the duration of day andnight), Ishtakala or Ishtaghati which forms the basis tocalculate the lagna rising by the traditional method, Kaalhoras, Kaal velaas, Bora lagna, Mandi, Rahu kaalam etc-, ,which have great significance in the Hindu Astrology.

7.2 Sunrise

The exact moment at which the sun first appears at theeastern horizon of a place is time of sunrise. As the Sun hasa definite diameter, the solar disc takes some time i.e. about5 to 6 minutes to rise. Therefore, from the first visibility ofthe upper limb of the solar disc to the time when the bottomlimb of the solar disc is just above the horizon of the place,there will be a time diference of about 5 to 6 minutes. It has,therefore, been acknowledged that for astrological purpose

(57)

.58 Mathematical Astrology

we may take the moment at which the centre or the middleof the solar disc is at the eastern horizon of the place as thesunrise time for that place.

7.3 Sunset

Similarly the sunset for a particular place is the exactmoment at which the centre or the middle of the solar discis at the western horizon of the place.

7.4 Apparent Noon

This is marked when the centre of the sun or the middleof the Solar Disc is exactly on the meridian of the place..The apparent noon is almost the same for all places.

7.5 Altas and Ratri

Ahas is the duration of day i.e. the duration of timefrom sunrise to sunset. Ratri is the duration of time fromsunset to sunrise. On the equator, the Ahas and Ratri arealways 30 ghatis or 12 hours each, while on other latitudesthe sum of Ahas and Ratri will be 24 hours or 60 ghatis.

7~6 Calculation of time of Sunrise and Sunset

In this lesson we propose to calculate the time of Sunriseand Sunset by the method of 'interpolation' from the givendata in the Ephemeris. However there is a proper method tocalculate the time of sunrise and sunset without making anyreference to the given data in the Ephemeris. We don'tpropose to discuss that method through this lesson' as thesame is not only cumbersome but involves too muchmathematical calculation needing enormous time which isnot warranted being beyond the scope and purview of these

• lessons. However we may advise our those students whowants to dive deep into the subject of sunrise and sunset torefer to Chapter V (Sunrise and Sunset) of the book entitled


A manual of Hindu Astrology by Dr. B.V. Raman, where ina detailed exposition of the subject has been given by thelearned author.

7.7 Calculation of time of Sunrise and Sunset byMethod of Interpolation

Step 1: As the time of sunrise or sunset differs fromlatitude to latitude we must first of all note the

(J( latitude for the place where the time of sunriseetc., is desired.

Step 2: Refer to page 93 and 94 of Lahiri's IndianEphemeris for the year 2002 and select two suchconsecutive dates that the date for which thesunrise time is desired falls in between the twoselected dates. Similarly select two suchconsecutive latitudes from the table at page 78so that the latitude of our desired place falls inbetween the two latitudes so selected.

Step 3 Note down the timings of sunrise or the sunsetas the case may be, for the above selected datesand latitudes as given in the table.

Step 4: Find the time of sunrise and/or sunset byinterpolation (simple ratio and proportionmethod). The time so obtained will be the Localmean Time (LMT) of the time of visibility of theupper limb of the solar Disc. Add 3 minutes tothe time of sunrise and deduct 3 minutes fromthe time of sunset to get the LMT of coincidenceof the centre of the solar disc with the horizon.

Step 5 In case the time is required in terms of 1ST orZST, apply LMT correction as applicable byreversing the (+) or (-) sign prefixed to the LMT


correction as given in the list of table ofAscendants from Page 100 to Ill.

7.8 The above method has also been indicated at page95 of Lahiri's Indian Ephemeris for the year 2002 andstudents are advised to follow the same with advantage.However we also give below the illustration to explain thesteps mentioned above more clearly to our students.

Example 1 : Desired 1ST of Sunrise and Sunset atDelhi on Oct 27.

Solution: Use page 94 of Lahiri's Indian Ephemerisfor 2002 and page 102 of Tables oj Ascendants.

Step 1 : Latitude ofDelhi (page 140 ofEphemeris for 2002)= 28°39'N or 28.65°N

Step 2 : Dates selected are Oct 23 and Oct 31,Latitudes selected are 200N and 35°N

Step 3 : The data given for the above mentioned dates andlatitudes at page 94 of the Ephemeris is as follows:

Sunrise (LMT) Sunset (LMT)Date Latitudes Latitude

200N 35°N 200N 35°NOct 23 5:58 6:13 5:31 5:16Oct 31 6:01 6:20 5:26 5:07

Step 4 : We can now obtain the values for the Oct 27 bysimple interpolation which are as follows :

Oct 27 5:59 6:16 5:28 5:11

•variation for 15°= (+) 17m

variation for 8.65° = (+) ~~ x8.65 (-) ~~ x8.65

(Delhi's Lat (-) 20°); (28.65°-20°=8.65°)

\


= 9:80 minor say = (+) 10 minTherefore LMT ofupperlimb visibility= 6:09 AM

LMT for centre ofsolar disc = (+) 0:03

6.12 AM

61

= 9:80 min.= (-) 10 min

5:18 PM

= (-)0:03

5.15 PM

·1

Step 5 : Students may now compare this with the Time ofsunrise and sunset (upper Limb) for Delhi givenon page 91 of Ephemeris which is as follows for27 Oct.

6:30 AM1ST of Sunrise(Upper limb)

Deducting 21m 0:21

6:09 AM

f LMT of Sunrise(Upper limb)

5:40 PM1ST of Sunset(Upper limb)

0:21

5:19 PM

LMT of Sunset(Upper limb)

(\

Step 6 : Solar Disccorrection (+) 0 : 03 (-) 0 : 03LMT for Center 6 : 12 AM 5 : 16 PMof Solar Discwhich agrees with that worked out in Step 4.

EXERCISE - 7Find out the 1ST or ZST (as applicable) of Sunrise and

Sunset for the dates and places given below :

(a) July 27 at New York(b) Feb 21 at Meerut (UP) India(c) Oct 17 at Munich(d) Dec 25 at Tokyo (Japan)(e) Jan 26 at Calcuttaif) June 06 at Washington D.C.(g) April 09 at Harare(h) Sept. 11 at Sydney

CHAPTER 8..

CASTING OF HOROSCOPE IMODERN AND TRADITIONAL METHOD

8.1 The horoscope is a map of heavens for a givenmoment at a particular place. It indicates the sign of Zodiacrising on the eastern horizon of the place at the given momentwhich is known as the lagna or the Ascendant. It is alsoknown as the first house and the successive Rashis/signsbecomes the successive houses or Bhavas (as called in HinduAstrology). Apart from the lagna or the Ascendant this mapalso indicates position of various Rashis and Planets at thegiven moment/epoch.

8.2 Forms of Horoscope

There are many types/forms presently in vogue indifferent parts of India as well as in the European countries.For the reference of students we give here some of the mostcommonly used formats by Astrologers in India and abroad.Students are advised to make themselves familiar with these'Formats', though they may follow anyone of these appealingto be the most convenient :

Type I

(62)

Pisces Aries ITaurus Gemini

Meena Mesha Vrisha Mithuna

-Asc

IType II


8.2.1 TYPE 1 : This is the format which is commonlyused in North/North-west part of India, The top middleportion is always treated as the lagna or Asc or the I Houseand the number of the Rashi/sign rising at the moment ofbirth on the eastern horizon of the place is indicated heree.g. 10 for makar or Capricorn. Then the counting of housesis done anti-clockwise. So the II house will have the sign!Rashi next to Capricon (Makar) i.e. Kumbha or Aquariuswritten there as No.II. The number of the successive Rashi/sign is then written consecutively one after the other in thesucceeding houses, anticlockwise. Then the position of theplanets at the moment is worked out and posted in thehoroscope in the respective rashi/sign occupied by them inthe Zodiac.

8.2.2 TYPE II : This type of format of Horoscope iscommonly used in the Southern part of India. In this typethe counting of houses is in clockwise direction. Here theposition of Rashis/sign are fixed for all the horoscopes, e.g.the top left hand square in the chart represent the sign Pisces(Meena) and succeeding Squares in clockwise direction willrepresent Aries (Mesha), Taurus (Vrisha), Gemini (Mithuna),and so on. As this sequence of sign/Rashis is fixed for all thehoroscopes, these are never written in chart. The sign/Rashisrising on the eastern horizon of the place or the lagna orAsc is marked in the appropriate sign in the chart as shownand word lagna or Asc is written in that sign. Afterwardsthe planets according to their position in the Zodiac at themoment are posted in the respective sign in the chart tomake the map or the horoscope complete.

8.2.3 TYPE III : This type of chart is commonly usedin Bengal and Neighbouring area. In a way it combines thetwo charts discussed earlier i.e. Type I and Type II in asmuch as the counting of houses is done anticlockwise (likeType I) but the position of Rashis/signs is fixed for all the

" .


horoscope (as in the case of Type II). The other aspects likeposting the position of planets etc., are similar to othercharts. The lagna is written in the appropriate sign in thechart.

Type III Type IV

8.2.4 TYPE IV: This chart is commonly used byWesternAstrologers. Nowadays some Astrologers in Indiaparticularly in Maharashtra have also started using this typeof chart for the horoscopes. This is a circular chart as shownin the figure, the twelve Bhavas or houses are marked inchart and symbol along with the degree is also indicated oneach bhava. In Indian (Hindu) Astrology, the cusps are treatedas bhava Madhaya or the middle point of the houses whereas in Western Astrology, the Asc cusp means the beginningof the first house, the II cusp means end of 1st house andbeginning of the II house and so on. The planets are alsoshown with their symbols only and the degrees of the zodiacacquired by a planet is also written along with the Planet inthe chart.

8.3 Casting of Horoscope

, The process of casting of horoscope involves two mainactivities. Firstly we have to find by calculation the exactdegree of longitude of the Ascendant or the lagna. Secondly


we have to calculate the longitudes of all the nine planets orgrahas mentioned earlier in chapter 1.

8.3.1 There are mainly two important methods to findout the lagna and the planetary position at the time of birthof a child or a question, event, or incident/accident. The firstmethod is called the modern method by using the table ofAscendants and ephemeris. The other method is traditionalmethod adopted by the Hindu astrologers where thehoroscopes are prepared with the help of traditionalPanchangas (almanacs, a kind of traditional ephemeris). Nowa days with the advent of calculators, log tables, computersetc. comparativelymore accurtae horoscopes can be preparedby using modern method. In these lessons, therefore, ouremphasis will be more on to the modern method. Howeverfor the academic interest of the students we will discuss thetraditional method also at the appropriate time and place.But for the present let us proceed with the modern methodof casting horoscope.

8.4 Modern Method of Casting Horoscope

As already metnioned in para 8.3 above it involves orconsists of two stages, viz:

(a) calculation of longitude of lagna/Asc(b) calculation of longitudes of planets

We will therefore take up the above two stages one byone.

8.4.1 CALCULATION OF LONGITUDE OF LAGNA:We have already discussed in earlier lessons that the long.of lagna or the Ascendant is calculated by using the Tablesof Ascendants which gives the Ascendants rising at differentlatitudes for each 4 minutes interval of Sidereal time.Accordingly the Sidereal time of Birth/epoch is veryimportant to know the lagna/Ascendant. In lesson 7 we havediscussed at length how to find out the sidereal time ofbirth/epoch and we hope that by now our students are well


conversant with the calculation of sidereal time of the epoch.We will now advise our students to proceed as follows tocalculate the longitude of the lagna or the Ascendant:

Step 1: Calculate the Sidereal time of birth/epoch byfollowing the 8 steps given in chapter 7.

Step 2 In the book Table ofAscendants by N.C. Lahiri,locate the page where Ascendants for the

';1 !'" appropriate latitude i.e. the latitude of the placeof the Birth are given. In case table for exactlatitude is not available, then the other table forthe latitude which is nearest to· the latitude ofthe place of birth could be made use of. In casea more precise work is needed, the students mayfind out/calculate the Ascendant at twoconsecutive latitudes falling either side of thegiven latitude & then find out the exact longitudeby interpolation of the two Ascendants. Howeverwe feel that in most of cases the calculation ofAscendant for the nearest latitude may serve thepurposes and the interpolation may not benecessary.

Step 3: Calculate the Ascendant/lagna with the help ofthe appropriate Table.

Step 4: As the table of Ascendants by N.C. Lahiri givesthe Nirayana longitudes of Ascendants for theyear 1938, it is necessary to apply the Ayanamshacorrection as given at Page 6 of the book to getthe correct lagna. The above steps can be bestexplained with the help of an example.

" Example 1 : Calculate the long of Ascendant/lagna forthe Native of Example 1 in Para 6.3.

Solution: Referring to the example 1 of chapter 6 we get:

Step 1: Sidereal Time of Birth = l lhrs 22mts 22secs.


Step 2: Asc for Delhi have been given at page 48. Sowe use the table given at page 48. (Also availableat page 134-35 of Indian Ephemeris for 2002).

Step 3 The Ascendant/lagna is calculated as follows:

(Refer Page 134 of Ephemeris for 2002)Sidereal Time Long. of Ascendant

-, 11 h 22m oo- 7s 16° 30'o 0 22s« 0 0 04'

For additional 22 sec of Sidereal Time increase\ I ' , will be = 12 -i- 60 x 22 = 4'

.. for 11 hrs 22mts 22secs= T' 16° 34'.

Step 4: Ayanamsha correction for the year 2002 (Refer

Page 135 of Ephemeris for 2002) = (-) 0°54'Therefore correct lagna/Asc = 7s-15°-40'or Scorpio 15°-40'(As 7 signs i.e. upto Libra already passed)

Example 2 : Calculate the Asc of lagna for the nativeof example No.2 in para 6.3.

Solution:

Step 1 :

Step 2 :

Step 3

Sid. Time of Birth = 11-49-15

The latitude of New York is 40° 43'N(This can be noted from the table given at pageIll). An appropriate table giving the longitude(nearest latitude 41°_0' North) is given at page62. So we use this table to calculate the Asc.

Calculate the lagna or Asc as follows :

Sidereal Time Ascendant/lagna

I1h 48m osee 7s 15° 28'

11 h 52m osee t- 16° 17'

variation in 4 minute = 49'

(or 240 sec)

or


Variation for

49lmts l5secs (or 75 sees) = - x75

240

=15' (Appx.)

=75 15° 28' + IS'

=75 15° 43'

Step 4: Ayanamsha correctionfor the year 2002 = -54'Therefore correct Lagna = 78 14° 49'or Ascendant is Scorpio 14° 49'

EXERCISE - 8

Question : Students may please choose the placessituated in northern Hemisphere out of the 10 places givenin Question of Exercise 6 and work out the longitude oflagnaJAsc in all those cases.

" ,/

CHAPTER 9CASTING OF HOROSCOPE II

MODERN METHOD

9.1 Calculation of Ascendant for places situated inSouthern Hemisphere (or the Southern Latitudes)

The methodology for calculation of lagna/Ascendantfor places located in Southern hemisphere/southern latitudeis exactly similar as for Northern latitude, if we have withus Tables of Ascendants for Southern Latitudes. The Lahiri'stables available to us are for Northern latitude. If the sametables are to be used for calculating the Lagna rising inplaces situated in the Southern latitudes, it is but obviousthat some modification is definitely called for. As such forcalculating the Lagna in Southern Latitude with thehelp of Tables for Northern Latitude, we have to proceedas follows:

Step 1: Find out the Sidereal Time of Birth by followingthe eight steps, 1 to 8 given in chapter : 6 asdone in the case of Northern Latitude.

Step 2: Add 12 hours to the Sidereal time worked outin step 1. If the total Sidereal Time after adding12 Hours exceeds 24 hrs., then subtract 24 Hoursfrom it, and retain the remainder. The SiderealTime so modified will be called as modifiedSidereal Time.

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Step 3

Step 5 :

Step 4 :

\ ~,'" f,.:

Step 6 :

Locate the appropriate table for the Latitude ofthe place of birth in the Tables of Ascendants for

Northern Latitudes.By using the Modified Sidereal Time workedout in step 2 above, calculate the Ascendant in

the similar way as in chapter 8 using the Tablelocated in step 3.

Apply Ayanamsha correction (Page-6) for theappropriate year, i.e. the year of birth.

Add 6 Signs to the Ascendant Calculated/workedout in step 5 to get the correct Lagna. If theAsc. exceeds 12 signs then subtract 12 signsfrom it.

9.2 Students may please note that modificationincoported above is applied only for the places in SouthernLatitudes if the Tables of Ascendants used is for NorthernLatitudes and vice-versa. If the Tables of Ascendants areavailable for the same hemisphere in which the birth hastaken place, no modification is necessary. Students are alsoadvised to read the Example 3 given in the Tables ofAscendants for Northern Latitudes by N.C. Lahiri, at page- (viii) in the beginning of the book. We will now explainthe above mentioned 6 steps with the help of an example.(

Exampie 1 : Calculate the lagna for the native ofexample no. 3 in chapter 6. (DOB 17-8-2002 TaB 15-25hrs. ZS 1')

Solution: Place Sydney, Latitude: 33° 52' South

~ Step 1 : Sid. Time of Birth = 13h 11 m 325ec

Step 2 : By adding )2h we get the modified Sidereal Timeas 25h 11 m 325ec

. As it exceeds 24\ deduct 24 hrs.Therefore, Modified Sidereal Time = 1h 11m 325ec

.


Step 3 Latitude of Place of Birth is 33°52'S. Hence usethe Table for 34°0'N (Page-55)

Step 4 The Lagna is calculated as under :Sidereal Time Lagna @1h 8m 05 35 6° 18'

1h 12m 05 35 7° 8'@ To be correctedVariation in 4 Mins. = 50'(or in 240 Sees)

Therefore, variation in 212 Sec. = 50+240x 212= 44.17'

or Say = 44'Hence Lagna for 1h 11 m 325ec = 356° 18' + 44'

= 357°02'

Step 5 Apply Ayanamsha Correction for 2002 = (-)0° 54'Corrected Lagna in North Latitude 357°02' (-)54'

= 356°08'

12°-02' southfrom ZST(-)8 min

Add 6 signs to get the lagna in Southern Latitude= +65

= 956°8'

Step 6

Therefore, Lagna or AscCapricon 6°8'

Example 2 : Calculate the lagna for the native born on14th November 2001 at 4hrs 48mts (ZST) in Lima (Peru).

Solution: Refer N.C. Lahiri's Table of Ascendant at page110 and note birth place i.e. Lima (Peru) and latitudes,longitudes, time corrections etc.

Time Zone (-) 5 hours LatitudeLongitude 77°-02' west L.M.T.

-08 sec.

I.S.T. from Z.S.T. + 10h-30m, correction to Indian

Sidereal Time (+) 1mt. 45 sees.


= 15: 35 : 30

=(+) 0 : 2 : 08

=(+) 0 : 01 : 45

Step 1 :

Step 2 :

Step 3 :

Step 4 :

Sidereal Time of 14 Nov. 190012 noon at Longitude 82°30'East (Page 3)=

Correction for the vear 200I(page 4)

Correction to I. Sid. Time (P-II0)

Sid. Time of 14th Nov. 2001 of Peruat 12 noon (A)

hills15:31:37

= 20: 14 : 10

= 4: 48 : 00

=(-J ,0 : 8 : 08

= 4: 39 : 52

Step 9 :

Step 10:

Step 11:

Step 5 : ZST of the birth of native

Step 6 : . LMf Local Tune Correction (page-lIO)

Step 7: L.M.T. of birth

Step 8: As it is fore noon birthT.I. from noon (12 hours(-) 4h39m52s<c) = 7: 20 : 08

Correction to increase the T.I. (Page 5)=(+) 01 : 12

Hence the increase T.I. (B) = 7: 21 : 20

Being A.M. birth (A)-(B) 8 : 14 : 10(15 : 35 : 30 (-) 7 : 21 : 20) 8 : 14 : 10

Step 12: The Sidereal time of birth 8 : 14 : 10

Step 13: The Latitude indicates the birth. place is in southernHemisphere. But the Lahiri's Table of Acendant is forNorthern latitudes. Therefore the method prescribed in para9.1 is to be used i.e. add 12 hours to the sidereal timeavailable at step 12.

Step, 14: Modified Sidereal Time12hrs + 8hrs 14mts 1osee

Step 15: Calculate Ascendant on the basis of Latitude 12°-02' North.. (P-19 of Table of Ascendant), thetable is for 12° North,

which is nearest. The use is as under:


Sidereal Time AscendantHrs Mts Sees Rasi degree mts20 16 00 . i 0 16 3620 12 00 0 15 30

o 04 00 .0 1 06'

Modified S.T. of birth = 20 : 14 : 10, which is more byo: 2 10 (20 : 14 : 10 (-) 20 : 12 : 00) or 130 seesVariation is 4 mins or 240 sees = 66'

= (-)

~ Mesha

Hence Ascendant is 0115°-30' + 36'or MeshaAynamsha correction (P-6)

Correct Ascendant

Variation in 130 seconds = 26:0

x i30 = ~48 = 35.75

or =36'or 0/16°-06'

= 16° 06'

0° -~3'

Step 16:

Step 17:

12° 2' is Southern Latitude, henceadd 6 signs to the above W + 0115°-13')= 68/15°-13'

i.e. Tula Ascendant of 15° 13'

Hence the native born with Tula 15°13' 'Ascendant

EXERCISE - 9

Calculate the Ascendants for the data given below :(a) Jakarta 21-4-1943 5:25 AM (lST);(b) Mombasa 11-7-1923 10:30 PM (rST)(c) Narobi 17-8-1986 6:24 PM (ZST)(d) Canbera 23-4-1972 4:40 PM (ZST)(e) Sydney 15-9-1936 3:25 AM ·(lST)

CHAPTER 10CASTING OF HOROSCOPE III

MODERN METHOD

10.1 Calculation of Longitudes of Planets/PlanetaryPosition at Birth or Graha·Spashta

We have already advised our students to purchase andhave with them a complete set of Lahiri's Indian Ephemeris(Please refer Para 3.13 in Chapter 3). A perusal of theseEphemeris reveals that :

(a) In the yearly Ephemeris e.g. for the year 2001,2002, 2003, the daily position of all planets including Moonhas been given at 5:30 AM (1ST).

(b) In the condensed Ephemeris for the year 1941-51,1951-61,1961-71,1971-81,1981-85,1986-1990,1991-1995& 1996-2000 etc., daily position of Moon has been givenfor 5:30 AM (1ST) where as for the remaining Planets exceptRahu/Ketu, the position has been given at 5:30 AM (1ST)for every alternate day. Rahu's position has been given for1st of each month for true as well as mean Rahu.

. (c) In the Ephemeris (condensed) for the years 1900 to1941, the position have been given for 5:30 PM (1ST) dailyfor Moon, twice in a week i.e. for Sundays and Wednesdays

, for Mercury and weekly position i.e. for every Sunday inrespect of Saturn, Jupiter, Mars, Sun, and Venus. Rahu'sposition has been given monthly i.e. for 1st of each month.The Rahu's position in this Ephemeris is for 'Mean' Rahu

(74)

Mathematical Astrology 7S

only and not for 'True' Rahu. True Rahu is by consideringthe actual ova/elliptical shape of orbit of Moon and the

ecliptic, where as Mean Rahu is calculated by consideringtheir orbits as perfect circle. As the later is not factually

correct we prefer to have only True Rahu in our calculationsas far as possible.

10.2 Keeping in view the above three different types ofdata available in the Ephemeris, we propose to discuss thecalculation of planetary positions in three different parts.Accordingly we will first of all take the Ephemeris for theyear 2002 and calculate the planetary position for the giventime of Birth of a native. It should be noed that the Lahiri'sIndian Ephemeris gives the position of Planets either for5 :30 AM (1ST) or 5:30 PM (IST). Accordingly any time ofBirth whether it is given ill LMT or ZST or GMT must befirst converted to 1ST so as to use these Ephemeris.

10.3 Calculation of Planetary Position by usingYearly Ephemeris

The calculation of Planetary position is best explainedwith the heIp of an example. However before we take up anexample it is necessary to advise the students that whileselecting the two consecutive dates from the ephemeris forobtaining the reference position of planets, care must be

taken to see that the dates should be such so that our dateand time of birth falls in between the two for convenience

in interpolation.

Example 1 : Calculate the planetary position at the

time of birth of a native at Delhi on Sunday the 25 Oct.2002 at 09:30 am (1ST) [Para 6.3 and para 8.4].

,...,;1, •


Solution: Use Lahiri's Indian Ephemeris for 2002 wewill calculate the moon's position first.

MOON (Page 32)Position at 5:30 AM (1ST) on 2511 0/02 = i- 18°3'58"Position at 5:30 AM (1ST) on 26110/02 = ZS 00°19' .52"

Motion in 24 hours 0512°15'54"

Time elapsed from 5:30 AM to 9:30 AM = 4 hoursTherefore motion in 4 hours (1/6th of 24 hourly motion)

052°2'39"

Add position at 5:30 AM of 25-10-2002 = 1"18°3'58"

Position at Birth = 1"20°6'37"or Vrish = 20°6'37"or rounding off we can say position of Moon = Vrish20°7'

Note: The position at 5:30 AM is indicated in the 7thcolumn. The first column gives the dates of the month.

10.4 The above method of finding out the proportionatemotion in 4 hours is by simple arithmetic or by using anelectronic calculator. We can also find out this motion byusing the log tables given at page (156-57) of the Ephemeris.However, as these log tables are proportionate and are meantfor use with 24 hourly motion. .

Therefore motion of Moon in 24 hours =12° 15' 54"Log of motion (i.e. 12° 15' 54" or 12° 16')(page 156) =0.2915Log of 4 hours =0.7781(TlITle Interval from 5:30 AM to Birth TlITle)

Total =1.0696

By taking antilog of this we will get the desired motionin 4 hours. Since there is no separate table, we have tolocate the nearest figure to 1.0696 in the table and then readthe degrees and minutes. We find that antilog of (nearest)


1.0720 is 2° 2'and 1.0685 is 2° 3'

Therefore variation of 35 is equal to l' or 60"

So variation of 1.0696 (-) 1.0685 is ~~ x 11 = 18.85T'

or say = 19"

1"18°3'58"1"20°6'39"

1520°7'

2° 2' 41"

=

Deducting 19" from 2° 3' we getthe motion of Moon in 4 hoursAdding this to position at 5:30 AMon 25-10-2002Position of the Moon at Birthor say

10.5 By looking at the above calculation student mayfeel that using logarithms is rather a cumbersome process.Actually it is not so. In the above calculations we have triedto show to the students that if more precision is required wecan work out the longitudes of planets upto seconds (") ofarc by log table also. However in most of the cases,calculation of longitudes of planets upto nearest Minute (')of arc will suffice or meet our requirement. Therefore weneed not interpolate the figures while working out the Antilogand only the nearest figure will do. In the context of Moon,while taking antilog the nearest figure is 1.0685 for whichantilog is 2°03' and this will meet our requirement. Moreover in the instant example the time interval from 5:30 AMto time of birth i.e. 9:30 AM is 4 hours which is a roundfigure and students can easily make 1/6 (of 24 hours motion)to get the 4 hours motion. However more often than not,the time interval may be like 7 Hrs 21 Min., 11 Hrs 39 Min.and so on. In such cases the use of logarithms will be easierand quicker. Students may threfore decide for themselves as


to which method i.e. the calculator method or the logarithmmethod appears to be the easier one and may adopt thesame. The whole idea is only to get the proportionate motionof planets during the time interval from the given referenceposition to the time of birth.

10.6 With the above background we can now proceedto find out the longitudes of other planets at the time ofbirth. It may further be mentioned here that unless theplanetary positions are required correct upto seconds (") ofarc, we may round off the same to the nearest minute (') ofarc by neglecting 30" or less and by adopting next higherminute for 31" and above. In the case of remaining planets,we have 24h position for each. Our time interval 4h is alsofixed for all the planets. So we can find out/calculate theirplanetary position simultaneously in one operation in a tabularform. (See next page)

As Ketu is always opposite to RAHU or 6 sign awayfrom RAHU, its longitude is calculated by adding 6 sign tothe longitude of Rahu. Accordingly :

Longitude of True Rahu = Is 15° II'Add 6 sign :;;:: +6s

Longitude of Ketu = 7s 15° 11 '(If it exceeds 125, deduct 12 signsbut this is not the case here,

Therefore Longitude of Ketu = 7515°11'

Students will recall that we had calculated the longitudeof lagna for this native vide Example 1 of Chapter 8 (Para

, 8.4.1) as 7s 15° 40'. We can now draw the chart as follows:

Mathematical Astrology 7'-)

Calculation of Planetary Position at 09:30 AM (1ST)25-10-2002Position of Sun Mercury Venus Mars Jupiter Saturn RahuPlanets at 530 ."M (R) IR) (D)1ST on (Page 32)

26-10-2002 6'8°30'12" 5~26°12' 6'17°14' 5'12°41)' 3'21"48' 2'5°0' 1~15°12!

25-10-2002 6~'fJ30'2~" 5'24°33' 6'17"46' 5'12°01' 3'21°41' 2sSo0:' 1'15°11'

Motion in 24 Hrs. 59'47" 1°39' (-)0°32' 39' 7 (-)2 I

Log of Motionin 24 Hrs (P-156) 1.3802 11627 I 6532 1.5673 23133 2.8573 3.1584Log of Time Intervali.e. 4 Hrs. 0.7781 07781 07781 0.7781 0.7781 0.7781 0.7781

Total 21583 19408 24313 23454 3.0914 3.6354 3.9365

Nearest figure givenin the Log Table 21584 1.9279 24594 23133 3.1584 - -ByTaking Antilogof above figure

we get proportion

Motion in 4 Hrs. 0°10' 0°17 (-)0°5' 0°7 0°1' (-)0°0' (+)0°0'

Add position on

25-10-2002 6'7°30'25" 5'24°33' 6'17"46' 5'12°01' 3'21°41' 2'5°02' 1'15°11'

Position at 930 Alvl

on 25-10-2002 6'7"40'25" 5'24°50' 6'17"41' 5'12°8' 3'21°42' 2s5°2' P1So11'

RahlSOll'

Moon Sat 5°02'

2007'

Jup

25-10-2002 21°42'

09:30AM(1ST)

DELHI

VAse ""'" Sun 7°40 Mat2°g'

15°40' Ven Mer

~Ke j) 17°41' 24°50'

10.7 Students may please note that the position ofPlanets in the heavens is dependent on the date & time onlyand is independent of the place of Birth. The place of birthis important for calculating the Rising Sign or Lagna or


Ascendant. Before we close this discussion we will take upanother example to work out the longitude/positionofplanet.

Example 2 : Calculate the longitude of Planets for anative born at 10:24 PM (1ST) on 11 July, 2002.

Solution : As the place of birth has not been given wecan not calculate the lagna. As such only the longitudes ofplanets are required to be calculated. This has been workedout in the tabular form in the next page which is selfexplanatory.

EXERCISE 10

Question 1 : Calculate the Planetary Position(longitudes of Planets) for following date and time :

(a) 26-1-2003 10:20 AM (1ST)

(b) 25-12-2003 7:30 PM (ZST) London

(c) 15-08-2003 7:30 AM (1ST)

(d) 25-04-2003 00:45 AM (ZST) New York

Note: For (b) & (d) students may refer to Para 10.2.

Example 2: Calculation of Planetary Positioin at 10 : 24 P,M, (1ST) on 11-7-2002

Position at Sun Moon Mere Venus Mars Jup Sat Ra (R)

5.30 AM 12-7-2002 2525'36'22" 3516'2'16" 2515'02' 4'7'22' 3s5'03' 351"30' 1'28'42' 1'23'40'

5.30 AM 11-7-2002 2s24'39'08" 35f5i'23" 2"13'01' 4s6'15' 3s4'25' 351'16' 1'28'35' 1'23'44'

Motion in 24 Hrs 57'-14" 14'04'53" 2'-01 1"-07' 0'-38' 0"-14' 0'-07' (-) 04'LogMotion in 24 Hrs, 1.4025 0.2315 1.0756 1.3323 1.5786 2.0122 2.3133 2.5563Log of Time interva'*(16'54"') 0.1523 0.1523 0.1523 0.1523 0.1523 0.1523 0,1523 0.1523

Total 1.5548 0.3838 1.2279 1,4846 1.7309 2.1645 2.4656 2.7086

Nearest figure given in Log 1.5563 0.3838 1.2289 1.4863 1.7270 2.1584 2.4594 2.6812table

Taking anti-log we getthe motion till time of -- .birth 0040' 9055' 1025' 0047' 0°27' 0010' 0°5' (_)003'

Add reference position 2s24'39'08" 351'57'23" 2s13'01' 486'15' 354'25' 351'16' 1828'35' 1'23'44'

Position at birth 28 25'19'08" 3811052'23" 2"W26' 487°2' 384°52' 3801°26' 1828°40' 1523°41'

*Time Interval for all planets from 5 : 30 A.M. to 10 : 24 P.M. = 16 Hrs 54 Min.(R) Means Retrograde i.e, the planet appears to be moving backwards.

Note: Ketu's position would be six signs away from Rahu and hence not calculated separately.

(81)

Example 3 : Calculate the position of all planets for the native hom 011 1~-2-2001 at 7.55 p.m. (19.55 HI·s.)

Position I Sun Moon Mer (R) Venus Mars Jup Sat Ra (R)

S S S S,

S S,

S S,

5.30 AM 15-2-2(1)) 10 2 30 7 n 51 9 28 11 11 15 35 7 6 13 I 8 02 I 0 36 2 20 50

5.30 A,..\1 14-2-200 I 10 I 29 G 17 54 9 29 20 11 14 54 7 5 42 I 7 58 I 0 34 2 20 51

24 hrs motion 1 I 12 57 (-) 1 09 0 41 0 31 0 4 0 2 (-) 0 1Log of24 hrs Motion 1.3730 0.2679 1.319'i 1.5456 1.6670 2.5563 2.8573 3.1584

+log of Time interval" 11.2213 0.2213 0.2213 0.2213 0.2213 0.2213 0.2213 0.2213

Total 1-';943 0.4892 1.5408 1.7669 1.8883 2.7776 3.0786 3.3797

Nearest figure given in Log 1.5902 0.4890 1.5456 1.7604 1.8796 2.8573 3.1584 3.1584

table

Taking anti-log we getthe motion till time ofbirth 0'37' 7°47' (-) 0°41' 0°25' 0°19' 0°2' 0°01' (-)0°01'

Add .reference position 10 1 29 6 17 54 9 29 20 11 14 54 7 5 42 1 7 58 1 0 34 2 20 51

lOS 2° 06' 63 25° 41' 95 28° 39' 11515°19' r 6° 01' IS 8° 00' IS 0° 35' 25 20° 50'

*The interval for all planets from 5.30 A.M. to 19.55 Hrs = 14.25

(82)


Therefore Motion in 24 hours = 14° 12'

Time interval from 5:30 PM on Tuesday to 08:00 AM onWednesday = 14 h 30 mints.

Now using the Prop logarithm table at P-118 and 119weget:

Log of Motion in 24 hrs. i.e. log of 14° 12'

= 0.2279

Log of Time Interval 14h30m = 0.2188

Total = 0.4467

Nearest Figure in log table = 0.4466

Anti log of 0.4466 = 8° 35'

Add this to the position ofMoon at 5:30 PM on Tuesdaythe 22-5-1928, we get the position ofMoon at Birth

= 2s 19° 19' + 8° 35'

or = 2s 27° 54'

Step 4 : Next we work out the position ofMercury. OnPage 58 the position ofMercury has been given for 5:30 PM(IST) for Sunday the 20-5-1928 and the following Wednesday i.e. 23-5-1928. As our date and time falls in between thesetwo dates, these dates will meet our requirement. So let usnote down:

Position of Mercury at 5:30 PM (1ST)

On 23-5-1928 / = IS 29° 25'

On 20-5-1928 = IS 24° 29'

motion in 3 days = 4° 56' = (4x 60) +56 =296'

Therefore motion in 7 days

. = 296+3x7=690.67

or say I = 691' or 11 °3 I'

Adding this to the Position on 20-5-1928

we get the positionrn 27-5 -1928 ~ 2' 60 0'


Important Note: The position of Mercury worked outby us for 27-5-1928 does not agree with the position shownin the Ephemeris which is 2s 5° 15'.This is due to the fact thatno Planet keeps a uniform rate of motion. We have thereforefound the position ofMercury on two consecutive Sundays inorder to use the prop logarithm table given on page 120 oftheEphemeris which is from Sunday to next Sunday. Studentswill appreciate that had we taken the position of mercury for27-5-1928 for use of table at page 120, the final position being calculated by us would have become incorrect and thepurpose of giving the position of Mercury for two days in aweek i.e. for every Sunday and Wednesday in the Ephemerisby N.C. Lahiri would have been defeated. In case Wednesdayposition was not given in the Ephemeris, we have no optionbut to take the take the position for 20-5-1928 and 27-5-1928only. The idea behind all this is to make use of the data givento work out the longitude as correct as possible.

Step 5 : Now we can proceed to calculate the positionof Planets as given in the Tabular form on page 93 which isself explanatory.

EXERCISE 12

Question 1. Work out the Planetary positions (long ofPlanets) for the following birth dates :,. 'Date Time' Place

(a) 25-10-1918 5:25 AM (1ST) Delhi

(b) 15-5-1921 9:13 PM (LMT) Meerut (UP) India

(c) 23-3-1940 1:27 PM (2"ST) Sidney

(d) 5-7-1911 1:27 AM (GMT) Tokyo

(e) 9-6-1901 3:40 PM (Z T) England

Calculation ofLongitudes ofPlanets at 08:00 A.M. (1ST) on 23.5.1928

Position at 5:30P.M. Sat (R) Jup Mars Sun Ven Mere MeanRahu

27-5-1928 7s23°45' 085° 32, 11815°09' 1813°05' 18 13°32' .286°00' Refer page 59 of the

20-5-1928 7824°14' 084°01' Ii 809° 53, 1806°21' 0824°57' 1824°29' Ephemeris at the bottom

Position at 5: 30P.M.

Motion in 7 days (-)0°29' 1°31' 5°16' 6°44 ' S035' Ii °31' Log ofMotion for 7 days

1-5-1928 = 181S022'

Log ofMotion in 7 days

(page 118, 119) 1.6960 1.1993 0.6587 0.5520 0.4466 0.3189 1-6-1928 = 1s16°43'

Log of 8.00 A.M. (lST) on Motion in 31 days

Wednesday (page 120) 0.4294 0.4294 0.4294 0.4294 0.4294 0.4294 = 1°39' = 99'

22 days = 1°10' = 70'

Total 2.1254 1.6287 1.0881 0.9814 0.8760 0.7483 21 days = 1°7' = 67'

NearestFigure(p. 118,119) 2.1170 1.6269 1.0865 0.9823 0.8751 0.7484 Position at 5:30 P.M.

Antilog (-)0°11' 0°34' 1°5S' 2°30' 3°12' 4°17' (1ST) on 22-5-192S = 181701S'

AddPositionon20.5.1928 7824°14' 054°0 I' Ii s09053' 186°21' 0824°57 18 24°29' 23-5-1928 = 1817°12'

By adding we get the 7824°03 084°35 II 8 1i ° 5 1, I~S051' 082SO O9 1828°46' Motion in 24 Hrs. =3'

Position at Birth Motion in 14 Hrs 30 Min.

= 3+24 x 14.5

= LSI = 2'

Position of Rahu at Birth

= 1817°13'

Position of Ketu at Birth

= 7817°13'

• As calculated and not given in the Ephemeris.

(R) mean Retrograde i.e. the Planet appears to be moving backward.

(93)


13.4 Janma Rashi

Each ofthe twelve signs ofthe Zodiac is known as Rashi.However in Hindu Astrology the term Rashi has a differentmeaning also. The Rashi/or sign occupied by the Moon at thetime ofbirth ofa native is known as his .Janma Rashi or simply

as Rashi. If someone says that my rashi is Leo, it means that atthe time of his birth the Moon was in Leo Rashi.

13. 5 Janma Nakshatra

Similar to' Janma Rashi, we have another concept knownas Janma Nakshatra. At the time ofbirthofa native, the Moonmust occupy one or the other of the 27 Nakshatras. TheNakshatra so occupied by the Moon at the time of a birth ofthe native is known as his Birth-star, Birth-Constellation orthe Janma Nakshatra. If some one says that his Birth star isPoorva Phalguni it means that at time of his birth, the Moonwas transiting through the asterism ofPoorvaPhalguni.

13.6 The Basis of Vimshottari Dasha System

The basis of Vimshottari Dasha System is the Birth starof the Native. Students will recall that each Planet has beengiven the lordship over 3 stars. Therefore the nine Planetshave lordship over the 27 stars/Nakshatras (refer para J.8 'Supra) Accordingly the planet who has the lordship over theJanam Nakshatra of the native will have the First term or theFirst Period in the Vimshottari Dasha system for that native.The other lords (planets) will follow one after the other in thecyclic order mentioned in Para 13.3 above.

13,;7 Calculation of Vimshottari Dasha Balance atBirth of a native.

Students are aware that each Nakshatra extends to 13°20'ofthe arc of the zodiac. These 13°20' (or 13 x 60 + 20=800')are equated to the number of years allotted to the Nakshatra

Mathematical Astrology . 97

Lord. As such depending on the longitude ofMoon at birth,we can work out the degrees or minutes of arc of zodiac yetto be covered by the Moon in that star. Equating the full extent of a star i.e. 800' of arc to the full term of span (period)granted to the lord ofNakshatra in the Vimshottari Dasha, wecan work out by simple rule of3, the balance period equal tothe balance of star yet to be covered by the Moon. Thesecalculations can be best understood with the help of a practical example.

13.8. Example. : In the example I of Para 10.3 we workedbut the longitude of the Moon as JS-200-7'. From the tablegiven in the Para 3.8 (SI. No.4) we know that the Moon is inRohini Nakshatra which extends from Vrish 10°20' to Vrish23°20'. Since at the time of birth of native theMoon had already covered 20°-7' (-) 10°00' = 10°-7' or 607' of the total800' of Rohini Star, the balance ofRohini star yet to be covered by the Moon will work out to 800'-607'=193'

800' ofRohini whose Lord is Moon = 10 Yrs.

So 193' of Rohini will be193 x 10

=800

= 2 Yrs 4 Months 28 Days 12 Hrs.

As the lord of birth star Rohini is Moon the first periodof Vimshottari Dasha will be that of the Moon. Hence wesay:

Vimshottari Dasha balance at Birth is that of Moon =2Yrs 4 Months 28 Days 12 Hrs.

Alternatively:

We can work out the Dasha balance with the help ofTables given at Page 108 and 109 ofLahiri Indian Ephemerisfor the year 2002 as follows:


Longitude ofMoon at Birth = Vrish 20°-7' under column3 on page 109 and against 20° the following Dasha Balancehas been given:

Long. ofMOO/1 Balance ofMoon20° 2Y 6m o- AThe long of Moon at Birth is 20°-7' which is more by 7'

from 20'. We also know that as the long of Moon increases,the balance of Nakshatra to be traversed by the Moon willdecrease and consequently the Dasha Balance will decrease.We can therefore deduct the Proportional part for 7' from (A).

From the table of Proportional part for Dashas given atthe bottom of Page 109 of the ephemeries for 2002 undercolumn (5) ofMoon, we get the Proportional parts as under:

For 7' = l month 2 days (B)Now deducing (B) from (A) we get

=2Y6mOd_lm2d

= 2Y 4m28d

EXERCISE 13

Questions: Work out the Vimshottari Dasha balance atBirth in respect of:

(a) 5 cases in exercise 12

(b) 5 cases in exercise 11

(c) 4 cases in exercise 10

CHAPTER 14CASTING OF HOROSCOPE VII

MODERN METHOD

14.1 Major and Sub Periods of Vimshottari DashaSystem

Students have seen that the dasha ofplanets run into several years ranging from 6 years for Sun to 20 years for Venus.With the periods running to as long as 20 years, it will not bepossible to give the precise timing of an event. It is of no useto tell the father of a daughter of marrigeable age that fromthe next month your daughter is to run the dasha of Venus soin that dasha she will get married as Venus is the karaka formarriage. As Venus dasha has to run for 20 years, the daughter of the consulter will definitely get married during these 20long years if the marriage is promised in the horoscope. Therefore in order to time the events more precisely our sages havedivided these dashas-mahadashas (called as Major period) intoantardashas (Sub period), pratyantar dashas (Sub-Sub periods) sookshma dashas (Sub-Sub-Sub period) and Prana Dashas(Sub-Sub-Sub-Sub periods)

14.2 Antar Dashas or Sub-Periods

In the mahadasha (Major period), of each planet, all thenine planets will have their antardashas (sub periods). The

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first antardasha period belongs to the same planet whosemahadasha is divided into antardasha. For example in themahadasha of Sun, the 1st antardasha will belong to Sun andthe subsequent antardashas will follow the same cycle orderofdasha system given in Para 13.3 Supra. The period allottedto the lord of each antardashawill be in the same proportionas the antardasha lord has been allotted inthe VimshottariDashasystem of 120 years, say for example we want to know howmuch will be the antardasha of Moon in the mahadasha ofVenus, we can find it out by the following method:

In 120 years system Moon has 10 yearsso in 20 years (Venus) period it will have

10= 120 x 20 years

= 1.667 yearsor = 1 years 8 months

By following the above simple mathematical calculation,we can calculate all the nineantardasha of any mahadasha.However a ready made table of these antardashas andpratyantar dasas for all the nine mahadashas is available atpage 107 and 110-116 ofLahiri's Indian Ephemeris for 2002which may be used by the students with advantage.

14.3 The same principle as discussed in para 14.2 aboveis applicable to the pratyantar dashas (Sub-Sub periods) un

der any antardasha. Similarly, we may work out all thesookshma dashas (Sub-Sub-Sub periods) under any pratyantar

dasha and also prana dashas (Sub-Sub-Sub-Sub periods) un-t der any sookshrna dashas. This way the time periods is re

duced to few hours and minutes only for attempting accurateand precise timing of events by experienced and learned Astrologers. However for the purpose of this course, working

Mathematical Astrology WI

out the mahadasha and antardashas i.e. Major period and Subperiods only will suffice as further minute divisions are beyond the scope of this course.

14.4 How to work out present Mahadasha andtj\ntardasha operating on a native

Suppose a native is born with a dasha balance ofMars 'as

3 years-8 months-12 days and his date of birth is 14-3-2002.His present dasha can be calculated as under:

Mars Dasha already passed = 7 Yrs (-).3:",8~ 12?,(n= 3Y 0)"\ 18°

From the table given at page 107 of Lahiri Ephemeris of2002, we see that the sub-period of Saturn in Major Period ofMars ends after 3 years 6 months. Hence balance of Saturn

sub period at Birth = 3 years 6 months (-) 3 Y3m 18 days

I = 0 yrs 2 months 12 daysWe can now proceed as follows:

Y M D

Date of Birth of native = 2002-03-14

In Mars Dasha, Balance of Saturn = 0-02-12

.', Antar Dasha of Saturn

(Mars/Sat) ends 2002-05-26

Antardasha of Mercury = 0-11-27

End of Mars/Mere = 2003-05-23

Antardasha ofKetu 0-04-27

End of MarslKetu = 2003-10-20

Antardasha of Venus = 1-02-00

End of Mars/Ven = 2004-12-20

Antardasha of Sun = 0-04-06

End of Mars/Sun = 2005-04-26

Antardasha of Moon = 0-07-00

End of Mars/Moon = 2005-11-26

10-1- Mathematical Astrology

15.2 We have already stated in earlier chapters that aHindu day begins with the sunrise and ends with the next sun

rise. The duration of the Hindu day is taken as 60 Ghatis, the'0' Ghati starting at the time of sunrise at that place. Ac

cordingly measurement of time starts from time of'sunrise-i.e.

"0" ghatis. The interval from the time of Sunrise to the time ofbirth is called Ishtakaal. This lshtakaal is very important fac

tor in casting the horoscope by traditional method. All calcu

lations viz. Lagna, Graha. spashta; Dasha etc. are based onthis Ishtakaal only.

15.3 Rashimaan

Students will recall that we had earlier also discussed theterm Rashimaan vide Para 2.13. The Rashimaan is also known

as the timeof oblique Ascensions. As discussed earlier this isthe duration of tithe taken by each of the twelve signs of zodiac to rise through its 30° on the eastern horizon of a place.The Rashimaans differ from Rashi to Rashi as well as fromlatitude to latitude. The Rashimaan is computed in Sayanasystemi.e. to say it is computed for the signs of Sayana ormoveable zodiac. The unit of measurement of Rashimaan isASu where 1 Asu is equal to 4 seconds or 6 Asus is equal to24 seconds or 1 Pal (Vighati). The rising periods of Sayana

Rashis at equator are as follows :Vighati Hours

Aries Virgo Libra Pisces 1674 Asus 279 1hr51m36 sec

Taurus Leo Scorpio Aquarius 1795 Asus 299.17 1hr 59m 40 secor 299,

Gemini Cancer Sagittarius Capricorn 1931 Asus 321.83 2hr 8m 44 secl

or 322

In order to calculate the time of oblique Ascension orRashimaan on other latitudes, the Ascensional differences or


charkhandas are addedto/substracted from the. Rashi Maan

for the equator. The table for these chakhandas have been

given by Dr.B. V Raman in his book A manual (if Hindu Astrology at page 161 (Table 1) For places in Northern Hemi

sphere, these charkhandas are deducted .from Rashimaan at

equator for Aries to Gemini and Capricorn to Pisces and added

for Cancer to Sagittarius. This addition and substraction is

reversed in case of places situated in the southern latitudes.

Thus with the help of table of charkhandas, we can calculate

the Rashimaan for any place on earth. For example we willworkout the Rashimaan for Delhi. The charkhandas for Delhi

(latitude 28° 39'N) (rounded off to nearest whole Pal) are as

follows: 65, 52, 22.

Rashi Rashi Charkhandas Rashi Rashi Maan at DelhiMaan at for Delhi Maanat Ghati PalEquator (Pal) Delhi

.(Pal) {Pal)

Aries 279 - 65 = 214 3 34Taurus 299 - 52 =247 4 07Gemini 322 - 22 =300 5 00Cancer 322 +22 =344 5 44Leo 299 +52 = 351 5 51Virgo 279 +65 =344 5 44Libra 279 + 65 =344 5 44Scorpio 299 +52 = 351' 5 51Sagittari 322 +22 =344 5 44Capricorn 322 - 22 =300 5 00Aquarius 299 - 52 =247 4 07Pisces 279 - 65 = 214 3 34Total 3600 60' 00

Pal Ghati Pal


In 54hOJrnffioontransits 30° of Sagittarius

so in 24h18rn it will transit

=30 x-~- = 13°29'15"3243

Therefore longitude of Moon at birth= Dhanu 13°29'15"

(B) For the Planets : The methodology is the same as forMoon. However in the case of planets, their transit throughNakshatra or even Nakshatra charan (or Pada, Quarter)particularly in case of slow moving planets like Rahu, Ketu,Saturn and Jupiter is taken into account and not the transit ofRashi as the planets will take too much time to transit throughone Rashi,

15.6 Calculation of Dasha Balance

This is worked out based on the Nakshatra alreadytransited by moon and yet to be transited. From the Panchangfor Delhi we note the following data for the aforesaid example:

On 25-6-2002 Mula nakshatra upto 12 Gh 23 Pal

On 26-6-2002 P. Asadha nakshatra upto 12 Gh 53 Pal

Nakshatra maan for P. Asadha will be

=60 Ghati-(12 Gh 23 Pal) + (12Gh 53 Pal) =60 Gh - 30

Pal

,Nakshatra already covered upto birth

Ishta Kaal (-) Mula's Ghati Pal

= 13 Gh 50 Pal- 12 Gh 23 Pal

= 1 Gh 27 Pal


Therefore Nakshatra Balance

109

=

60 Ghati

(-) I Ghati

59 Ghati

30 Pal

27 Pal

03 Pal

Lord ofP. Asadha is Venus who has a dasha period of20years in Vimshottari Dasha system.

Therefore 60 Ghati 30 pal = 20 Years

So 59 Ghati 03 Pal will be

Therefore Venus Balance

2059.05

= x--years60.5

= 19Years 6months 07 days

EXERCISE 15

Question 1 : Cast a Nirayan horoscope and find out thedasha balance at birth by traditional method for a native bornat Delhi on 25 October, 2003 at 9:30 AM (1ST)

Question 2 : Cast a Nirayana horoscope and find out thedasha balance at birth by traditional method for a native bornat New York city (USA) at 10:30 P.M. (recorded ZonalStandard Time) on 22May, 1928.

CHAPTER 16BHAVAS

16.1. Students are aware that the Zodiac consistson60°Though it is oval/elliptical in shape we consider it to be acircle for all practical purposes and ease in calculations asfar as Astrology is concerned. The Zodiac is dividedinto twelveequal parts of 30° each and each part is known as a Sign!Rashi. All these twelve signs appear to be rising one afterthe other on the eastern horizon of any place, graduallydue to the rotation of the Earth on its axis from West toEast. The particular point of the Zodiac (Ecliptic) whichis intersected by the Eastern horizon of a place at a givenmoment becomes the Lagna or the Ascendant and .thispoint Lagna or the Ascendant marks the-beginningof the horoscope for that moment. The Horoscope which is a map ofheavens at the given moment has twleve houses and as twelvehouses are the parts ofthe Zodiac itself, the sum total oftheextension of these houses is again 360°. However, the extension ofeach individual house is not necessarily 30°. The twelvedivisions of the Zodiac taking the Lagna as the point of reference, are known as Bhavas in the Hindu Astrology or Houses

, in the Western Astrology.

16.2 As we have already said that the twelve divisions ofthe Zodiac known as Bhavas or Houses are not necessarily

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Mathematical Astrology III

equal, it is essential to work out the extension of each houseto know precisely as to in which house a particular planet isposted or falls in the horoscope prepared for a moment. Forworking out or calculating the extension of a house, it is necessary to decide first as to which point is the starting point ofa house and which point is the end point of that house. Wehave already calculated one most important point on the Zodiac which is called Lagna. We have also defined vide Para3.10 Supra, the Tenth house or Me as the point of the intersection of the Ecliptic with the meridian of the place at thegiven moment. But the mute question remains whether thesepoints are the starting points or the middlepoints ofthe housesthey represent viz. the First House and the tenth House. Asalready stated there is a controversy over the issue. According to Western system of Astrology, these points are taken asthe starting or beginnig points where as according to HinduAstrology, these points are the middle points or the "BhavaMadhayas '.' of the houses 1st and 10th. Maharishi Parasharain his Brihat Parashara Hora Shastram has favoured and advocated the later view. In these lessons, we therefore followthe later view.

16.3 Yet another controversy exists in the matter ofhousedivisions. According to one school of thought, all the housesare of equal extension and therefore, there is no necessity tocalculate the longitude of the 10th cusp (Bhava Madhaya orthe middle point of the tenth house) separately as was donefor the Ascendant. According to the equal house division system, the longitudes of the 10th cusp will not be the same asthat of the M.e. Another school of thought advocates theunequal extension of houses (Bhavas) and there are severalmethods to calculate the longitudes ofthe cusps ofthe housesother than the 1st and the 10th. However in all the methods of


Solution : Sidereal Time of Birth as calculated videExample 1 of Lesson 6. = 11h 22m 22sec

For this Sidereal Time, from table at pages 124-125 of

unequal house divisions, the 10th cusp is the same as the M.C.In the lesson we do not propose to discuss all the methods ofunequal divisions of houses but restrict our discussion only tothe one most commonly used by the Hindu Astrologers and issupported by the classical texts on the subject. Students whodesire to study the subject in detail are advised to refer to thestandard works on the subject, particularly related with theAstronomy. They may also read Appendix II (pages 86 to 97)ofthe Tables ofAscendants by N.C. Lahiri which gives a fullertreatment of the subject.

16.4 In order to work out th extent ofdifferent houses, itis essential to work out first the longitude of the 10th cusp inaddition to the Lagna. The longitude of the 10th cusp is calculated with the help of Table of Ascendants exactly in thesame way as the Lagna. The only difference is that while thelongitude ofLagna varies from latitude to latitude, the X cusplongitude is same for all places at a given moment. As suchonly one table will suffice to calculate the X cusp which hasbeen given at page 8 as well as at page 80 of the Tables ofAscendants and also page 124-25 of Ephemeris of 2002 byN.C. Lahiri. By using the same Sidereal time as for calculating the Ascandant, we can calculate and find out the longitude of the 10th cusp from this table. We will illustrate thiswith the help of an example.

16.5 Example 1 : Find out the longitude of the 10th

Cusp for the native of example 1 of Chapter 6 (Longitude ofAscendant for this native has already been calculated videExample 1 Chapter 8),


the Ephemeris for 2002 the longitude ofX cusp is worked out

as

\ "}I

4S 26° 39'

o 0° 6'

4s 26° 45'

Ayanmasha correctionfor 2002 = (-) 0°54'

Therefore Nirayana longitude of X cusp = 4s25°_1'

16.6 The point exactly opposite to the 1st cusp is the VII

cusp and similarly the point opposite to the X cusp is the IV

cusp. These 4 points on the Zodiac are known as the cardinal

points ofany horoscope and are therefore given specific namesas follows:

I cusp is known as Ascendant and the X cusp is called ZenithVII cusp is known as Descendant and the IV Cusp is called

Nadir-

For example under consideration! these can be repre-sented as follows:

X

Zenith4'25 C51'

VIIAscendant I------I---------l Descendant

7'15°40' 1'15°40'

IV

Nadir10'25°51'

1I~ Mathematical Astrology

From the figure one can easily see that if the Zodical Arcbetween the X cusp and the Ascendant (l Cusp) is divided

into 3 equal parts, the intervening points will indicate the

longitudes ofthe XI and XII cusps. Similarly the Arc between

the Ascendant and the IV cusp when divided into three parts

will give us the longitudes of the II and III cusps. Further bythe adding 6 signs to the longitudes of the XI, XII, II and IIIcusps, we can find out the longitudes of the opposite cuspsnamely the V, VI and VIII and IX. Thus we will be able to getthe longitudes of all the remaining Eight cusps. This can bedone as follows:

Longitude of Ascendant= 7s 15° 40'

Deduct longitude of X = 4s 25° 51'

Length of Arc X to I = 2s-19°-49' (A)

(Note: Students are advised to note that to get the Arclength between the X cusp and the I cusp, we Must alwayssubstract the longitude ofX from the longitude ofAsc. (i.e. IX) and Never reverse of it (i.e. X-I). In case longitude ofX ismore than the longitude ofthe 1 cusp, we may add 12 signs tothe longitude of 1 cusp and then do the subsctraction).

Now by dividing (A) by 3 we get

2S19°49'

_ 79°49' = 260 36' 20"3 3

We can now get the longitudes of the XI and XII cusps

as follows:

Longitude of X cusp =Add =

Longitude of XI cusp =

4525°51 '00"


Add = (+) 26°36'20"

Longitude of XII cusp = 6519°03'40"

Add = (+) 26°36'20"

Longitude of Ascendant = 7s15°40'OO"

Similarly by substracting the longitude ofIst from the

IV, we get = 10'25°51' - 7515°40' = 3510°11'

And dividing this by 3 we get = 1'3°23'40" (B)

We can now calculate the longitude ofthe II and III

cusps as follows:

Longitude of Ascendant = 7515°40'00"

Add = (+) 153°23'40"

Longitude of II cusp = 8519°03'40"

Add .= (+) 1"3°23'40"

Longitude ofIII cusp = 9522°27'20"

Add = (+) 1"3°23'40"

Longitude ofIV cusp = 10525°51'00"

We have thus calculated the longitudes of X, XI, XII, I,II and III houses and by adding 6 signs to each ofthem we canfind the longitudes of the remaining 6 houses. This can berepresented diagrammatically as follows:

16.7 Students will recall that in Hindu Astrology the

cusps are the middle points of the houses or the BhavaMadhyas and not the beginning of the Bhavas as followed by

the western Astrologers. As such in order to find out the extentof Bhavas we have yet to calculate the longitudes of thestarting/end points ofBhavas. It should however be noted that


Similarly starting from the longitude of the X cusp andadding successively 13°18'10" we can obtain the Bhava

Sandhis between X and XI cusps, XI and XII cusps and XII and

I cusp. Then having obtained all the Bhava-Sandhis between X

to I and I to IV and by adding 6 signs to those, we can obtain

the longitudes ofthe remaining Sandhis between IV to VII and

VII to X cusps. These have been worked out and shown in thefigure given on previous page.

RASHICHART BHAVACHART

16.8 Having worked out the extension of each of thetwelve houses as above, we can now m~rk the position of allthe nine planets based on their longitudes (for the example

horoscope these have already been calculated vide example 1(DOB 25-10-2002) at 9.30 a.m. 1ST chapter lOin the aforesaid

diagram and see for ourselves as to in which particular Bhava

a particular planet is posited. We give below the Rashi chart

(common1yknown as Janma Kundali or Birth Horoscope) and

the Bhava chart for comparison by the students.

, A comparison of the above two charts will reveal that

there is no difference in the two charts.

16.9 We may however mention here that some Astrologersare ofthe opinion that Bhava Chart or the Chalit ofthe planets


does not have much significance andjudgement ofa horoscopewith reference to the Rashi Chart alone is sufficient and yieldsreasonalbly satisfactory results. We are however neither infavour nor against this view as we prescribe the use ofDivisional charts. We therefore leave this to our students toapply the phenomenon to as many practical horoscopes aspossible and verify the results themsleves.

EXERCISE 16

Question : Calculate the longitudes of all the BhavaSandhis and Bhava Madhyas in respect of horoscopes ofnatives of all the 5 cases of Question 1 Exercise 11.

1" I

CHAPTER 17SHADVARGAS

17.1 Students will recall that vide Lesson 13 (Para 13.1)while discussing the subject of dasha systems we have statedthat dasha systems propounded by our ancient sages is a marvellous and unique Astrological tool for precise timing ofevents that are likely to take place in the life ofaNative. Similarly the concept of Divisional Charts or the Shodasvargasis yet another instrument, unique to Hindu Astrology, forcorrect and accurate assessment ofworth ofan Astrological Nativity.

17.2 Maharishi Parashara in his Brihat Parashar HoraShastram has mentioned about the different Vargas or theDivisional Charts" as follows :

(a) Shad Vargas or the Six charts: It includes the Lagna,Hera, Drekkana, Navamsa, Dwadashamsha and Trimshamsha.

(b) Sapt Vargas or the seven charts: It includes all the

above mentioned six charts or Shadvargas plus Saptamsha.

(c) Dash Vargas or the ten charts : It includes all the

~ above mentioned seven charts plus Dashamsha, Shodashamshaand Shashtyamsha.

(d) Shoda Vargas or the Sixteen charts : It includes allthe above mentioned charts plus Turyamsha (or

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Chaturthamsha), Vimshamsha, Chatur Vimshamsha, Sapt

Vimshamsha (orBhamsha) Chatteriamsha (or Khavedamsha)

and Panch-Chatteriamsha (or Akshavedamsha).

17.3 It is significant to know and understand that each

divisional chart or the varga chart is symbolic of certainaspect of human life. As the name Divisional Charts itself

is indicative, a Rashi is divided into as many as 60 divi

sions and each division envisages a particular aspect of

life, whether material, spiritual or physical. Out ofthe afore

said 60 divisions, the 16 divisions as mentioned in Para 17.2above are specifically considered to be more significant. Apart

from affording the Astrologer a ready recknor to know and

assess the strength and/or weakness of the planets in the different vargas (depending on whether the planet is in the vargaof exaltation, mooltrikona, own sign, neutral, enemy sign or

debilitation etc), it also enables the Astrologer to refer to a

divisional chart according to the. particular aspect of the lifeindicated by that divisional chart. The indications/use ofeach

of these 16 charts or Shodasvargas are as follows :

(i) Lagna chart: Judgement about body, structure, built,constitution, health, complexion, etc.

(ii) Bora Chart: One's wealth, finance, prosperity, pov

erty, etc.

(iii) Drekkana: Relations with brothers and sisters, their in

fluence on the native, as well as their property, etc.

(iv) Turyamsa or Chaturthamsha : Luck or fortune of the

native, the assets and liabilitiesofperson whether move

able or immovable, etc.

(v) Saptamsha: Children -and Grandchildren, their pros-


perity, etc. According to one school of thought, thischart in a female nativity can be used for assessing thehusband's prosperity and well being.

(vi) Navamsha : Strength or weakness of the planets. Wifeor Husband and how will be the partner in life married

life, etc.

(vii) Dashamsha: Prosperity and upliftment, one's achievements, honour, professional success in life, etc.

(viii) pwadashamsha: Parents, Parental happiness, etc.

(ix) Shodashamsha : Happiness, Miseries, Conveyances, etc.

(x) Vimshamsha: Prayer, Worship, Upasana, etc.

(xi) Chatur-Vimshamsha : Education knowledge, learning,etc.

(xii) Sapta Vimshamsha or Bhamsha : Strength, weakness,etc.

(xiii) Trimshamsha : Miseries, danger in life (arishta), etc.

(xiv) Chatteriamsha or Khavedmsha : General good/bad, auspicious/inauspicious results that a native may enjoy.

(xv) Panch-Chatteriamsha or Akshavedamsha, and

(xvi) Shashtyamsha: All other indications, Good or Evil inlife, etc.

17.4 Method of Preparation of Divisional Charts

We will like our students to note that Astrology is a subject where far too many different schools ofthought are prevalent and therefore for preparation, of divisional charts also,

,several methods are in vogue. However, in this lesson we pro-. pose to discuss only one method which is most commonly

used and applied by the majority of the Astrologers of theyore and present times. The methods given in this lessons are


the same as given by the Greatest Hindu Astrologer of histime, (Late) Dr. B.Y. Raman in his book A Manual ofHinduAstrology.

17.4.1 Further it is stated that while we have listed andacquainted our students with all the 16 charts orshodashvargas, the method of working out the Shadvargas

only, is discussed in this lesson, as mentioned in the syllabusfor Jyotisha Praveen examination. Those students who desireto work on the remaining 10 charts or vargas are advised torefer to chapter XII of Dr. B.Y. Raman's book mentionedabove.

17.4.2 LAGNA CHART or RASHI CHART: This isthe basic chart or the natal chart erected/cast for the momentofbirth ofa native or incident or question. As a matter offact,all the remaining 15 chart are the divisions of this charts onlyand therefore can be stated to emanate from this chart. Wegive below this chart for a native born on 25-10-2002 at 09:30AM (1ST) at Delhi.

NORTH INDIA STYLE SOUTH INDIA STYLE

~1S'1l

Moon Sat 5°02'20°7' (R)

25-10-2002 Jup

09:30AM 21°42'

(1ST)DELHI

~Asc":::: Sun 7°40' Ma 12°08'

15°40' Ven Mer

~Ke /;17041'

24°50'

17.4.3 HORA CHART: Each Rashi is divided into twoequal halves and the Sun and the Moon becomes the rulers of

Jthese divisions as follows:

I


(a) In odd signs: <

(i) First 15° are ruled by the Sun (Leo Sign)

(ii) Last 15° are ruled by the Moon (Cancer Sign)

(b) In Even Signs:

(i) First 15° are ruled by Moon (Cancer sign)

(ii) Last 15° are ruled by Sun (Leo sign)

The Hora chart for the above native will therefore be as

under:

" HORACHART

Mars4 Venus

Lagna, Sun

5 Moon, RahuSaturn, KetuJup, Mer

DREKKANA

NORTH INDIA STYLE SOljTH INDIA STYLE

Ase.Mer SatKe

Jup

Ven

DREKKANAMoon

Ma

Sun Ra

,I,

Mathematical Astrology 12~

In Airy Signs:

\::.,.

17.4.4 Drekkana Chart. Each Rashi is divided into threeequal parts of] 0° each. The First Drekkana (0° to 10°) falls inthe same Rashi itself, the second Drekkana (> 10° to 20°) fallsin the 5th Rashi therefrom and the third Drekkana (>20° to30°) falls in the 9th Rashi from the Rashi under consideration.The Drekkana chart for the example horoscope will be as follows:

17.4.5. Navamsha Chart: In this case each Rashi isdivided into 9 equal parts of3°20' each (i.e. Equal to a quarteror Pada of a Nakshatra)

I,. . In Fiery Signs: The nine parts are ruled by the lordsof nine signs from Aries.

In Earthy signs: The nine parts are ruled by the lordsof nine signs from Capricorn.

The nine parts are ruled by the lordsof nine signs from Libra.

In Watery Signs: The nine parts are ruled by the lordsof nine signs from Cancer.

The Navamsha chart for the horoscope is givn below:

NAVAMSHA

Yen Ma Ra

Moon

NAVAMSHA

Jupiter, Mer.

! ~ ,..

AscSun ~at

~Ke


17.4.6 Dwadshamsha Chart: Each Rashiis divided into12 equal parts of 2°30' each. The 12 parts are ruled by thelords of the 12 signs successively from the sign under consideration.

DWADASHAMSHA

JupAsc~Ven MerKetu~

DWADASHAMS··MoonSun Saturn

Mars

Rahu

17.4.7 Trimshamsha Chart: Each rashi is divided into30 equal parts of 1° each.

(a) In Odd Signs:First 5 parts (0° to 5°) ruled by MarsNext 5 parts (5° to 10°) ruled by SaturnNext 8 parts (10° to 18°) rule~ by JupiterNext 7 parts (18° to 25°) ruled by MercuryNext 5 parts (25° to 30) ruled by Venus

(b) In Even signs:First 5 parts (0° to 5°) ruled by VenusNext 7 parts (5° to 12°) ruled by MercuryNext 8 parts (12° to 20°) ruled by JupiterNext 5 parts (20° to 25°) ruled by SaturnNext 5 parts (25° to 30°) ruled by Mars.

The Trimshamsha Chart for the example horoscope isgiven below :


TRIMSHAMSHA

127

KeAsc

MarsVn"'"

SatSun

Mer TRIMSHAMSHAMoon

Jup

Ven

EXERCISE 17Question : Prepare theShadvarga charts ofallthe5 cases

of Question 1 ofExercise No. 11

';

SAPTAVARGA CALCULATIONNote : 1. Hnra; 2. Drekana, 3. Saptamsha ... Navamsa 5. Dwadasamsa ti. Trisarnsa

v: Deg.n 2 3 4 5 G 7 8 10 12 12 12 13 15 16 17 17 18 20 21 22 23 25 25 26 27 30z; 1\1t. (') 30 20 17 0 40 30 34 0 0 30 51 20 0 40 8 30 0 0 25 30 20 0 42 40 30 0~ Sec (") 0 0 9 0 0 0 17 0 0 0 26 0 0 0 34 0 0 0 43 0 0 0 51 0 0 000

Hora 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4

Drekana I I 1 1 I 1 1 1 5 5 5 5 5 5 5 5 5 5 9 9 9 9 9 9 9 9To

1 1 2 6r;o;: Saptamsa 1 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 7 7 7....Cl: Navamsa 1 1 2 2 2 3 3 3 4 4 4 4 5 5 6 6 6 6 7 7 7 8 8 8 9 9< Dwadsamsa 1 2 2 2 3 3 4 4 5 5 6 6 6 7 7 7 8 8 9 9 10 10 11 11 11 12

Trisamsa I 1 1 1 11 11 11 11 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5

00 Drekana 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10;:;l Saptamsa 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 1 1 I 1 2 2 2Cl:;:;l Navamsa 10 10 11 11 11 12 12 12 1 1 I I 2 2 3 3 3 3 4 4 4 5 5 5 6 6

~ Dwadsamsa 2 3 3 3 4 4 5 5 6 6 7 7 7 8 8 8 9 9 10 10 11 11 12 12 12 1Trisarnsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 12 10 10 10 10 8 8 8 8

Hora 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4

Drekana 3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7 7 7 11 11 11 11 11 11 11 11....Z Saptamsa 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9....~ Navamsa 7 7 8 8 8 9 9 9 10 10 10 10 11 11 12 12 12 12 I I I 2 2 2 3 3r;o;:

Dwadsarnsa 3 4 4 4 5 5 6 6 7 7 8 8 8 9 9 9 10 10 11 II 12 12 I I I 2eTrisamsa 1 1 I I II 11 11 11 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

.Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5

Cl: Drekana 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 12 12 12 12 12 12 12 12r;o;: Saptamsa 10 10 10 II II II 11 12 12 12 12 1 I 1 I' 2 2 2 2 3 ~ 3 3 4 4 4UZ Navamsa 4 4 5 5 5 6 6 6 7 7 7 7 8 8 9 9 9 9 10 10 10 11 11 11 12 12< Dwadsamsa 4 5 5 5 6 6 7 7 8 8 9 9 9 10 10 10 II II 12 12 I I 2 2 2 3U

Trisarnsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 12 10 10 10 10 8 8 8 8

(128)

SAPTAVARGA CALCULATIONNrite: L'Hnra; 2. Drekana, 3. Saptamsha -I. Navamsu 5. O,vada'samsaTlIisamsa

tr: Deg.{"l 2 3 4 5 6 7 8 10 12 12 12 13 15 16 17 17 18 20 21 22 23 25 25 26 27 30z MI.(') 30 20 17 0 40 30 34 0 0 30 51 20 0 40 8 30 0 0 25 30 20 0 42 40 30 0~ Sec (") 0 0 9 0 0 0 17 0 0 0 26 0 0 0 34 0 0 0 43 0 0 0 51 0 0 0'LJ

Hora 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4Drekana 5 5 5 5 5 5 5 5 9 9 9 9 9 9 9 9 9 9 I 1 1 1 1 1 1 1

o Saptamsa 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11~ Navamsa 1 I 2 2 2 3 3 3 4 4 4 4 5 5 6 6 6 6 7 7 7 8 8 8 9 9

Dwadsamsa 5 6 6 6 7 7 8 8 9 9 10 10 10 II II 11 12 12 1 1 2 2 3 3 3 4Trisamsa I 1 1 1 11 II 11 11 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5- 5 5 5 5 5 5 5 5Drekana 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 2 2 2 2 2 2 2 2

8Saptamsa 12 12 12 I 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6c:: Navamsa 10 10 11 11 II 12 12 12 I I 1 I 2 2 3 3 3 3 4 4 4 5 5 5 6 6....;;.. Dwadsamsa 6 7 7 7 8 8 9 9 10 10 II II 11 12 12 12 1 I 2 2 3 3 4 4 4 5

Trisamsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 12 10 10 10 10 8 8 8 8

Hora 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4Drekana 7 7 7 7 7 7 7 7 11 II II II II II II II II 11 3 3 3 3 3 3 3 3

~ Saptamsa 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 II II II 12 12 12 12 1 I I=Navamsa 7 7 8 8 8 9 9 9 10 10 10 10 11 11 12 12 12 12 1 1 1 2 2 2 3 3:i Dwadsamsa 7 8 8 8 9 9 10 10 II 11 12 12 12 I I 1 2 2 3 3 4 4 5 5 5 5

Trisamsa 1 1 1 1 II 11 11 11 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5

o Drekana 8 8 8 8 8 8 8 8 12 12 12 12 12 12 12 12 12 4 4 4 4 4 4 4 4 4;:: Saptarnsa 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8~ Navamsa 4 4 5 5 5 6 6 6 7 7 7 7 8 8 9 9 9 9 10 10 10 11 11 11 12 12U Dwadsamsa 8 9 9 9 10 10 11 11 12 12 1 1 1 2 2 2 3 3 4 4 5 5 6 6 6 7~ Trisamsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 . 12 10 10 10 10 8 8 8 8

(129)

SAPTAVARGA CALCULATIONNote ~ 1 Hora: 2. Drekana 3 Saptamsha 4 Navamsa 5 Dwadasamsa 6 1'risanmI ....:

, ,

'7J Deg. (0) 2 3 4 5 6 7 8 10 12 12 12 13 15 16 17 17 18 20 21 22 23 25 25 26 27 30zc Mt.(') 30 20 17 0 40 30 34 0 0 30 51 20 0 40 8 30 0 0 25 30 20 0 42 40 30 0...'7J Sec (") 0 0 9 0 0 0 17 0 0 0 26 0 0 0 34 0 0 0 43 0 0 0 51 0 0 0

Hora 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4'7J

Drekana 9 9 9 9 9 9 9 9 I I I I I I I I I I 5 5 5 5 5 5 5 5;:J...Saptamsa 9 9 9 10 10 10 10 II II II II 12 12 12 12 I I I I 2 2 2 2 3 3 3~

~ Navamsa I I 2 2 2 3 3 3 4 4 4 4 5 5 6 6 6 6 7 7 7 8 8 8 9 9

~Dwadsamsa 9 10 10 10 II II 12 12 I I 2 2 2 3 3 3 4 4 5 5 6 6 7 1 7 8Trisamsa I I I I II II II II 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

'7J

Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5Z Drekana 10 10 10 10 10 10 10 10 2 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6~0 Saptamsa 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10U... Navamsa 10 10 II II 11 12 12 12 1 1 1 I 2 2 3 3 3 3 4 4 4 5 5 5 5 6~

~Dwadsamsa 10 II II II 12 12 1 I 2 2 3 3 3 4 4 4 5 5 6 6 7 7 8 8 8 8Trisamsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 12 10 10 10 10 8 8 8 8

Horn 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4

'7J Drekana II II II 11 11 II II II 3 3 3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7;:J Saptamsa II 11 II 12 12 12 12 I 1 I I 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5...

i Navamsa 7 7 8 8 8 9 9 9 10 10 10 10 II 11 12 12 12 12 I I I 2 2 2 3 3Dwadsamsa II 12 12 12 I 1 2 2 3 3 4 4 4 5 5 5 6 6 7 7 8 8 9 9 9 10Trisamsa I I I I II II II 11 9 9 9 9 9 9 9 9 9 3 3 3 3 3 7 7 7 7

Hora 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5Drekana 12 12 12 12 12 12 12 12 4 4 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8

'7J Saptamsa 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 II 11 II 11 12 12 12~ Navamsa 4 4 5 5 5 6 6 [, 7 7 7 7 8 8 9 9 9 9 10 10 10 II II II 12 12'7J.... Dwadsamsa II 12 12 12 I I 2 2 3 3 4 4 4 5 5 5 6 6 7 7 8 8 9 9 9 10I:l.

Trisarnsa 2 2 2 2 6 6 6 6 6 12 12 12 12 12 12 12 12 12 10 10 10 10 8 8 8 8

(130)

'J

Ahas 58

Akshansha 1

Angular distance 12

Antar dasa 99

Anomilistic Year 34

Apparent Noon 58

Apparent Solarday 33

Ascendant 28Asterisms 26

ASU 103

Autumnal Equinox 23

Ayanarnsha 2, 24

Bhutaganas (i)

Brahma 33

Budha (ii)

Cardinal Points 113Celestial Equator 1, 16

Celestiallat. 2, 19

Celestial long 2, 18Celestial Object 19

Celestial Poles 1Celestial Sphere 1, 16

Constellations 26

Cosmic Sphere 1, 16

Cusps 111

Dasa 95

Day 32

Declination 2, 19

Dhruva 2,19

Dwapar Yuga 32

Earth 1, 4

( Index)

Ecliptic 1, 17, 20

Epoch 24,50

Equator 1, 5

Equinoctial Points 2, 23

Five elements (i)

Fixed Zodiac 2, 24

Ganesha (i) r

Geographical LAT & LONG 1 7,Ghati 32

G.M.T. 38

Hemisphere 1, 6

Imaginary Circle 9

Incarnations (ii)

Interpolation 59

Ishta Kaal 104

Janma Nakshatra 96

Janma Rasi 96

Kaliyuga 32

Kalpa33

Koorma (ii)Kranti 19

Krishna (ii)

Lipta 32

Local Time 36

Lords of Constellations 26

L.M.T. 37

Lunar Day 34

Lunar month 34(131)

H2

Lunar Year 3~

Mahayuga 32Matsya (ii)

Mean Solar Day 33

Medium Codi (MC) 29

Midday 36

Months 33

Moveable Zodiac 2, 24

Nakshatras 26

Nakshatra Dina 33

Nakshatra Year 34

Narasimha (ii)

Nirayana System 2, 24

Oblique Ascension 2, 22

Para 32

Parsu Ram (ii)

Perihelion 34

Precession of Equinoxes 2, 23

Rama (ii)

Rashimaan 2, 22, 104

Ratri 58

Rekhansha 1

Right Ascension 2, 19

Savana Day 33

Savana Year 34

Satyuga 32

Sayana System 2, 24

Sayana Zodiac 25

Sidreal Day 33

Sidreal Time 48

Sidreal Year 33

Sidereal Zodiac 25

Solar Day 33


Solar System I. 2

Spring 23

Standard Time 37

Stars 26

Sunrise/Sunset 57Surya (ii)

Table of Ascendant 2, 29

Table of Houses 2, 29

Tatpara 32

Tenth House 28

Terrestrial Equator 5Time Measure 32

Time Zone 39

Traditional Method 103

Treta Yuga 32 .

Tropical Year 34

Tropical Zodiac 25

Unidirectional 19

Vilipta 32

Varah (ii)

Vernal Equinoctial Point 24

Vernal Equinox 23

Vighati 32, 104

Vighneshwar (i)

Vikshepa 19

Vipala 32

Vimshotteri Dasa 95

Years 34

Yuga 32

Zodiac 2, 18

Zodiac of Constellation 25

Zodiac of Signs 25

Zonal Standard Time 38

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