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Example of Tibetan Astronomical Calculations

  • By Kim Lai and Tsering Dolma.   Copyright 1996.

  • This method is the official system of His Holiness the Dalai Lama, and is not a creation based upon speculation.  It represents the basis for further specialised calculations.  Here you may appreciate why the major task in training of a Tibetan Astrologer is calculation.



     
  • Synopsis of calculation methodology:

  •  

     

    THE TEN STEPS FOR THE FIVE PLANETS (mars jup venus merc sat)
    1.  zla dag
    2.  spyi zhag  (GENERAL DAY)
    3.  sgos zhag
    4.  dal bar of three wrathful planets
    5.  rkang ‘zin of two peaceful planets
    6.  zhi dal drag rkan  -or-  nyi bar of solar day
    7.  dal rkang
    8.  dal dag   (rang ‘gros - self movement)
    9.  myur rkang
    10.  myur dag

    FOR THE SUN AND MOON
    1.  ‘das lo - (the bygone year)
    2.  zla dag - (completed month)
    3.  gza’ dru - (root of planet)
    4.  nyi dru - (root of sun)
    5.  ril cha - (full and partial)
    6.  gza’ bar
    7.  gza’ phey dag
    8.  nyi bar
    9.  gza’ dag
    10.  nyi dag
    11.  zla skar (moon constellation)
    12.  sbyor ba
    13.  byed pa
    = sun and moon positions

    THE CALCULATION OF DACHEN: (dachen rtsis)
    1.  zla dag
    2.  spyi zhag
    3.  rza ba  (root of dachen)
    4.  Constellation of the head  (dachen gdong)
    5.  Constellation of the tail   (dachen mjug)
    In this section we provide an example of the stages in calculating the Kar Tsee horoscope as it is nowadays prepared by Men Tsee Khang astrologers, using the Tibetan almanac.  The almanac is calculated directly from  astronomical principles.   Similar to the western method of using an ephemeris to calculate a chart, the almanac is the primary reference book for palnetary positions etc.  Tibetan almanacs are in short supply and for several years there was no almanac (lo tho) published.  In those cases the calculation of the birth chart must follow the arduous path of calculation from first principles.

    These calculaitons are done in a traditonal fixed format for which a special calculation sand tray board is used.  This is called a sa gzhong lit. wooden board.  This board is suitable for the format of calcualtions and Tibetan astrologers have a saying that if you have good practice they you can calculate faster using the sa gzhong than an electronic calculator.

    Calculations are of two types called:
    a.  Siddhanta system (dub pa)
    this type of calculation can be termed the full tenet system and calculations are made from first principles of Kalacakra astronomy.

    b.  Karana system (byed pa)
    this type of calculation can be termed the precise system (or shortened system) because it requires less calculation time.

    the difference between the two systems is that in the dub pa system the weekday result is more accurate and in the byed pa system the rgyu skar is more accurate.  For eclipses the byed pa system is employed.  Therefore to calculate the almanac both systems are utilised.
    In Ladakh and Spiti the almanac is calculated using only the byed pa system, but at MTK both systems are used.  For the calculation of horoscopes the dub pa system is the one most frequently engaged, as it is most importatn to find the daily planet ie weekday.
     

  • Information required.

  • Name:  Person
    Birth date:  June 3rd 1999
    Time of birth:  9.30 am
    Gender: Female
    Place of birth:  Dharamsala, INDIA.
     
  • Steps in calculation: using the full system.

  •  

     

    1.  The first step is to calculate the 5 inclusive calendar features (lnga bdus- lit.  5 collect)
    In our example these are:
    a.  First find the ‘das lo (bygone years) from 1987 fire rabbit year to the birth date;  The Kalacakra Era of Tibet was 1027 and marked the commencement of a new series of 60 cycles called (rab jung) therefore we are currently in the 17th Rab jung which commenced in 1987.

    thus in our example this is 12 years from 1987.

    then multipy the ‘das lo by 12 [for the 12 zodiac signs in each year (Khyim)]
    therefore
    12X12=144
    then add the bygone year from Tibetan 3rd month (due to Kalacakra new year being in Tib 3rd month)  the kalcakra year is always commencing when its the 15th of 3rd month. usually during Aries.

    our example date is Tib 19th day of 4th month of earth rabbit year. Therefore we need to add one month (sign) to the above figure
    thus
    144+1= 145.
    Now we place the sum of this calculation into two rows as follows

    145

    145

    the bottom row is multiplied by 2.

    145

    145X2= 290  (due to the change from solar day to lunar day)

    then add zero because our example occurs in the 13th rab jung of 1987 starting from 1987 fire rabbit there is no remaining year (rtsis ‘phro).  After every cycle of 60 years the method of calcualtion must change otherwise the results will become innnacurate.  If the person was born in the 16 rabjung then 55 is added.

    table may be inserted here for addings and subtractions for previous rabjungs

    145

    145X2= 290+0=290

    our result is of 290 is divided by 65 because>

    Note: after every 32.5 lunar months there will be an intercalary month (zla bshol - lit-extra month) later to get explantion form Tserings notes.
     

    290/65= 4 (quotient )and remainder 30

    then add these as follows
    145 + quotient ie  145+4= 149 and 30 rem written like this>>

    149  (this is called the zla dag - clear month)
     30   (this is called the zla ‘phro - remaining month)

    now put the zla dag in five rows with space in between

    149

    149

    149

    149

    149

    then multiply the first row by the following five constants

    which are
    1
    31
    50
    0
    480

    therefore

    149 X 1 = 149

    149 X 31 = 4619

    149 X 50 = 7450

    149 X 0 = 0

    149 X 480 = 71520
     

    then add the following constants

    3
    11
    27
    2
    332
     

    149 X 1 = 149 + 3 = 152

    149 X 31 = 4619 + 11 = 4630

    149 X 50 = 7450 + 27 = 7477

    149 X 0 = 0 + 2 = 2

    149 X 480 = 71520 + 332 = 71852

    then divide by the constants

    note when dividing the Tibetan rule is always do from bottom to top.

    7
    60
    60
    6
    707

    thus
     

    149 X 1 = 149 + 3 = 152 + 79 = 231 / 7 = 33 rem 0

    149 X 31 = 4619 + 11 = 4630 + 124 = 4754 / 60 = 79 rem 14

    149 X 50 = 7450 + 27 = 7477 + 17 = 7494 / 60 = 124 rem 54

    149 X 0 = 0 + 2 = 2 + 101 = 103 / 6 = 17 rem 1

    149 X 480 = 71520 + 332 = 71852 / 707 =  101 rem 445
     
     

    important note always the quotient moves upwards to be later added and the remainder is kept in the same row.

    after this calculation we have the final results of gza dru  (lit root of the weekday) as below
    =========
    gza dru results are:

    0
    14
    54
    1
    445
    =================
    next step is to find the suns position.

    now we have to find the nyi dru (root of the sun) to find the sun’s position in the zodiac.

    take the zla dag (in our example 149) and place in five rows

    149

    149

    149

    149

    149

    then multiply by top to bottom by the constants

    2
    10
    58
    1
    17

    thus

    149 X 2 = 298

    149 X 10 = 1490

    149 X 58 = 8642

    149 X 1 = 149

    149 X 17 = 2533

    Then sometimes an addition of constants is used however in this rab jung since 1987 there is no addition required due to nyima stong bzhuhs (sun empty enter) so therefore we move staight onto division of the following constants

    27
    60
    60
    6
    67

    thus

    149 X 2 = 298 + 27 = 325 / 27 = 12 rem 1

    149 X 10 = 1490 + 144 = 1634 / 60 =  27 rem 14

    149 X 58 = 8642 + 31 = 8673 / 60 = 144 rem 33

    149 X 1 = 149 + 37 = 186 / 6 = 31 rem 0

    149 X 17 = 2533 / 67 = 37 rem 54

    now nyi dru results are as follows

    1
    14
    33
    0
    54

    ========
    the next step is ril cha -ril bu means full cha means partial of he ril bu

    Take the zla dag  in our example this is 149
    then place it in two rows

    149

    149
    then multiply by the constants

    2
    1

    thus
    149x2= 298
    149x 1= 149

    then add the constants
    21
    90

    thus
    149x2= 298 + 21 = 319
    149x 1= 149 + 90 = 239

    then divide by the constants remember to start at bottom and add upwards
    28
    126

    thus
    149x2= 298 + 21 = 319 + 1 = 320 /28 = 11 rem 12
    149x 1= 149 + 90 = 239 / 126 = 1 rem 113

    thus the result for ril cha is
    12
    113

    which is the same as in the almanac (insert example here in picture)

    ========

    Now arrage the numbers in a diagram format in the following manner

        upper
        zla dag
    left side      right side
    zla dru      nyi du

        lower
        ril cha

    therefore in our example we have as the table below

    *********

    Thus we have the table as appears for the month in the almanac
     

    now we must calculate the lnga bdus by the follwoing method>

    take the  gza dru  and add the rtag long of the gza (gza ‘rtag long) then divide by each of the days hours minutes etc

    then from this we gza bar

    our gza dru is

    0
    14
    54
    1
    445

    then we find the rtag long of the 19th day in our example
    which is found in the table of connstants for each day of the lunar month
    4
    42
    9
    4
    304

    insert the rtag long table form page 64-5 tse nams book
     added together

    0 + 4 = 4
    14 + 42 = 56
    54 + 9 = 63
    1 + 4 = 5
    445 + 304 = 749

    now divide by the constants (‘khor lo)

    7
    60
    60
    6
    707

    thus (starting at the bottom)

    0 + 4 = 4 + 0 = 4/ 7 = 0 rem 4
    14 + 42 = 56 + 1 =57 /60= 0 rem 57
    54 + 9 = 63 + 1 = 64 /60 = 1 rem 4
    1 + 4 = 5 + 1 = 6 /6 = 1 rem 0
    445 + 304 = 749/707 = 1 rem 42

    therefore the result is called gza bar which for our example is
    4
    57
    4
    0
    42
    =======
    next to calculate the gza phyed dag (half weekday calc) but before we can calculate this we need to calculate zla rkang

    therefore before we proceed we have to calculate our zla rkang as follows

    for the zla rkang we take the ril cha put in 2 rows

    12  ie ril bu

    113  ie cha shas

    add the day of the Tibetan date of example (ie the 19th day) at ril bu

    in our example this is 12
    so
    12 plus 19 = 31
    then divide by constant 14 (due to point of waxing and waning)

    31 / 14 = 2 rem 3

    when the quotient is 1, 3, 5, 7, 9 ie odd numbers then it is unequal and we have to subtract later
    when the quoient is 2,4,6,8, and even numbers which is equal then we have to add later

    next we refer to the table with remaining number  (zla rkang rei’ mig - table fo the moon full pg. 59)
    then find the rkang sdom () for the rem number in the table which in this example is 15
    then multiply by rkang bzung (note that in the table the rkang bzung is the number diagonally below the row of the key figure see table below)

    eg.
     
     
     

    which in the example the table gives 4.

    place the rkang sdom at the side thus

    15

    the important numbers now are the (derived from ril bu)
    rkang sdom = 15
    rkang bzung = 4

    no further need for the rkang ‘zin (3)

    Now we multiply the cha shas by the rkang bzung which in our example is 4.
    thus
    cha shas 113 X 4 = 452
    then divide by the constant for all rab jung c=126
    113 X 4 = 452 / 126 = 3 rem 74

    then put the quotient below the rkang dom
    thus
    15 (rkang sdom)
    3  (quotient) (yang dag rgyu’ chu tsod)

    then multiply the remainder by constant 60
    thus
    74X60= 4440
    then eivide by constant 126

    thus 4440 / 126 = 35 rem 30

    this quotient (ie 35) write it below the yang dag rgyu’ chu tsod

    15 (rkang sdom)
    3  (quotient) (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)

    now multiply the rem (ie in this case 30) by constant 6 to find the dbugs (ie seconds)
    30 X 6 = 180

    then divide by 126
    30 X 6 = 180/126 =1 rem 54

    then put the quotient below the yang rgyu’ srang

    thus
    15 (rkang sdom)
    3  (quotient) (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)

    with the remainded (ie 54) multiply by the constant 707

    54X707 = 38178

    divide by constant 126
    thus
    54X707 = 38178 / 126 = 303 rem 0

    if the answer is correct the remainder is always zero- if there is any remainder at this point of the calculation then a mistake in calculation has been made.  the remainder has to be placed under the previous figures.
     

    15 (rkang sdom)
    3  (quotient) (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)
    303 (cha shas)

    with the table of zla rkang you will find that from 1 to 7 is the snga rkang (like early foot ) from 8 to 14 is bhyi rkang (late foot).
    NB  IT IS VERY IMPORTANT TO NOW THAT the rkang bzung of the rkang ‘zin is diagonally below since the rkang bzung of 7 is phyi rkang and not snga rkang
     

    A special rule if our answer is snga rkang then we have to add the rkang sdom to yang dag rgyu’ chu tsod.  A special rule if our answer is phyi rkang then we have to subtract the rkang sdom from yang dag rgyu’ chu tsod.

    in our example we have snga rkang and add those two numbers ie 15 and 3 which now equals 18

    15 (rkang sdom)
    3  (quotient) (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)
    303 (cha shas)

    therefore

    15 +3 = 18  which is the final yang dag rgyu’ chu tsod
    thus it comes like

    18 (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)
    303 (cha shas)

    now we have zla rkang so we can now proceed with the gza phyed dag (half weekday calc)
     

    to do this take the gza bar  calculated previoously and add or subtract (according to the previously described odd and even numbers rule) the zla rkang (motion of moon )

    thus

    gza bar  for our example is

    4
    57
    4
    0
    42

    becuase the quotient is 2 (ril bu plus date of example divided by constant 14 eg. 12 + 19 = 31 / 14 = 2 rem 3 (ie the quotient is 2 therefore add ) we add the zla rkang to gza bar

    thus in our example gzar bar is
    4
    57
    4
    0
    42
    and zla rkang is

    18 (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)
    303 (cha shas)
    so we add together (easiest in this calculation to add bottom to top becuase full units may be transposed upwards)

    4
    57
    4
    0
    42
     

    18 (yang dag rgyu’ chu tsod)
    35 (yang rgyu’ srang)
    1  (dbugs)
    303 (cha shas)

    4 + the transposed 1 from below => 4+1=5
    57+18 = 75 (here divide by 60 => 1 rem 15, so 1 transposes upward)
    4+35= 39
    0+1= 1
    42 + 303 = 345

    therefore our results are
    5
    15
    39
    1
    345
    which is call gza phyed dag  and therefore at this point we have completed the half weekday calculation.
    To make a nyi bar, one must take the nyi dru and add it with the nyi mai rtag longs.
    1+1=2

    14+22=37

    33+56=30

    0+5=0

    54+13=0

    Then,take the nyi bar which we did before and  place it into two columns.
    Our nyi bar is
    2-6 = 27+2=29-6=22                                                       2

    37-45= 60+37=97-45=52                                               37

    30                                                                               30

    0                                                                                  0

    0                                                                                  0

    Substract the 6, 30 from one of the nyi bar, if you are unable to substract from the nyi bar then add 27 at constellation and substract it.
    3-6, for this example, we could not able to substract it.  So add 27+ 3= 30-6= 24 for constellation and substract the below number by 45.  For this again we could not, then , take one down from constellation(24) which  becomes 23 and 1 constellation is 60 hours accoridng to astronomical hours.  60+ 37=97-45=52
    Now we have:

    22

    52

    30

    0

    0
    Then, divide the first two column by 13, 30.

    22/13=1 rem 10

    52/30=22

    30

    0

    0
    When you could divide the 13, 30 after substracting by 6, 45 then , it is called dor.  And multiply the remaining number of constellation by 60 and add hours( which is 22 in  our example) and divide by 135 then, we could find the nyi rkang.

    9x60=540+22(hours)=562/135=4 rem

    2(4 is rkang ‘zin in this calculatin, the rkang sdom is 10 and the rkang bzung is 4.  Then multipy the rkang bzung all the four i.e. hours to partial.
    nyi rkang

    10  rkang sdom

    22x4=88

    30x4=120

    0x4=0

    0x4=0

    Then divide by constant wheel which is  60, 6, 67(from down to top)

    88+2=90 /135= 0 rem 90

    120/60=2 rem 0

    0

    0

    Nyi rkang
    10 rkang sdom
    0 chu tsod
    40
    0
    0

    If it is sNga rkang then add and if it is phyi rkang then you have to substract the nyi rkang from rkang sdom to yang dang rgyui chu tsod.

    Let’s say, here our example , the rkang sdom is 10 and chutso is 55 and it is phyi rkang,  So we have to substract it from rkang sdom to cha shas.

    10

    0

    40

    0

    0

    10-o=10,  9

    60-40=20

    0

    0

    Therefore, our nyi rkang is :
    9
    20
    0
    0
    0

    Now, we have to add these numbers to the gza phyed dag and nyi bar to find out the fully gza and nyi dag.

    Our nyi bar is

    2

    37+9=46

    30+20=50

    0

    0

    Nyi dag is:
    2
    46
    50
    0
    0
    That  means that the sun is in Taurus<

    To make a gZa dag.
    First take the gZa phyed dag and add the nyi rkang on it which becomes gZa dag.

    gZa phyed dag plus nyi rkang = gZa dag.
    5=5

    15+9=24

    39+20=59

    1+0=1

    345+0=345

    Therefore, our gZa dag is

    4(Wednesday).
    24(hours)

    59(minutes)

    1(second)

    345(Chashas)

    Now find the moon constellation:
     First take the nyi dag and place it into two like that.  Add one of nyi dag with the unique constant of the moon(zla bai mthun min rtag longs) which we call tses ‘khyud.

     2                              2

    46            46

    50            50

    Let’s add the rtag longs of our example dated 19th.  (Table tsenam page 61)
     2+17=19
    46+6=52
    50
    Therefore, our tses ‘khyud is:
    19
    52
    50
    0
    0

    To make a res grogs zla skar, substract the hours, minutes, second etc from tses which makes res grogs:
    Tses khyud
    19
    52
    50
    0
    0
    The hours , minutes, seconds of the weekday is :
    24
    59
    0
    0

    Let’s substract:

    19
    52-24=27
    50-59=51
    0=0
    0=0

    Therefore, the moon constellation are:
    19
    27
    51
    0
    0

    The fourth calcualtion of the five inclusive calendar feature is sbyor ba wich is the fourth line in the almanac.
    This is the easiest method of calcualting, add the nyidag and the moon conselation which is sbyor ba.

    Nyidag + Moon Constellation = sbyor ba

    2+19=22

    46+27=14

    50+50=40

    Therefore the sbyor ba of our exaple is :
    22
    14
    40

    The three days are Solar, lunar and zodiac days.  Among these three days, for the five inclusive calendars features are important for lunar days whereas solar day are important for the movement of five planets.

    gZa    Moon constellation     Nyi dag    sbyor ba

    5               19                      2              22
    24             27                     46              14
    59             50                     50              40
    1                0                       0                0
    345             0                       0                0
     

    RAPID CALCULATION OF THE FIVE INCLUSIVE CALENDAR FEATURES:

    Ist steps:
    Add  any date of your example  to the nyi dru and substract the nyi rags which makes the phyed dag reu mig.

    IInd steps:
    The way of making gza phyed dag and nyi dag:
    After finding the phyed reu mig, add the spyi nor of the gza and nyima which becomes gza phyed dag and nyi dag.

    IIIrd steps:
    The formula of making gza dag:
    Take the rilbu and add any date of your example then divide by 14 ,and look whether the quotion is odd or even.
    And use the table by the remaing numbers, and add or substract with the  hyed dag gza which becomes the full gza or gza dag.

    Then rest of the calculation are same as before.

    CALCULATION OF THE FIVE PLANETS(gZA lNga):
    Example:
    1994, 3rd month of 8th day to the Tibetan lunar calendar:
     

    Ist make the spyi zhag( lit. general days)
    We already the know  calculation of zla dag and multiply the zla dag by  30.
    Let’s do the same example of zla dag 86 x30= 2580(This means the day of month are changed into the days.

    IInd
    Turn the lunar day to solar days:
    add any date to the above numbers, lets say “8” which becomes
    2580+8=2588
    After adding the date, place it into three rows and add the 51 and 551 to the middle and last rows , then divide by 707 and 64 to bottom to top.

    2588-41=2547

    2588+51=2639+4=2643 /64= 41rem 19

    2588+551=3131/707=4 rem 311

    This is called unclear day( Mi gsel zhag).

    2547

    19

    311

    To make a clear day or gsel zhag.
    Take the spyi zhag or general day and place it into two rows, then add 3 to one row and divide by 7 and compare the remaining number to weekday.  If it is less than the weekday add one, it is more than week than substract one.  Let’s take an example, if the weekday is Saturday and your remaing number is 6(friday) then add.  Then if your remaining number is 0 or Sunday then substract one.

    2547+3=2550/7=364 rem 2

    The weekday on the following example day is Tuesday and we have gotten the Monday which is 2.  So we have to add one to those three rows because it is less than the weekday.

    2547+1=2548

    19+1=20

    311+1=312
    This is called gsel zhag(clear day)

    Now calculation of the sGos zhag or private day.
    Take the general day which is 2547 and place it into 6, then add some constant number of each planets and divide by their own constant wheel or cycle:

    Mars

    2547+115=2662/687=3 rem 601, remember the remaining number is the sgos zhag.

    Jupiter

    2547+4246=6893/4332=1 rem 2461
     

    Saturn

    2547+6696=9243/10766=0 rem 9243
     

    Mercury

    2547x100=254700+8386=263086/8797=29 rem 7973
     

    Venus
     

    2547x10=25470+1762=27232/2247=12 rem 268
     

    Sun(nyi mai sgos zhag mang ba)

    2547x18382=46818954+14872=46833826/6714405=6 rem 6547396

    To make less nyi mai sgos zhag(nyi mai sgos zhag nyung ba)
    Take the nyi sgos mang ba and divide by 18382 and the remaining will be the nyi sgos:

    6547396/18382=356 rem 3404

    Table:

    Mars     Jup      Sat        Mer      Ven    Sun(more)   Sun(less)
    601      2461    9243     7973    268    6547396     3404
     

    Calculation of the three wrathful planets of dal bar and rkang ‘zin of two peace planets.

    Dal bar of the three wrathful planets:
    Take the sgos zhag of each planet and place it into 6 rows and multiply by 27, 60,69,6, and their own chashas(229-mars, 361-Jupiter, 5383-Saturn) then divide by their constant cycle.

    MARS:

    601x27=16227/687=23 rem 426

    426x60=25560/687=37 rem 141

    141x60=8460/687=12 rem 216

    216x6=1296/687=1 rem 609

    609x229=139461/687=203 rem 0
     

    The dalbar of Mars is
    23
    37
    12
    1
    203
     

    JUPITER:

    2461x27=66447/4332=15 rem 1467

    1467x60=88020/4332=20 rem 1380

    1380x60=82800/4332=19 rem 492

    492x6=2952/4332=0 rem 2952

    2952x361=1065672/4332=246 rem 0
     

    The dal bar of Jupiter is
    15
    20
    19
    0
    246
     

    SATURN:
    9243X27=249561/10766=23 rem 1943

    1943X60=116580/10766=10 rem 8920

    8920x60=535200/10766=49 rem 7666

    7666x6=45996/10766=4 rem 2932

    2932x5383=15782956/10766=1466 rem 0

    The dal bar of Saturn is
    23
    10
    49
    4
    1466

    this completes the dal bar of wrathful planets.

    Now comes the calculation rkang zin of the peaceful planets.
    (note: fro wrathful we have to make dal bar but for peaceful we have to make rkang zin)

    MERCURY  in our example the figure is 7973

    7973x27=215271/8797= 24 rem 4143
    4143X 60=248580/8797=28 rem 2264
    2264x60=135840/8797=15 rem 3885
    3885x6=23310/8797=2 rem 5716
    5716x8797=4281284/8797=5716 This is alwqays no remainder
    we should always find 0 at the ned of the calculation as this will somehwat demonstrate tehat the calculation is correct.

    therefore the rkang ‘zin of mercury is
    24
    28
    15
    2
    5716

    the calculation of the dal bar of venus
    take the quotient of venus ie in this example 268

    268x27=7236/2247=3 rem 495
    495x60=29700/2247=13 rem 489
    489x60=29340/2247=13 rem 129
    129x6=774/2247=0 rem 774
    774x749=579726/2247=258 rem 0

    result for dal bar of venus is
    3
    13
    13
    0
    258

    =============
    Calcualtion of zhi dal drag rkang of all planets
    this will be calculated from the sun long ie 6547396
    also called the nyi bar of solar day

    6547396x27=176779692/6714405=26 rem 2205162
    2205162x60=132309720/6714405=19 rem 4736025
    4736025x60=284161500/6714405=42 rem 2156490
    2156490x6=12938940/6714405=1 rem 6224535
    6224535x149209=928756642815/6714405=138323 rem 0

    thus the nyi bar of solar day (nyin zhag nyi bar) is
    26
    19
    42
    1
    138323
     
     

    *
    now that we have these tables we can make the calcualtion of dal dag

    the wrathful palnet dal dag

    Mars
    before making the dal dag we first need the dal bar which from the table is
    and place them into two columns
    then subtract the birth sign of mars from table ie 9-30

    23-9 =14   23
    37-30=7   37
    12    12
    1    1
    203    203

    if th resuolt is more than 13-30 then it is called dor which you have to add later; if not then ma dor which you have to subtract.

    in our example it is
    14
    7

    so we have to subtract 13-30
    thus
    14-13=1=broken down to 60 mins? leaving 0 so we add

    7+60=67-30=37
    thus result is
    0
    37

    then take the rest with that
    thus
    0
    37
    12
    1
    203

    after this multiply the constellaiton by 60
    0x60=0 then add the hours
    0+37=37 then divide by 135 = 0 rem 37
    then keep a record of the quotient separately ie. 0 and refer to the table of mars (to be done. p.70) where 0 is the rkang ‘zin - the rkang sdom is 0 and the rkang bzung is 25.  Now put the rkang sdom in a separate place and write sgna rkang (to add)  After that multiply the rkang bzung to the rest.

    37x25=925
    12x25=300
    1x25=25
    203x25=5075

    then divide by

    135
    60
    6
    229

    remember in division to alwasy go from bottom to top

    37x25=925+5=930/135=6 rem 120
    12x25=300+7=307/60=5 rem 7
    1x25=25+22=47/6=7 rem 5
    203x25=5075/229=22 rem 37

    now returning to the figure (ie 0)put aside place the result underlined above under it

    dal rkang =
    0 (rkang sdom)
    6 (yang gyur chu tsod)

    the remainder of 120 is multiplied by 60
    120x60=7200+7(from rem)=7207/135=53 rem 52

    then take the quoaitnet and place it under as followis

    dal rkang =
    0 (rkang sdom)
    6 (yang gyur chu tsod)
    53 (yang gyur srang)

    then take the 52 remainder multiply by 6
    52X6=312+5(ie from rem)=317/135= 2 rem 47
    then

    dal rkang =
    0 (rkang sdom)
    6 (yang gyur chu tsod)
    53 (yang gyur srang)
    2 (dbugs)

    thenthe remainder agsain 47x229=10763+37 (past remainder)=10800/135=80 rem 0

    now this is the dal rkang of mars finally result is

    dal rkang =
    0 (rkang sdom)
    6 (yang gyur chu tsod)
    53 (yang gyur srang)
    2 (dbugs)
    80 (cha shas)

    so now we have to add rkang sdom plus chu tsod so

    dal rkang =
    0+6=6 (rkang sdom)+(yang gyur chu tsod)  Note:
    53 (yang gyur srang)
    2 (dbugs)
    80 (cha shas)
    Note: the 0 and 6 ar added becuase it is snga rkang in our example, for this snga rkang only add the forst two.  However if it was chi rkang then it would have to be subtracted.  BUT in chi rknag subtraction ALL are subtracted.  for example only

    [[dal rkang=
    5
    2
    20
    3
    200

    then if it was chi rknag then would be
    5-2=3 so it becomes 2 and 60 with the 60 placed below and the next number subt form it
    60-20=40 and so becomes 39 and 6 so
    6-3=3  and so becomes 2 and 229
    229-200=29 so final result is

    2
    39
    2
    29    }}}}} finsh example of this variation]]]]]]

    so to continue we find the dal dag by taking the second column of figures and add dal rkang just finsihed above

    23
    37+6=43
    12+53=65
    1+2=3
    203+80=283

    so now divide form below upwards

    23
    37+6=43+1=44/60=0 rem 44
    12+53=65+0=65/60=1 rem 5
    1+2=3+1=4/6=0 rem 4
    203+80=283/229=1 rem 54
    this is called dal dag of mars
    thus
    23
    44
    5
    4
    54

    the same process is used for the resto f the wrathful planets ie, sat and jupiter, but they have different cha shas and ‘khor lo which is given in the table below.  Also birth signs are different and are abtained from tables above.
     

    these tables and those above are clooectively used in many astro texts of phugs lugs and could be somewhat likened to the Cassini tables of medieval European astronomy.

    ===========
    For peaceful planets a different method is employed- whilst for wrathful planets we start with the dal bar of each planet for he peaceful we start with the nyi bar of solar day, also called zhi dal drag rkang

    FOR MERCURY=>

    Take the already calculated nyi bar of solar day.  In this confusion should not need to arise because of the names ahving different expressions.

    nyi bar of solar day placed inot 2 columns

    26   26
    19   19
    42   42
    1   1
    138323  138323

    then subtract the birth sign figures of mercury from table which is

    16
    30

    thus
    26
    19  ie 26:19 minus 16:30 =9:49
    42
    1
    138323

    thus
    9
    49
    42
    1
    138323

    next subtract 13:30
    so in our example we cannot so its ma dor so we need to subtract later on.
    now we are giong to calcualte dal rkang, so to do this we

    9x60=540+49=589/135=4 rem 49 []
    formt his we have to look at the table on pg 70 using the quotient as our key figure which in our case is 4.  Then the rkang sdom is 17 the rkang bzung is 7.  {note the diagonaly reference note well above]
    next multiply by rkanh bzung all the remaining numbers

    49x7=343
    42x7=294
    1x7=7
    138323x7=968261

    then divide by 8797 (cha shas of mercury above in table) from bottom to top.
    then 6 then 60 then 135

    49x7=343+4=347/135= 2 rem 77
    42x7=294+2=296/60=4 rem 56
    1x7=7+6=13/6=2 rem 1
    138323x7=968261/144755(cha shas of nyi ma)=6 rem 99731 so up

    correct till here now

    dal rkang of mercury is 17
    17 (rkang sdom)
    then the result of above calc
    2 (yang rgyu chu tsod)
    the rem 77x60=4620+56(mins)=4676/135=34 rem 86
    now take the 34 from the above line thus
    34 (yang rgyu srang)
    then take the 103 from above
    86X6=516+1(above higher)=517/135=3 rem 112
    3 (dbugs)
    now 112 (rem)x149209 (whihc is the cha shas of nyi ma)=16711408+99731=16811139/135= 124526 rem 129

    [answer still has remaider so it seems something is wrong in this calculation, but it is written in the text that its ok to have a remainder which becomes called the cha shas of 135.]

    thus so far result of mercury dal rkang is
    17
    2
    34
    3
    124526
    but since we had chi rkang previously, accroding to the rule we must subtract it

    17-2=15 = 14 and 60 chu srang
    next 60-34=26 = 25 and 6 dbugs
    6-3=3=2 and 149209 (which is chas shas of nyi ma)
    149209-124526=24683

    so now we have final result of dal rkang for mercury
    14
    25
    2
    24683

    now we are going ot make the dal bar of mercury (nyi bar of soalr day) then subtract or add with dal rkang .  [note: we are subtracting rather than adding because of the rule of above and below 13-30 ie half consteallation.

    nyi bar of solar day=
    26
    19
    42
    1
    138323

    minus dal rkang of merc

    14
    25
    2
    24683

    thus

    26
    19-14=5
    42-25=17 (16 plus 6)carry down
    1-2= can’t do so break down previous line 6+1=7-2=5
    138323-24683=113640

    so now our dal dag of mercury is
    26
    5
    16
    5
    113640
    ===========
    Now we have to prepare the myur dag for the wrathful and peaceful planets.  From the myur dag we can find the planets positions.

    In this process we first have to equalise (chas shas shed snyon) the ‘chas shas of dal dag’ of each peaceful planet and the chas shas of rkang ‘zin of wrathful.  So we will now take the example of Mars.

    rkang ‘zin of mars is (nyi of solar day)(previously calculated).  this is due to the fact that the nyi bar of solar day is the rknag ‘zin of wrathfuyl and as well the dal bar of peaceful.  This is whay it can also be called the zhi dal drag rkang.  (zhi dal means dal bar of peaceful) (drag rkang means rknag ‘zin of wrathful)

    nyi bar of solar day (zhi dal drag rkang)

    26
    19
    42
    1
    138323

    then the cha shas of mars from the table is 229
    thus

    138323x229=31675967
    which is then dividied by 149209 which is the chas shas of the sun in the case of all planets wrathful and peaceful the chas shas of sun is used to equalise
    thus

    31675967/149209= the quotient will become the equalised chas shas of the planet and the remainde the equalised chas shas of the sun
    thus
    31675967/149209=212 rem 43659 in which 212 becomes chas shas of 229 and 43659 becomes chas shas of 149209.
    thus we have the equalised rkang ‘zin of mars
    26
    19
    42
    1
    212
    rem 43659

    so now that we done the equalisation we can make the myur dag of mars by taking the dal dag of mars and place into two columns then subtract it from the equalised rknag ‘zin of mars from one of the columns.

    23   23
    44   44
    5   5
    4   4
    54   54

    so now minus one column fron the equalised rkang ‘zin of mars

    26-23=3 (becomes 2 and 60)
    19+60=79-44=35
    42-5=37 (becomes 36 and 6)
    1+6=7-4=3
    212-54=158
    rem 43659

    the result is
    2
    35
    36
    3
    158
    43659

    Note:  so now we subtract 13:30 which cannot be done so it is ma dor means remember to add later.  If the constella tion could be subtracted it is subtraceted at this point.

    then we refer to the table of myur rkang of mars table on p.71.

    from the table the 2 in our example becomes
    the rkang sdom is 47
    the rkang bzung is 23

    therefore the 2 can be scrapped and becomes

    35
    36
    3
    158
    43659

    so next multiply the remaining figures by the rkang bzung which is 23 and then collect into appropriate units by dividing by the approapriate figure.  remember to dvide from bottom to top

    35x23=805+14=819/60=13 rem 39
    36x23=828+14=842/60=14 rem 2
    3x23=69+15=84/6=14 rem 0
    158x23=3634+6=3640/229=15 rem 205
    43659x23=1004157/149209=6 rem 108903

    so we place the final figure of above calulation ie 13 below the rkang sdom as below to make the myur rkang

    myur rkang
    47 (rkang sdom)
    13 (yang rgyu’ chu tsod)
     

    now the remanider from the 13 is 39 which is multiplied by 60
    thus
    39X60=2340+2( from above calc)=2342/60=39 rem 2

    myur rkang
    47 (rkang sdom)
    13 (yang rgyu’ chu tsod)
    39 (yang rgyu’ srang)

    now remainder again
    2x6=12+0(from up)=12/60=0 rem 12

    myur rkang
    47 (rkang sdom)
    13 (yang rgyu’ chu tsod)
    39 (yang rgyu’ srang)
    0  (dbugs)

    now rem again
    12X229=2748+205=2953/60=49 rem 13
    note for myur dag alwayas use /60 rather than /135

    myur rkang
    47 (rkang sdom)
    13 (yang rgyu’ chu tsod)
    39 (yang rgyu’ srang)
    0  (dbugs)
    49 (chas shas of 229)

    so agian atek rem whichi is 13
    13x149209=1939717+108903=2048620/60=34143 rem 40
    therfore
    myur rkang
    47 (rkang sdom)
    13 (yang rgyu’ chu tsod)
    39 (yang rgyu’ srang)
    0  (dbugs)
    49 (chas shas of 229)
    34143 (chas of 149209)

    now we have to add rkang sdom and chu tsod which is 47 plus 13 = 60/60=1 rem 0

    now we write the myur rkang
    1 (constellation)
    0 (yang rgyu’ chu tsod)
    39 (yang rgyu’ srang)
    0  (dbugs)
    49 (chas shas of 229)
    34143 (chas of 149209)

    now take the second column of dal dag at the beginning and add the myur rkang above to it]

    dal dag  myur rkang  equals
    23   1    24
    44   0    44
    5   39    44
    4   0    4
    54   49    103
    34143      34143

    so this finally the myur dag which the position of mars

    24
    44
    44
    4
    103
    34143

    to translate mars is in the 24th constellation at 44 rgyu rkang and the 44th etc.  usually only to the hour is enough.
    in terms of zodiac position this is somewhere in the last degree of aquarius {at 45 it enters pisces. }
    ===========
    for the peaceful planet equalisation the example follows,

    first take dal dag of mercury
    26
    5
    16
    5
    113640

    and chas shas of mercury which form the table is 8797

    thus
    26
    5
    16
    5
    113640

    113640x8797=999691080

    which is then dividied by 149209 which is the chas shas of the sun in the case of all planets wrathful and peaceful the chas shas of sun is used to equalise
    thus

    999691080/149209=6699 rem139989

    so the equalised chas shas of mercury is
    26
    5
    16
    5
    6699
    rem 139989

    Calculation of myur dag of Mercury
    Take the rkang ‘zin of the mercury and substract the dal dag from it.

    24-26=25
    28-5=23( which becomes 22 and 60)
    15+60=75-16=59(58 and 6)
    2+6=8-5=3(2 and 8797)
    5715+8797=14512-6699 =7813
    149209 -139989=135220
    After that ,we have to look whether the remainder number is below or above 13 30.
    25-13=12(11 and 60)
    22+60=82-30=52
    58
    2
    7813
    135220
    Thus,
    11
    52
    58
    2
    7813
    135220
    Then, we have to look the table of myur rkang of mercury of the remaining number which our example is 11.  The rkang sdom is 82 and rkang bzung is 20 then scrappe the number 11.
    we have
    52
    58
    2
    7813
    135220

    Thus, multiply all the remaining number by the rkang bzung which is 20

    52x20=
    58x20=
    2x20=
    7813x20=
    135220x20=

    pagemarker  pagemarker pagemarker pagemarker pagemarker pagemarker
    ================
    EXAMPLE FOR DACEN CALCUALTION

    for 8th day 3rd month, 1994.

    1.  zla dag = 86
    take the zla dag and add 10 (the constant used as it was the remainng number of the previous rabjung ie that at the start of this one)
    => 86+10=96

    then divide this by 230 (the 230 comes from the cycle of dachen- see later)
    =>96/230=0 rem 96 then multiply by the remainder number by 30 ( due to days in month.
    96x30=2880
    Then add 8 because it is the 8th day .
    Note:
    Even if there is a quotient do not multiply by 30.

    2880+8=2888
    Make it into 5 rows, then multiply by the constant numbers, 0,0,14,0,12 for current rabjung.

    2888x0=0

    2888x0=0

    2888x14=40432

    2888x0=0

    2888x12=34656
    Then divide by 23,  6,  60, 60, 27 bottom to top
    0+11=11/27=0 rem 11

    0+678=678/60=11 rem 18

    40432+251=40683/60=678 rem 3

    0+1506=1506/6=251 rem 0

    34656/23=1506 rem 18

    So the rza ba of dachen is
    11
    18
    3
    0
    18

    Now we fnd the dachen gdong (head of the dachen)
    It is easy take a full 27 constellation and minus the rza ba.
    27-11=16=15 and 60

    60+0=60-18=42=41 and 60

    60+0=60-3=57=56 and 6

    6+0=6-0=6=5 and 23(cha shas of dachen)

    23=0=23-18=5
    So the dachen gdong skar  i.e Rahu(  )  position in constellation is
    15
    41
    56
    5
    5

    Tail(dachen) mjug
    it is easy just add or substract 13:30 to gdong.
    15-13=2
    41-30=11
    56      56
    5         5
    5         5

    Tail is at
    2
    11                     i.e 41 hours 56 minutes of 15 th constellation same as libra.
    56
    5
    5       Late Aries.

    Now we have the positon of all the nine planets for the day- as in almanac which is like a “sun rise ephemeris” or nam lang yoes- the hour of the rabbit i.e 5-6 a.m.
    These positon are not further adjested except for the moon.
    Asc is calculated on two hours basis on direction from sun sign.
    Note:
    Used to be 2 hours table but now prof. Dagthon uses a more refined table.



    GLOSSARY OF TERMS

    1)  Thobnor-quotient (it is a number of a thob skel which was divided

    2)  Zla dag-

    3)  gZa dru-It is a root of the weekday from which weekday are formed.

    4)  Nyi dru-It is a root of the sun from which one can find the positon of the sun.

    5)  gZa bar-

    6)  Nyi bar- the postion of the constellaton on solar day may change or not change which means uncertain.  And so called bar ba lit means middle.  It is also a drag rkang zhi dal in the five planets calculation.

    7)  Ril cha-It has two rows, the above one is rilbu which means full and it is a number of the zla rkang .  Whereas the below one is a partial of it.

    8)  gZa phyed dag-after adding or substracting the zla rkang to the gza bar and not yet add or substract by the nyi rkang to make a weekday.  It is called as half weekday which is not exact weekday.

    9)  nyi dag-From this, one can know where the sun is in which sign.  It is in Aries or Taurus etc.

    10) gza dag-It is a one of the five inclusive calendare feartures and show the weekday and its hours, minutes, second etc.

    11) nyi rkang-It is considered because of the sun’s movement towards constellations.

    12) zla rkang-It also considered becaused of the moon’s movement towards the constellation.

    13) rkang sdom-It is a total hours of the foot of the planet or weekday which had completed or yet to complete.

    14) rkang ‘zin-

    15) rkang bzung-

    16) Dachen rtsa ba-The self movement of dra chen is always revolve from right which is from namdu and the remaining of the constellation and the nges pa of dachen is called dachen rtsa ba.

    17)  Dachen gdong-In general, the menaing of the head of dachen and the root of dachen are same but

    18)  Dachen mjug-the movment of ketu is called dachen mjug.  It is just a tha snyad.

    19)  spyi zhag-It is a general day of all the five planets and the sun.

    20) sGos zhag-It is not a genral day of the planet and it is a private day of each planet.

    21) dal rkang-It is a source of dal dag.

    22) Myur rkang-It is a source of myur dag.

    23) Drag rknag zhi dal-It is also called the nyi bar of the particular date.

    24)  Drag gza gsum gyi rkang zin-The rkang zin of the three wrathful planets i.e. Mars, Jupiter and Saturn.

    25) Zhi gza gnyis ki dal bar-The dal bar of both peaceful planets i.e Mercury and venus.

    26) Zhi rkang drag dal-It is a short form of the rkang zin of two peaceful planets and dal bar of three wrath ful palnets.

    27) Dal dag-It shows the self movement.

    28)  Myur dag-movement with the sun.  From the mhyur dag, we could find the position of the five planets.

    29)  gza lnga-the five planets-Mars, jupiter, saturn, mercury and venus.

    30)-lnga bsdus-The five inclusive calendar features-gZa, tshes, skar, sbyor and byed pa.

    gZa-the weekday
    tshes-at the time of date-ga, zang, rgya, tong and zog
    skar-moon constellation
    sbyor-it comes from the sun and moon
    byed pa-it is the earlier and later of byed pa

    31) yang gyu’ chu tsod- When calculating rkang longs, it is a quotient of the 135 hours and its remaining.

    32) 135 - It is a number of constelation hours of one sign



     
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