caliculation of hora cusp

7/30/2019 caliculation of hora cusp

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For Sothern Latitudes, add 12:0:0 to the RAMC. Compute the houses and then add 1800

(if less than 1800) or subtract 180

0

(if it is more) to each house to get the house cusps. (See the main text for details). Page 1

Manual Calculation of Star Time at Birth

for computation of Houses using

Astrological Tables of Houses

Karanam Ramakumar

India


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Manual Calculation of Star Time at Birth for computation of Houses using

Astrological Tables of Houses

Karanam Ramakumar, India

Introduction

The exact zodiac degree (minutes and seconds) that is rising in the eastern

horizon at the time of birth is called Janma Lagnam or Ascendant. The zodiac degree that

is at the zenith (exactly overhead 900 to the horizon) at the time of birth is the 10th

house, mid-heaven or the meridian cusp. As the entire zodiac consisting of 12 signs

describes a great celestial circle of 3600, each sign comprises 300 of zodiac arc and all the

12 houses (cusps or Bhavas) fall within these 12 signs. For example, if one says at the

time of birth 215th degree of zodiac sign was rising in the eastern horizon, we say birth

took place during Vrischika laganm as the zodiac sign Vrischikam is assigned an arc

between 2100 and 2400. The twelve zodiac signs and their arc span are given in the table

below.

Table 2 Zodiac signs and their span in the celestial arc

No. Zodiac sign Arc span

degrees


degrees


degrees

1 Mesham

(Aries)

00-300 5 Simham

(Leo)

1200-

1500

9 Dhanus

(Sagittarius)

2400-

2700

2 Vrishabham

(Taurus)

300-600 6 Kanya

(Virgo)

1500-

1800

10 Makaram

(Capricorn)

2700-

3000

3 Mithunam

(Gemini)

600-900 7 Thula

(Libra)

1800-

2100

11 Kumbham

(Aquarius)

3000-

3300

4 Karkatakam

(Cancer)

900-1200 8 Vrischikam

(Scorpio)

2100-

2400

12 Meenam

(Pisces)

3300-

3600 (or

00)

It may be mentioned that as the earth takes 24 hours to rotate on its axis, all the

12 zodiac signs would be rising in the eastern horizon sequentially one after another in24 hours. That is to say each sign of 300 takes about 2 hours to come up entirely, all the

12 signs taking 24 hours. For example, as a thumb rule, around April 15 of every year,

00 of zodiac (Mesham) will be rising at the eastern horizon along with Ravi. Let us

suppose that Sunrise on that day is at 6:00 AM; then by 8:00 AM, the entire Mesham

would have risen. For next two hours (up to 10:00 AM) the sign Vrishabham rises and if

birth occurs during this time interval, Janma Lagnam will be Vrishabham. The sequence


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continues. Thus depending on the time of reckoning, whichever sign would be rising in

the eastern horizon, becomes Lagnam at that time.

(In this notes, whenever the term minutes is mentioned, it refers to time. The term arc minutes

refers to the measure of zodiac arc in space.)

Ravi (the Sun) also traverses through the zodiac. But unlike the earth, Ravi is aslow moving Graha (Planet) and travelling about 10 (57 arc minutes to 63 arc minutes) of

zodiac per day, takes nearly one year to complete one cycle. That is Ravi will be in any

zodiac sign for 30 days (almost one month). Usually according to Nirayana Paddhathi of

computing Panchangam, Ravi enters Mesham (Aries) around April 15 and on that day

along with Ravi 00 of zodiac (Mesham) also rises. Next day, along with Ravi 10 of Mesham

rises and the sequence continues. For next 30 days Ravi travels through the sign. Then

around May 15 He enters Vrishabham and so on. This gets repeated every year. We

know Ravi rises in East and as the zodiac sign also rises in East, along with Ravi, every

day a particular degree of zodiac will also be rising. Thus knowing the date and month it

is possible for us to identify the zodiac sign rising at the time of sunrise. Thus Ravi is avery good zodiac keeper.

(Guess what zodiac sign would be rising on August 25.

On April 15, Ravi enters Mesham and for next 30 days He is that sign. Next 30 days He traverses

through Vrishabham. From April 15 to August 25, there are 132 days. 300 of zodiac are covered in

30 days, so in 132 days, 4 zodiac signs (a total of 1200) are already traversed by Ravi and and He

will be in the 5th sign (Simham). Depending upon the daily motion of Ravi (between 57 and 63 arc

minutes), He will be rising along with 80 to 120 of Simham.)

It should be mentioned that identification of Lagnam computed as mentioned

above is only a gross one. The reasons are many. For example, the orbiting paths of theplanets including our own earth do not describe perfect circles in space and their daily

motion is also not uniform. Added to this the very concept of time as we normally use in

our daily life also contributes to deviations. Further, as the Lagnam is the zodiac degree

rising in the Eastern horizon, the rising degree depends on the Latitude of the place.

Even for the same time, Lagnam would be different for different places depending upon

the Latitude. For accurate calculation of all the zodiac houses the positions of planets at

any given time and rigorous computations are absolutely necessary. Knowledge of

Logarithms, Trigonometry and Spherical Geometry is required. In this notes an attempt

is made to describe the methodology to be used to compute all the 12 houses in the birth

chart. The positions of the planets can be calculated using the procedures given in anearlier book Panchangam calculations. The method described here is not entirely

manual. The computation of Star time at Birth is done manually. Then Astrological

Tables of Houses are used to compute the 12 Houses.


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The concept of measurement of Time

Even though Time has the same meaning in the entire world, each Country uses

her own Standard Time concept. This is purely an administratively convenient concept

to suit the requirements of her populace for optimum use of daytime. That is why the

concept of Time Zone has been defined. To understand the concept of time zone, we

need knowledge of Longitude and standard longitude of a Country. Longitude is an

imaginary line drawn on the earth from North Pole to South Pole crossing the earths

equator. For correct identification of longitude of a place on the earth, the longitude is

always referred to a reference place. Greenwich in UK has been accepted by the entire

world as this reference point. The longitude passing through Greenwich is arbitrarily

assigned zero degrees (00) value. All the longitudes East of Greenwich are referred to

as East Longitudes and those West of Greenwich are West longitudes. For instance, our

Country India is east of Greenwich, East longitude passes through our Country. The USA

is in western hemisphere; so West longitudes pass through that Country.

As the earth rotates from West to East, Countries east of Greenwich will have

sunrise earlier than Greenwich. The Countries west of Greenwich will have sunrise later

than Greenwich. We can imagine 12 main longitudes East of Greenwich at 150 intervals

and an equal number of longitudes west of Greenwich. Thus there are 24 main

longitudinal divisions of the Earth 12 on each of Greenwich. 800 E means eighty

degrees east of Greenwich. 700 W means seventy degrees West of Greenwich. For the

sake of convenience, the world is divided into different time zones depending on the

main longitudes passing through a region. As the earth takes 24 hours for one rotation

(3600) for every 150 of change in longitude, time is changed by one hour. (3600 are

covered in 24 hours; so in one hour 3600/24 hours = 150/hour.) It is one hour ahead of

Greenwich for every 150 East of Greenwich and one hour behind of Greenwich for every

150 West of Greenwich. Each Country may have accepted one or more Longitudes

passing through her territory as standard longitudes. Time zones are expressed by

referring to these standard longitudes. India has 82.50 E as its standard longitude. Hence

our time zone is 82.50/150 x 1 h = 5h-30m east (or + 5h-30m east of Greenwich). What

it means is if it is 0:0 hours (midnight) at Greenwich, time in our Country is 5:30 AM.

Time as read at 82.50 E is our Countrys standard time. It is called Indian standard time

(IST). Similarly other Countries have their own standard longitudes and their standard

times. Large Countries like the USA and Russia have different standard longitudes on

their territories and hence different time zones. Now each Country may have sunrise

everyday around 6:00 AM. But 6:00 AM in a Country will not be 6:00 AM in other

Countries because of the time zones!

Another factor to be considered is the concept of summer time or daylight saving

time. Some Countries advance their standard time during summer by one or two hours

to save on daylight. This is called daylight saving time of summer time. During winter

they revert back to standard time. This also should be considered while computing

Lagnam.


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Even though having a standard time is very convenient administrative practice for

a Country, it cannot be used for computing Lagnam. Our Country is located roughly

between 690 E (Bhuj in Gujarat) and 940 E (Kohima in Nagaland) longitudes. According to

standard longitude 82.50 E, if it is 12:00 noon, officially it is noon throughout the

Country. But the local time at a place could be different. Knowing the relation between

longitude and the time it is possible to compute local time. If at 82.50 it is 12:00 noon, in

Bhuj at 690, it would be 11:06 hrs (how?) and 12:46 hrs in Kohima (How?). These local

times are needed for computing Lagnam.

As if this is not enough, even after making all the necessary corrections to the

recorded time of birth, there is another very fundamental difficulty in accepting the same

for computing Lagnam. This arises due the way the time is measured. We define a day as

the time taken for the earth to rotate exactly 3600 on its axis. We take Ravi (the Sun) as

the reference point and the time taken by the earth to complete one rotation to come

back exactly in line with Ravi is 24 hours or one day. If we recall that during this time

Ravi would move by 10 in the cosmos, the earth has to cover that one extra degree (3610

instead of 3600) to be in line with Ravi. But if the rotation of the earth is viewed against a

distant stellar background, earth is seen to complete one rotation of 3600 in about 3m-

56s less than 24 hours as measured now. This measure is called Star Time or sidereal

time. For correct computation of Lagnam, this star time and not the familiar clock time

should be considered. In one year this difference comes to be exactly 24 hours of clock

time and both star time and clock time reference points synchronise. Next day onwards

sidereal time accelerates and moves faster than the clock time. It is thus seen that star

time is faster than clock time and this extra time needs to be added to the clock time to

keep in pace with the star time. Depending on the time of birth a proportional quantity of

3m-56s (or 3m-57s) need to be either added or subtracted. Sidereal times are normally

computed either at GMT noon or at 0:0 hrs GMT and are given in the respective

ephemeris (noon ephemeris or midnight ephemeris) along with positions of planets and

other astronomical data. We should consult them for incorporating necessary corrections

to the birth time. The sidereal time should then be corrected for the birth time and

longitude. Finally after incorporating all corrections and before proceeding to computation

of Lagnam we have to ensure that the corrected birth time is expressed in local time and

not in IST or GMT. It should be clearly understood that for House computations, we

should use local time. The final result is called Star Time at Birth (STB). This will then be

converted into arc degrees and arc minutes which is called Right Ascension to Meridian

Cusp (RAMC). Calculation of accurate star time at birth and hence RAMC is very crucial

for accurate casting of horoscope.

Another important thing to consider is whether one wants the horoscope be cast

according to Sayana Paddhathi or Nirayana paddhathi. If Nirayana horoscope is to be

cast we should subtract Ayanamsa from the longitudes of Houses obtained.

It must have become quite clear to the discerning reader that computation of sidereal

birth time and RAMC involves many factors and one should have patience to proceed

systematically to arrive at a correct value. We will take some examples to compute star


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time at birth and RAMC. Then we will use the astrological tables of houses to compute all

the Houses. We will attempt to compute RAMC by using both ephemeris namely zero

hour (0:0 UT) ephemeris as well as noon (12:00 UT) ephemeris.

(In Noon Ephemeris counting of sidereal time commences from noon of March 21 every year. In

midnight ephemeris counting of sidereal time commences from midnight of September 21 every

year.)Once we have calculated RAMC accurately, we have to use astrological tables of

houses to compute different houses (cusps or bhavas). Usually these tables of houses

are given for northern longitudes. For southern longitudes, add 12:00:00 to the RAMC if

it is less than 12 or subtract 12 from the RAMC if it is more than 12 and use the result

(new RAMC) to calculate the houses corresponding to this new value. Then subtract 1800

from each house to get the houses (bhavas or cusps) for the south longitudes (we will

solve some examples).

Example 1: Date of birth: 25-8-1952 (August 25, 1952)

Time of birth: 12:45:00, ISTPlace of birth: Cuddapah, India (14:30 N, 78:47 E)

Standard longitude: 82:30 E

Day light saving time?: No

Table 2 Sidereal time Table for selected dates in August 1952

Date ST at 0:0 UT (GMT) ST at 12:00 UT (GMT)

24:08:1952 22-08-51 10-10-49

25:08:1952 22-12-48 10-14-46

26:08:1952 22-16-44 10-18-42

Computation based on zero hour ephemeris

Step 1: Convert IST to GMT (Use standard longitude for converting)

Standard longitude = 820:30 E =82.50

Converting this into time zone we get82.5(deg )

5.5 5:3015(deg / )

reeshr

rees hr = =

Longitude is East of Greenwich.

Hence Birth time in GMT = 12:45:0 - 5:30:0 = 7:15:00 GMT

Step 2: Get the sidereal time on 25-8-1952 from ephemeris. Let us use Swiss ephemeris

for the year 1952 (see Table 2 above). Swiss ephemeris is computed for exactly 0:0 GMT(or Universal Time UT). The sidereal time on 25-8-1952 is given as 22:12:48 at 0:0 UT.

We have to compute the sidereal time at the birth time of 7:15 GMT. This can be

obtained by ratio proportional method. On 26-8-1952, the sidereal time is given as

22:16:44. That is in 24 hours from 25th to 26th, the sidereal time is changed by 22:16:44


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22:12:48 = 00:3:56 = 236 sec. Now for 24 hours change in sidereal time is 236 sec.

For 7:15:0, the change in sidereal time is7:15:0

236sec 71.3 sec 71sec24

x = = = 00:1:11

Sidereal time at birth time (GMT) = 22:12:48+00:01:11 = 22:13:59

Step 3: Compute star time at birth (at GMT). Add birth time (at GMT) and the sidereal

time at birth.

Star time at birth (GMT) = 7:15:0 + 22:13:59 = 29:28:59 (GMT)

Step 4: Convert star time at birth (GMT) to Star time at Birth (Local). Note that the

longitude to be considered is for the birth place and not the standard longitude (78:47 E

and not 82:30 E).

Star time at birth (Local) = 29:28:59 +78 : 47(deg )

5.2522215(deg / )

reeshrs

rees hr =

=29:28:59 + 5:15:8 = 34:44:7

Subtracting 24 hrs from the result we get RAMC = 34:44:7 24:00:00 = 10:44:7

Now let us compute Lagnam and other Houses (Cusps or Bhavas). We use astrological

tables of houses for this purpose. An extract of these Tables is shown below.

Table 3 Extract from Tables of Houses

RAMC

(H:M)10

LATITUDE : 14 N LATITUDE : 15 N

11 12 LAGNA 2 3 11 12 LAGNA 2 31 0 : 4 2 158:54 191: 2 220:22 2 4 6 : 4 4 275:52 306:30 190:60 220:11 246:21 275:35 306:23

1 0 : 4 5 159:42 191:49 2 21 : 6 2 4 7 : 2 4 276:34 307:15 191:47 220:54 24 7: 1 276:17 3 0 7 : 8

1 1 : 4 5 175:55 207:20 235:17 2 6 0 : 5 6 290:44 322:43 207:15 235: 4 260:31 290:28 322:37

1 1 : 4 8 176:44 208: 5 235:59 2 6 1 : 3 7 291:28 323:31 208: 1 235:46 261:12 291:11 323:25

2 2 : 4 2 338:54 1 1 : 5 1 4 5 : 4 8 7 7 : 3 7 103:21 129:36 11 : 53 4 6 : 2 7 8 : 2 103:38 129:42

2 2 : 4 5 339:42 12 : 41 46 : 36 7 8 : 1 9 104 : 2 130:19 12 : 43 46 :49 7 8 : 45 104:18 130:26

2 3 : 1 5 3 47:46 21: 2 54:23 8 5 : 2 1 110:52 137:38 21: 6 54:38 8 5 : 4 7 111: 8 137:44

2 3 : 1 8 3 48:35 21:52 55: 8 8 6 : 3 111:34 138:22 21:56 55:24 8 6 : 2 8 111:49 138:28



0

(if it is more) to each house to get the house cusps. (See the main text for details).

The latitude of birth place is 14:30 N and the RAMC is 10:44:7. If we look up in

the Table above, RAMC (first column) is in between 10:42 and 10:45. The latitude is in

between 14 and 15. We have to use interpolation to calculate the houses for 14:30 N andRAMC 10:44:7.

From the Table it is seen that for a change in RAMC of 3 min (180 sec), the 10 th

house changes from 158:54 to 159:42 = 48 arc min. The difference between RAMC of

10:44:7 and 10:45:00 is 53 sec. So in the period of 53 sec, the 10 th house changes


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by53

X48 14.133 14 arcmin.180

= = This should be subtracted from the 10th house value at

10:45 to get 10th house for RAMC.

10th house = 159:42:00 00:14 = 159:28

Similarly all the other houses are computed for RAMC of 10:44:7. These are given below.

RAMC = 10:44:7

House Latitude 14 N Latitude 15 N Latitude 14:30 N Rasi

10 159:28 159:28 159:28 Kanya 9:28

11 191:36 191:34 191:35 Thula 11:35

12 220:53 220:42 220:47:30 Vrischikam 10:47:30

Lagna 247:12 246:49 247:00:30 Dhanus 7:00:30

2 276:22 276:05 276:13:30 Makaram 6:13:30

3 307:02 306:55 306:58:30 Kumbham 6:58:30

It should be made clear that the house positions obtained as above refer to

Sayana houses. To compute Nirayana houses, we should subtract Ayanamsa for the birth

year. The Ayanamsa may be calculated using the equation:

For the beginning of the year:

6.92416 16.90709 0.7573711000 1000 1000

year year year A = +

1.15740741

30 1000

DayB Month x

= +

Ayanamsa = A + B. The result will be in degrees. Convert into Degrees, Minutes and

Seconds. For 25-8-1952, the Ayanamsa is 23-5-34. The Nirayana Houses are:

House Sayana system Nirayana system

(Sayana house-Ayanamsa)

10 Kanya 9:28 Simham 16:22:26

11 Thula 11:35 Kanya 18:29:26

12 Vrischikam 10:47:30 Thula 17:41:56

Lagna Dhanus 7:00:30 Vrischikam 13:54:56

2 Makaram 6:13:30 Dhanus 13:07:56

3 Kumbham 6:58:30 Makaram 13:52:56

The other houses namely 4, 5, 6, 7, 8 and 9 are exactly degreecally opposite of the

houses 10, 11, 12, Lagna, 2 and 3 respectively. In the above case, these are

respectively, Kumbham, Meenam, Mesham, Vrishabham, Mithunam and Karkatakam.

Nirayana houses are used in India for casting the horoscopes.

Now let us calculate RAMC using noon ephemeris for the example 1 given above.


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Computation of RAMC based on noon hour ephemeris

Step 1: Convert IST to GMT (Use standard longitude for converting)



5.5 5:3015(deg / )

reeshr

rees hr = =



As the birth occurred before noon, add 12:00:00 to get adjusted birth time: 12:00:00 +

7:15:00 = 19:15:00 GMT.

Step 2: In the above case, as we have added 12:00:00, take the sidereal time on the

previous day of the birth day. In this case it is 24-8-1952. The sidereal time on 24-8-

1952 is given as 10:10:49 at 12:00 UT. We have to compute the sidereal time at the

birth time of 19:15 GMT. This can be obtained by ratio proportional method. On 25-8-

1952, the sidereal time is given as 10:14:46. That is in 24 hours from 24 th to 25th, the

sidereal time is changed by 10:14:46 10:10:49 = 00:3:57 = 237 sec. Now for 24

hours change in sidereal time is 237 sec. For 19:15:0, the change in sidereal time is

19:15:0237sec 190.1sec 190sec

24x = = = 00:3:10



time at birth.




and not 82:30 E).


5.2522215(deg / )

reeshrs

rees hr =

=29:28:59 + 5:15:8 = 34:44:7

Subtracting 24 hrs from the result we get 34:44:7 24:00:00 = 10:44:7

So which ever may the ephemeris one uses, RAMC for a given birth time, date and place

should be identical.

Use the method given above to compute the Houses.


Time of birth: 12:45:00, LST

Place of birth: XXXXX, YYYYY (14:30 N, 78:47 W)

Standard longitude: 82:30 W



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Notice that birth time is given in Local standard time. The place is west of Greenwich

(78:47 W and standard longitude is 82:30 W).


Step 1: Convert LST to GMT (Use of standard longitude)

Standard longitude = 820:30 W =82.50


5.5 5:3015(deg / )

reeshr

rees hr = =

Longitude is West of Greenwich.

Hence Birth time in GMT = 12:45:0 + 5:30:0 = 18:15:00 GMT

Step 2: Get the sidereal time on 25-8-1952 from ephemeris (see Table 1). The sidereal

time on 25-8-1952 is given as 22:12:48 at 0:0 UT. We have to compute the sidereal

time at the birth time of 18:15 GMT. On 26-8-1952, the sidereal time is given as

22:16:44. That is in 24 hours from 25th to 26th, the sidereal time is changed by 22:16:44

22:12:48 = 00:3:56 = 236 sec. Now for 24 hours change in sidereal time is 236 sec.

For 7:15:0, the change in sidereal time is18:15:0

236sec 179.5sec 180sec24

x = = =

00:03:00



time at birth.



longitude to be considered is for the birth place and not the standard longitude (78:47 W

and not 82:30 W).

Star time at birth (Local) = 40:30:48 -78 : 47(deg )

5.2522215(deg / )

reeshrs

rees hr =

=40:30:48 - 5:15:8 = 35:15:40

As it is more than 24, subtracting 24 hrs from the result we get

RAMC = 35:15:40 24:00:00 = 11:15:40

Use the method given for example 1 to compute the Houses.

Computation of RAMC based on noon hour ephemerisStep 1: Convert LST to GMT (Use of standard longitude)



5.5 5:3015(deg / )

reeshr

rees hr = =




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As the birth occurred after noon, subtract 12:00:00 from the birth time to get adjusted

birth time: 18:15:00 - 12:00:00 = 6:15:00 GMT.

Step 2: Get the sidereal time at noon GMT on 25-8-1952 from ephemeris (see Table 1

above.) On 25-8-1952, the sidereal time at noon is given as 10:14:46. We have to

compute the sidereal time at the birth time of 6:15 GMT. On 26-8-1952, the sidereal

time is given as 10:18:42. That is in 24 hours from 25th to 26th, the sidereal time is

changed by 10:18:42 10:14:46 = 00:3:56 = 236 sec. Now for 24 hours change in

sidereal time is 236 sec. For 6:15:0, the change in sidereal time is

6:15:0236sec 61.5 sec 62sec

24x = = = 00:01:02



time at birth.




and not 82:30 W).


5.2522215(deg / )

reeshrs

rees hr =

=16:30:48 - 5:15:8 = 11:15:40


should be identical.

Use the method given for example 1 to compute the Houses.


Time of birth: 12:45:00, LST

Place of birth: UUUUU, VVVVV (14:30 S, 78:47 W)

Standard longitude: 82:30 W


Notice the birth place is south of equator (South latitude) and west of Greenwich (West

longitude)





5.5 5:3015(deg / )

reeshr

rees hr = =




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Step 2: Get the sidereal time on 25-8-1952 from ephemeris (Table 1). The sidereal time

on 25-8-1952 is given as 22:12:48 at 0:0 UT. We have to compute the sidereal time at

the birth time of 18:15 GMT. On 26-8-1952, the sidereal time is given as 22:16:44. That

is in 24 hours from 25th to 26th, the sidereal time is changed by 22:16:44 22:12:48 =

00:3:56 = 236 sec. Now for 24 hours change in sidereal time is 236 sec. For 7:15:0, the

change in sidereal time is

18:15:0

236sec 179.5sec 180sec24 x= =

= 00:03:00



time at birth.




and not 82:30 W).


5.2522215(deg / )

reeshrs

rees hr =

=40:30:48 - 5:15:8 = 35:15:40

As it is more than 24, subtracting 24 hrs from the result we get

35:15:40 24:00:00 = 11:15:40

As it is south latitude, add 12:0:0 to the result to get

New RAMC = 11:15:40 + 12:00:00 = 23:15:40

Now let us compute Lagnam and other houses for this South latitude.

The latitude of birth place is 14:30 N and the new RAMC is 23:15:40. If we look up

in the Table 3, RAMC (first column) is in between 23:15 and 23:18. The latitude is in

between 14 and 15. We have to use interpolation to calculate the houses for 14:30 N and

RAMC 23:15:40.

From the Table it is seen that for a change in RAMC of 3 min (180 sec), the 10 th

house changes from 347:46 to 348:35 = 49 arc min. The difference between new RAMC

of 23:15:40 and 23:15:00 is 40 sec. So in the period of 40 sec, the 10th houses changes

by40

X49 10.888 11arcmin.180

= = This should be added to the 10th house value at 23:15

to get 10th house for new RAMC.

10th house = 347:46 + 00:11 = 347:57

Similarly all the other houses are computed for new RAMC of 23:15:40. These are

given below.


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New RAMC = 23:15:40

House Latitude 14 N Latitude 15 N Latitude 14:30 N Add/subtract

1800 to column 4

10 347:57 347:57 347:57 167:57

11 21:13 21:17 21:15 201:15

12 54:33 54:48 54:40:30 234:40:30

Lagna 85:30 85:56 85:38 265:38

2 111.01 111:17 111.09 291:09

3 137:48 137:54 137:51 317:51

Recall that we are dealing with south latitude. What we obtained is the houses 4, 5, 6,

7, 8 and 9. To get the correct houses (10, 11, 12, Lagna, 2 and 3) add 1800 to the house

if it is less than 1800 or subtract 1800 if the value is more than 1800. This exercise results

are shown in the last column in the above Table.

It should be made clear that the house positions obtained as above refer to Sayana

houses. To compute Nirayana houses, we should subtract Ayanamsa for the birth year.

The Ayanamsa may be calculated using the equation:

For the beginning of the year:

6.92416 16.90709 0.7573711000 1000 1000

year year year A = +

1.15740741

30 1000

DayB Month x

= +

Ayanamsa = A + B. The result will be in degrees. Convert into Degrees, Minutes and

Seconds. For 25-8-1952, the Ayanamsa is 23-5-34. The Nirayana Houses are:

House House Sayana system Nirayana system

(Sayana house-Ayanamsa)

10 167:57 Kanya 17:57 Simham 24:51:26

11 201:15 Thula 21:15 Kanya 28:09:26

12 234:40:30 Vrischikam 24:40:30 Vrischikam 1:34:56

Lagna 265:38 Dhanus 25:38 Dhanu 2:2:26

2 291:09 Makaram 21:09 Dhanus 28:03:26

3 317:51 Kumbham 17:51 Makaram 14:45:26

Note: For South Latitudes, proceed up to the final result of step 4. Then add 12:0:0 to the result to

get new RAMC. Compute the houses for this new RAMC. Add or subtract 1800 from each house

value to get the correct houses.




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5.5 5:3015(deg / )

reeshr

rees hr = =



As the birth occurred after noon, subtract 12:00:00 from the birth time to get adjusted

birth time: 18:15:00 - 12:00:00 = 6:15:00 GMT.

Step 2: Get the sidereal time at noon GMT on 25-8-1952 from ephemeris (see Table 1

above.) On 25-8-1952, the sidereal time at noon is given as 10:14:46. We have to

compute the sidereal time at the birth time of 6:15 GMT. This can be obtained by ratio

proportional method. On 26-8-1952, the sidereal time is given as 10:18:42. That is in 24

hours from 25th to 26th, the sidereal time is changed by 10:18:42 10:14:46 = 00:3:56

= 236 sec. Now for 24 hours change in sidereal time is 236 sec. For 6:15:0, the change

in sidereal time is6:15:0

236sec 61.5 sec 62sec24

x = = = 00:01:02



time at birth.




and not 82:30 W).


5.2522215(deg / )

reeshrs

rees hr =

=16:30:48 - 5:15:8 = 11:15:40


New RAMC = 11:15:40 + 12:00:00 = 23:15:40.


should be identical. Proceed for computation of houses as described in the example 3.


Time of birth: 12:45:00, LSTPlace of birth: SSSSS, TTTTT (14:30 S, 78:47 E)

Standard longitude: 82:30 E


Notice the birth place is south of equator (South latitude) and East of Greenwich (East

longitude)


15/95



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Step 1: Convert IST to GMT (Use of standard longitude)



5.5 5:3015(deg / )

reeshr

rees hr = =



Step 2: Get the sidereal time on 25-8-1952 from ephemeris. Let use Swiss ephemeris for

the year 1952 (see Table 2 above). Swiss ephemeris is computed for exactly 0:0 GMT (or

Universal Time UT). The sidereal time on 25-8-1952 is given as 22:12:48 at 0:0 UT. We

have to compute the sidereal time at the birth time of 7:15 GMT. This can be obtained by

ratio proportional method. On 26-8-1952, the sidereal time is given as 22:16:44. That is

in 24 hours from 25th to 26th, the sidereal time is changed by 22:16:44 22:12:48 =

00:3:56 = 236 sec. Now for 24 hours change in sidereal time is 236 sec. For 7:15:0, the

change in sidereal time is7:15:0

236sec 71.3 sec 71sec24

x = = = 00:1:11



time at birth.




and not 82:30 E).


5.2522215(deg / )

reeshrs

rees hr =

=29:28:59 + 5:15:8 = 34:44:7

Subtracting 24 hrs from the result we get

34:44:7 24:00:00 = 10:44:7


RAMC = 10:44:7 + 12:00:00 = 22:44:7

Proceed for computation of houses as described in the example 3.


Step 1: Convert IST to GMT (Use of standard longitude)



5.5 5:3015(deg / )

reeshr

rees hr = =



16/95



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As the birth occurred before noon, add 12:00:00 to get adjusted birth time: 12:00:00 +

7:15:00 = 19:15:00 GMT.

Step 2: In the above case, as we have added 12:00:00, take the sidereal time on the

previous day of the birth day. In this case it is 24-8-1952. The sidereal time on 24-8-

1952 is given as 10:10:49 at 12:00 UT. We have to compute the sidereal time at the

birth time of 19:15 GMT. This can be obtained by ratio proportional method. On 25-8-

1952, the sidereal time is given as 10:14:46. That is in 24 hours from 24th to 25th, the

sidereal time is changed by 10:14:46 10:10:49 = 00:3:57 = 237 sec. Now for 24

hours change in sidereal time is 237 sec. For 19:15:0, the change in sidereal time is

19:15:0237sec 190.1sec 190sec

24x = = = 00:3:10



time at birth.




and not 82:30 E).


5.2522215(deg / )

reeshrs

rees hr =

=29:28:59 + 5:15:8 = 44:44:7

Subtracting 24 hrs from the result we get 44:44:7 24:00:00 = 10:44:7


RAMC = 10:44:7 + 12:00:00 = 22:44:7


should be identical. Proceed for computation of houses as described in the example 3.

In some countries during summer the clock time is advanced by one or two hours to save

on day light. This is called summer time or day light saving time. The standard longitude

is not changed and remains same and with respect this standard longitude the time

difference from GMT also remains the same. One should be vigilant and subtract the

number of hours as the case may be from the birth time and proceed with casting

of horoscope. Summer time concept is purely an administrative convenience. This should

never be used for horoscope casting.


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Summary and important points to be noted while computing Houses

1. Note down the birth time, Latitude and Longitude of the birth place and standard

Longitude

2. If summer time is being followed and day light saving time is used, subtract thistime (no. of hours of daylight saving as announced by the Administration) from the

birth time.

3. House cusps shall always be calculated for the Local time.

4. Have the ephemeris (either noon or midnight) containing sidereal time and the

positions of the planets and astrological tables of houses.

5. For South latitudes follow the principle of forward RAMC by 12, compute and

retreat by 1800 to get cusps. That is add 12:00:00 to the RAMC to get new RAMC.

Compute the houses and add or subtract 1800

from the cusps.

There could be other methods of RAMC computation. But I found the method described

here is relatively easy with minimum corrections. Converting the birth time to GMT and

carrying out all calculations to get RAMC at GMT and then converting the final result to

RAMC at LMT is very easy.

Carrying out computations at LMT is somewhat elaborate in the sense that not only

longitudinal corrections for birth time but also corrections to sidereal time (longitudinal

correction and accelerator or Doppler correction) need to be carried out.

One may use the method described in my earlier book Panchangam calculations to

calculate longitudes of Grahas (Planets). In this monograph, the computation of House

longitudes is given. The Astrological Tables of Houses required for this purpose is being

given in four parts. The first part covering Latitudes 0 N to 14 N is included in this

monograph. I have followed the method described by Alan Leo in his book The

Progressed Horoscope. House cusps have been calculated using Quick Basic Language.

Double precision mode was used to increase the accuracy in calculations.


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ASTROLOGICAL TABLES OF HOUSES

FOR NORTHERN LATITUDES

PART-1: 00 N TO 320 N

Based on the method described in Alan Leos book

The Progressed Horoscope

Compiled by

Karanam Ramakumar

India


19/95



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OAM OAM Shri Maha Ganapataye Namah

RAMCH:M

10LATITUDE : 0N LATITUDE : 1 N L A T I T U D E : 2 N

11 12 LAGNA 2 3 11 12 LAGNA 2 3 11 12 LAGNA 2 3

0: 0 0: 0 32:11 62: 5 90: 0 117:55 147:49 32:15 62:20 90:23 118: 9 147:54 32:20 62:34 90:46 118:23 147:58

0: 3 0:4 9 32:58 62:48 90:41 118:38 148:36 33: 2 63: 3 91: 5 118:52 148:40 33: 7 63:17 91:29 119: 6 148:45

0: 6 1:3 8 33:44 63:31 91:23 119:21 149:23 33:49 63:46 91:46 119:35 149:27 33:54 64: 0 92:10 119:49 149:32

0: 9 2:27 34:31 64:14 92: 4 120: 4 150:10 34:36 64:29 92:28 120:18 150:14 34:41 64:43 92:52 120:32 150:19

0:12 3:1 6 35:17 64:57 92:45 120:47 150:57 35:22 65:11 93: 9 121: 1 151: 1 35:27 65:26 93:33 121:15 151: 6

0:15 4: 5 36: 4 65:39 93:26 121:31 151:45 36: 9 65:54 93:50 121:44 151:49 36:14 66: 9 94:14 121:58 151:53

0:18 4:5 4 36:50 66:22 94: 8 122:14 152:32 36:55 66:37 94:32 122:28 152:36 37: 0 66:52 94:55 122:42 152:40

0:21 5:4 3 37:36 67: 4 94:49 122:58 153:19 37:42 67:19 95:13 123:11 153:23 37:47 67:34 95:37 123:25 153:27

0:24 6:3 2 38:22 67:47 95:30 123:41 154: 7 38:28 68: 2 95:54 123:55 154:11 38:33 68:17 96:18 124: 8 154:14

0:27 7:2 1 39: 9 68:29 96:12 124:25 154:54 39:14 68:44 96:36 124:38 154:58 39:19 68:59 96:59 124:52 155: 2

0:30 8:1 0 39:54 69:11 96:53 125: 9 155:42 39:60 69:27 97:17 125:22 155:46 40: 5 69:42 97:41 125:35 155:49

0:33 8:5 9 40:40 69:54 97:35 125:53 156:30 40:46 70: 9 97:58 126: 6 156:33 40:51 70:24 98:22 126:19 156:37

0:36 9:4 8 41:26 70:36 98:16 126:37 157:18 41:31 70:51 98:40 126:50 157:21 41:37 71: 6 99: 3 127: 3 157:24

0:39 10:36 42:12 71:18 98:58 127:21 158: 6 42:17 71:33 99:21 127:34 158: 9 42:23 71:49 99:45 127:47 158:12

0:42 11:25 42:57 72: 0 99:39 128: 5 158:54 43: 3 72:15 100: 3 128:18 158:57 43: 8 72:31 100:26 128:31 158:60

0:45 12:14 43:42 72:42 100:21 128:49 159:42 43:48 72:57 100:44 129: 2 159:45 43:54 73:13 101: 8 129:15 159:48

0:48 13: 3 44:28 73:24 101: 2 129:34 160:30 44:34 73:39 101:26 129:46 160:33 44:39 73:55 101:49 129:59 160:36

0:51 13:51 45:13 74: 6 101:44 130:18 161:18 45:19 74:21 102: 7 130:31 161:21 45:25 74:37 102:31 130:43 161:24

0:54 14:40 45:58 74:48 102:25 131: 3 162: 6 46: 4 75: 3 102:49 131:15 162: 9 46:10 75:19 103:12 131:28 162:12

0:57 15:28 46:43 75:30 103: 7 131:47 162:55 46:49 75:45 103:30 131:60 162:57 46:55 76: 1 103:54 132:12 162:60

1: 0 16:17 47:28 76:11 103:49 132:32 163:43 47:34 76:27 104:12 132:44 163:46 47:40 76:42 104:35 132:56 163:48

1: 3 17: 5 48:13 76:53 104:30 133:17 164:32 48:19 77: 9 104:54 133:29 164:34 48:25 77:24 105:17 133:41 164:36

1: 6 17:54 48:57 77:35 105:12 134: 2 165:20 49: 4 77:50 105:35 134:14 165:22 49:10 78: 6 105:58 134:26 165:25

1: 9 18:42 49:42 78:16 105:54 134:47 166: 9 49:48 78:32 106:17 134:59 166:11 49:55 78:48 106:40 135:11 166:13

1:12 19:30 50:26 78:58 106:36 135:32 166:57 50:33 79:14 106:59 135:44 166:59 50:39 79:29 107:22 135:55 167: 1

1:15 20:18 51:11 79:39 107:18 136:18 167:46 51:17 79:55 107:41 136:29 167:48 51:24 80:11 108: 4 136:40 167:50

1:18 21: 6 51:55 80:21 107:60 137: 3 168:35 52: 2 80:37 108:23 137:14 168:36 52: 8 80:52 108:46 137:26 168:38

1:21 21:54 52:39 81: 2 108:42 137:48 169:24 52:46 81:18 109: 5 137:60 169:25 52:52 81:34 109:27 138:11 169:27

1:24 22:42 53:23 81:44 109:24 138:34 170:12 53:30 81:60 109:47 138:45 170:14 53:37 82:16 110: 9 138:56 170:15

1:27 23:30 54: 7 82:25 110: 6 139:20 171: 1 54:14 82:41 110:29 139:31 171: 3 54:21 82:57 110:51 139:41 171: 4

1:30 24:18 54:51 83: 7 110:49 140: 6 171:50 54:58 83:23 111:11 140:16 171:51 55: 5 83:38 111:33 140:27 171:53

1:33 25: 6 55:35 83:48 111:31 140:51 172:39 55:42 84: 4 111:53 141: 2 172:40 55:49 84:20 112:16 141:13 172:41

1:36 25:53 56:19 84:30 112:13 141:38 173:28 56:26 84:45 112:36 141:48 173:29 56:32 85: 1 112:58 141:58 173:30

1:39 26:41 57: 2 85:11 112:56 142:24 174:17 57: 9 85:27 113:18 142:34 174:18 57:16 85:43 113:40 142:44 174:19

1:42 27:28 57:46 85:52 113:38 143:10 175: 6 57:53 86: 8 114: 0 143:20 175: 7 57:60 86:24 114:22 143:30 175: 7

1:45 28:15 58:29 86:34 114:21 143:56 175:55 58:36 86:49 114:43 144: 6 175:55 58:43 87: 5 115: 5 144:16 175:56

1:48 29: 3 59:13 87:15 115: 3 144:43 176:44 59:20 87:31 115:25 144:52 176:44 59:27 87:47 115:47 145: 2 176:45

1:51 29:50 59:56 87:56 115:46 145:29 177:33 60: 3 88:12 116: 8 145:39 177:33 60:10 88:28 116:30 145:48 177:34

1:54 30:37 60:39 88:37 116:29 146:16 178:22 60:46 88:53 116:51 146:25 178:22 60:53 89: 9 117:12 146:34 178:22

1:57 31:24 61:22 89:19 117:12 147: 2 179:11 61:29 89:35 117:33 147:12 179:11 61:37 89:51 117:55 147:21 179:11

2: 0 32:11 62: 5 90: 0 117:55 147:49 180: 0 62:13 90:16 118:16 147:58 180: 0 62:20 90:31 118:37 148: 7 180: 0

2: 3 32:58 62:48 90:41 118:38 148:36 180:49 62:56 90:57 118:59 148:45 180:49 63: 3 91:13 119:20 148:54 180:49

2: 6 33:44 63:31 91:23 119:21 149:23 181:38 63:38 91:38 119:42 149:32 181:38 63:46 91:54 120: 3 149:40 181:38

2: 9 34:31 64:14 92: 4 120: 4 150:10 182:27 64:21 92:20 120:25 150:19 182:27 64:29 92:36 120:46 150:27 182:26

2:12 35:17 64:57 92:45 120:47 150:57 183:16 65: 4 93: 1 121: 8 151: 6 183:16 65:11 93:17 121:29 151:14 183:15

2:15 36: 4 65:39 93:26 121:31 151:45 184: 5 65:47 93:42 121:51 151:53 184: 5 65:54 93:58 122:12 152: 1 184: 4

2:18 36:50 66:22 94: 8 122:14 152:32 184:54 66:29 94:24 122:35 152:40 184:53 66:37 94:40 122:55 152:47 184:53

2:21 37:36 67: 4 94:49 122:58 153:19 185:43 67:12 95: 5 123:18 153:27 185:42 67:19 95:21 123:38 153:35 185:41

2:24 38:22 67:47 95:30 123:41 154: 7 186:32 67:54 95:46 124: 2 154:14 186:31 68: 2 96: 2 124:22 154:22 186:30

2:27 39: 9 68:29 96:12 124:25 154:54 187:21 68:37 96:28 124:45 155: 2 187:20 68:44 96:44 125: 5 155: 9 187:19

2:30 39:54 69:11 96:53 125: 9 155:42 188:10 69:19 97: 9 125:29 155:49 188: 9 69:27 97:25 125:49 155:56 188: 7

2:33 40:40 69:54 97:35 125:53 156:30 188:59 70: 1 97:50 126:13 156:37 188:57 70: 9 98: 6 126:32 156:43 188:56

2:36 41:26 70:36 98:16 126:37 157:18 189:48 70:43 98:32 126:56 157:24 189:46 70:51 98:48 127:16 157:31 189:45

2:39 42:12 71:18 98:58 127:21 158: 6 190:36 71:26 99:13 127:40 158:12 190:35 71:33 99:29 127:60 158:18 190:33

2:42 42:57 72: 0 99:39 128: 5 158:54 191:25 72: 8 99:55 128:24 158:60 191:24 72:15 100:10 128:44 159: 6 191:22

2:45 43:42 72:42 100:21 128:49 159:42 192:14 72:50 100:36 129: 8 159:48 192:12 72:57 100:52 129:27 159:54 192:10

2:48 44:28 73:24 101: 2 129:34 160:30 193: 3 73:32 101:18 129:53 160:36 193: 1 73:39 101:33 130:11 160:41 192:59

2:51 45:13 74: 6 101:44 130:18 161:18 193:51 74:14 101:59 130:37 161:24 193:49 74:21 102:15 130:56 161:29 193:47

2:54 45:58 74:48 102:25 131: 3 162: 6 194:40 74:55 102:41 131:21 162:12 194:38 75: 3 102:56 131:40 162:17 194:35

2:57 46:43 75:30 103: 7 131:47 162:55 195:28 75:37 103:23 132: 6 162:60 195:26 75:45 103:38 132:24 163: 5 195:24

3: 0 47:28 76:11 103:49 132:32 163:43 196:17 76:19 104: 4 132:50 163:48 196:14 76:27 104:20 133: 8 163:53 196:12

3: 3 48:13 76:53 104:30 133:17 164:32 197: 5 77: 1 104:46 133:35 164:36 197: 3 77: 9 105: 1 133:53 164:41 197: 0

3: 6 48:57 77:35 105:12 134: 2 165:20 197:54 77:42 105:28 134:20 165:25 197:51 77:50 105:43 134:38 165:29 197:48

3: 9 49:42 78:16 105:54 134:47 166: 9 198:42 78:24 106: 9 135: 5 166:13 198:39 78:32 106:25 135:22 166:17 198:36

3:12 50:26 78:58 106:36 135:32 166:57 199:30 79: 6 106:51 135:50 167: 1 199:27 79:14 107: 7 136: 7 167: 5 199:24

3:15 51:11 79:39 107:18 136:18 167:46 200:18 79:47 107:33 136:35 167:50 200:15 79:55 107:49 136:52 167:53 200:12

3:18 51:55 80:21 107:60 137: 3 168:35 201: 6 80:29 108:15 137:20 168:38 201: 3 80:37 108:30 137:37 168:42 201: 0

3:21 52:39 81: 2 108:42 137:48 169:24 201:54 81:10 108:57 138: 5 169:27 201:51 81:18 109:12 138:22 169:30 201:48

3:24 53:23 81:44 109:24 138:34 170:12 202:42 81:52 109:39 138:51 170:15 202:39 81:60 109:54 139: 7 170:18 202:36

3:27 54: 7 82:25 110: 6 139:20 171: 1 203:30 82:33 110:21 139:36 171: 4 203:27 82:41 110:36 139:52 171: 7 203:23


20/95



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RAMCH:M



3:30 54:51 83: 7 110:49 140: 6 171:50 204:18 83:15 111: 4 140:22 171:53 204:14 83:23 111:19 140:38 171:55 204:11

3:33 55:35 83:48 111:31 140:51 172:39 205: 6 83:56 111:46 141: 7 172:41 205: 2 84: 4 112: 1 141:23 172:43 204:58

3:36 56:19 84:30 112:13 141:38 173:28 205:53 84:37 112:28 141:53 173:30 205:49 84:45 112:43 142: 8 173:32 205:46

3:39 57: 2 85:11 112:56 142:24 174:17 206:41 85:19 113:10 142:39 174:19 206:37 85:27 113:25 142:54 174:20 206:33

3:42 57:46 85:52 113:38 143:10 175: 6 207:28 86: 0 113:53 143:25 175: 7 207:24 86: 8 114: 8 143:40 175: 9 207:20

3:45 58:29 86:34 114:21 143:56 175:55 208:15 86:41 114:35 144:11 175:56 208:11 86:49 114:50 144:26 175:57 208: 7

3:48 59:13 87:15 115: 3 144:43 176:44 209: 3 87:23 115:18 144:57 176:45 208:59 87:31 115:33 145:11 176:46 208:54

3:51 59:56 87:56 115:46 145:29 177:33 209:50 88: 4 116: 1 145:43 177:34 209:46 88:12 116:15 145:57 177:34 209:41

3:54 60:39 88:37 116:29 146:16 178:22 210:37 88:45 116:43 146:30 178:22 210:33 88:53 116:58 146:43 178:23 210:28

3:57 61:22 89:19 117:12 147: 2 179:11 211:24 89:27 117:26 147:16 179:11 211:20 89:35 117:40 147:30 179:11 211:15

4: 0 62: 5 90: 0 117:55 147:49 180: 0 212:11 90: 8 118: 9 148: 3 180: 0 212: 6 90:16 118:23 148:16 180: 0 212: 2

4: 3 62:48 90:41 118:38 148:36 180:49 212:58 90:49 118:52 148:49 180:49 212:53 90:57 119: 6 149: 2 180:49 212:48

4: 6 63:31 91:23 119:21 149:23 181:38 213:44 91:31 119:35 149:36 181:38 213:40 91:38 119:49 149:49 181:37 213:35

4: 9 64:14 92: 4 120: 4 150:10 182:27 214:31 92:12 120:18 150:23 182:26 214:26 92:20 120:32 150:35 182:26 214:21

4:12 64:57 92:45 120:47 150:57 183:16 215:17 92:53 121: 1 151:10 183:15 215:13 93: 1 121:15 151:22 183:14 215: 8

4:15 65:39 93:26 121:31 151:45 184: 5 216: 4 93:34 121:44 151:57 184: 4 215:59 93:42 121:58 152: 8 184: 3 215:54

4:18 66:22 94: 8 122:14 152:32 184:54 216:50 94:16 122:28 152:44 184:53 216:45 94:24 122:42 152:55 184:51 216:40

4:21 67: 4 94:49 122:58 153:19 185:43 217:36 94:57 123:11 153:31 185:41 217:31 95: 5 123:25 153:42 185:40 217:26

4:24 67:47 95:30 123:41 154: 7 186:32 218:22 95:38 123:55 154:18 186:30 218:17 95:46 124: 8 154:29 186:28 218:12

4:27 68:29 96:12 124:25 154:54 187:21 219: 9 96:20 124:38 155: 5 187:19 219: 3 96:28 124:52 155:16 187:17 218:58

4:30 69:11 96:53 125: 9 155:42 188:10 219:54 97: 1 125:22 155:53 188: 7 219:49 97: 9 125:35 156: 3 188: 5 219:44

4:33 69:54 97:35 125:53 156:30 188:59 220:40 97:43 126: 6 156:40 188:56 220:35 97:50 126:19 156:50 188:53 220:29

4:36 70:36 98:16 126:37 157:18 189:48 221:26 98:24 126:50 157:28 189:45 221:20 98:32 127: 3 157:37 189:42 221:15

4:39 71:18 98:58 127:21 158: 6 190:36 222:12 99: 5 127:34 158:15 190:33 222: 6 99:13 127:47 158:25 190:30 222: 0

4:42 72: 0 99:39 128: 5 158:54 191:25 222:57 99:47 128:18 159: 3 191:22 222:51 99:55 128:31 159:12 191:18 222:46

4:45 72:42 100:21 128:49 159:42 192:14 223:42 100:28 129: 2 159:51 192:10 223:37 100:36 129:15 159:59 192: 7 223:31

4:48 73:24 101: 2 129:34 160:30 193: 3 224:28 101:10 129:46 160:38 192:59 224:22 101:18 129:59 160:47 192:55 224:16

4:51 74: 6 101:44 130:18 161:18 193:51 225:13 101:52 130:31 161:26 193:47 225: 7 101:59 130:43 161:34 193:43 225: 1

4:54 74:48 102:25 131: 3 162: 6 194:40 225:58 102:33 131:15 162:14 194:35 225:52 102:41 131:28 162:22 194:31 225:46

4:57 75:30 103: 7 131:47 162:55 195:28 226:43 103:15 131:60 163: 2 195:24 226:37 103:23 132:12 163:10 195:19 226:31

5: 0 76:11 103:49 132:32 163:43 196:17 227:28 103:56 132:44 163:50 196:12 227:22 104: 4 132:56 163:57 196: 7 227:16

5: 3 76:53 104:30 133:17 164:32 197: 5 228:13 104:38 133:29 164:39 197: 0 228: 6 104:46 133:41 164:45 196:55 228: 0

5: 6 77:35 105:12 134: 2 165:20 197:54 228:57 105:20 134:14 165:27 197:48 228:51 105:28 134:26 165:33 197:43 228:45

5: 9 78:16 105:54 134:47 166: 9 198:42 229:42 106: 2 134:59 166:15 198:36 229:36 106: 9 135:11 166:21 198:31 229:29

5:12 78:58 106:36 135:32 166:57 199:30 230:26 106:44 135:44 167: 3 199:24 230:20 106:51 135:55 167: 9 199:19 230:14

5:15 79:39 107:18 136:18 167:46 200:18 231:11 107:26 136:29 167:52 200:12 231: 4 107:33 136:40 167:57 200: 6 230:58

5:18 80:21 107:60 137: 3 168:35 201: 6 231:55 108: 8 137:14 168:40 201: 0 231:49 108:15 137:26 168:45 200:54 231:42

5:21 81: 2 108:42 137:48 169:24 201:54 232:39 108:50 137:60 169:28 201:48 232:33 108:57 138:11 169:33 201:42 232:26

5:24 81:44 109:24 138:34 170:12 202:42 233:23 109:32 138:45 170:17 202:36 233:17 109:39 138:56 170:21 202:29 233:10

5:27 82:25 110: 6 139:20 171: 1 203:30 234: 7 110:14 139:31 171: 5 203:23 234: 1 110:21 139:41 171: 9 203:17 233:54

5:30 83: 7 110:49 140: 6 171:50 204:18 234:51 110:56 140:16 171:54 204:11 234:45 111: 4 140:27 171:57 204: 4 234:38

5:33 83:48 111:31 140:51 172:39 205: 6 235:35 111:38 141: 2 172:42 204:58 235:28 111:46 141:13 172:46 204:51 235:22

5:36 84:30 112:13 141:38 173:28 205:53 236:19 112:21 141:48 173:31 205:46 236:12 112:28 141:58 173:34 205:38 236: 5

5:39 85:11 112:56 142:24 174:17 206:41 237: 2 113: 3 142:34 174:19 206:33 236:56 113:10 142:44 174:22 206:25 236:49

5:42 85:52 113:38 143:10 175: 6 207:28 237:46 113:46 143:20 175: 8 207:20 237:39 113:53 143:30 175:10 207:13 237:32

5:45 86:34 114:21 143:56 175:55 208:15 238:29 114:28 144: 6 175:57 208: 7 238:22 114:35 144:16 175:58 207:59 238:16

5:48 87:15 115: 3 144:43 176:44 209: 3 239:13 115:11 144:52 176:45 208:54 239: 6 115:18 145: 2 176:47 208:46 238:59

5:51 87:56 115:46 145:29 177:33 209:50 239:56 115:53 145:39 177:34 209:41 239:49 116: 1 145:48 177:35 209:33 239:42

5:54 88:37 116:29 146:16 178:22 210:37 240:39 116:36 146:25 178:23 210:28 240:32 116:43 146:34 178:23 210:20 240:25

5:57 89:19 117:12 147: 2 179:11 211:24 241:22 117:19 147:12 179:11 211:15 241:15 117:26 147:21 179:12 211: 6 241: 8

6: 0 90: 0 117:55 147:49 180: 0 212:11 242: 5 118: 2 147:58 180: 0 212: 2 241:58 118: 9 148: 7 180: 0 211:53 241:51

6: 3 90:41 118:38 148:36 180:49 212:58 242:48 118:45 148:45 180:49 212:48 242:41 118:52 148:54 180:48 212:39 242:34

6: 6 91:23 119:21 149:23 181:38 213:44 243:31 119:28 149:32 181:37 213:35 243:24 119:35 149:40 181:37 213:26 243:17

6: 9 92: 4 120: 4 150:10 182:27 214:31 244:14 120:11 150:19 182:26 214:21 244: 7 120:18 150:27 182:25 214:12 243:59

6:12 92:45 120:47 150:57 183:16 215:17 244:57 120:54 151: 6 183:15 215: 8 244:49 121: 1 151:14 183:13 214:58 244:42

6:15 93:26 121:31 151:45 184: 5 216: 4 245:39 121:38 151:53 184: 3 215:54 245:32 121:44 152: 1 184: 2 215:44 245:25

6:18 94: 8 122:14 152:32 184:54 216:50 246:22 122:21 152:40 184:52 216:40 246:14 122:28 152:47 184:50 216:30 246: 7

6:21 94:49 122:58 153:19 185:43 217:36 247: 4 123: 4 153:27 185:41 217:26 246:57 123:11 153:35 185:38 217:16 246:50

6:24 95:30 123:41 154: 7 186:32 218:22 247:47 123:48 154:14 186:29 218:12 247:39 123:55 154:22 186:26 218: 2 247:32

6:27 96:12 124:25 154:54 187:21 219: 9 248:29 124:32 155: 2 187:18 218:58 248:22 124:38 155: 9 187:14 218:47 248:14

6:30 96:53 125: 9 155:42 188:10 219:54 249:11 125:15 155:49 188: 6 219:44 249: 4 125:22 155:56 188: 3 219:33 248:56

6:33 97:35 125:53 156:30 188:59 220:40 249:54 125:59 156:37 188:55 220:29 249:46 126: 6 156:43 188:51 220:19 249:39

6:36 98:16 126:37 157:18 189:48 221:26 250:36 126:43 157:24 189:43 221:15 250:28 126:50 157:31 189:39 221: 4 250:21

6:39 98:58 127:21 158: 6 190:36 222:12 251:18 127:27 158:12 190:32 222: 0 251:10 127:34 158:18 190:27 221:49 251: 3

6:42 99:39 128: 5 158:54 191:25 222:57 252: 0 128:11 158:60 191:20 222:46 251:52 128:18 159: 6 191:15 222:34 251:45

6:45 100:21 128:49 159:42 192:14 223:42 252:42 128:56 159:48 192: 8 223:31 252:34 129: 2 159:54 192: 3 223:20 252:27

6:48 101: 2 129:34 160:30 193: 3 224:28 253:24 129:40 160:36 192:57 224:16 253:16 129:46 160:41 192:51 224: 5 253: 9

6:51 101:44 130:18 161:18 193:51 225:13 254: 6 130:24 161:24 193:45 225: 1 253:58 130:31 161:29 193:39 224:49 253:51

6:54 102:25 131: 3 162: 6 194:40 225:58 254:48 131: 9 162:12 194:33 225:46 254:40 131:15 162:17 194:27 225:34 254:32

6:57 103: 7 131:47 162:55 195:28 226:43 255:30 131:54 162:60 195:21 226:31 255:22 131:60 163: 5 195:15 226:19 255:14

7: 0 103:49 132:32 163:43 196:17 227:28 256:11 132:38 163:48 196:10 227:16 256: 4 132:44 163:53 196: 3 227: 4 255:56

7: 3 104:30 133:17 164:32 197: 5 228:13 256:53 133:23 164:36 196:58 228: 0 256:45 133:29 164:41 196:50 227:48 256:37

7: 6 105:12 134: 2 165:20 197:54 228:57 257:35 134: 8 165:25 197:46 228:45 257:27 134:14 165:29 197:38 228:32 257:19

7: 9 105:54 134:47 166: 9 198:42 229:42 258:16 134:53 166:13 198:34 229:29 258: 8 134:59 166:17 198:26 229:17 258: 1


21/95



0


RAMCH:M



7:12 106:36 135:32 166:57 199:30 230:26 258:58 135:38 167: 1 199:22 230:14 258:50 135:44 167: 5 199:13 230: 1 258:42

7:15 107:18 136:18 167:46 200:18 231:11 259:39 136:23 167:50 200: 9 230:58 259:32 136:29 167:53 200: 1 230:45 259:24

7:18 107:60 137: 3 168:35 201: 6 231:55 260:21 137: 9 168:38 200:57 231:42 260:13 137:14 168:42 200:48 231:29 260: 5

7:21 108:42 137:48 169:24 201:54 232:39 261: 2 137:54 169:27 201:45 232:26 260:55 137:60 169:30 201:35 232:13 260:47

7:24 109:24 138:34 170:12 202:42 233:23 261:44 138:40 170:15 202:32 233:10 261:36 138:45 170:18 202:23 232:57 261:28

7:27 110: 6 139:20 171: 1 203:30 234: 7 262:25 139:25 171: 4 203:20 233:54 262:17 139:31 171: 7 203:10 233:41 262:10

7:30 110:49 140: 6 171:50 204:18 234:51 263: 7 140:11 171:53 204: 7 234:38 262:59 140:16 171:55 203:57 234:25 262:51

7:33 111:31 140:51 172:39 205: 6 235:35 263:48 140:57 172:41 204:55 235:22 263:40 141: 2 172:43 204:44 235: 8 263:32

7:36 112:13 141:38 173:28 205:53 236:19 264:30 141:43 173:30 205:42 236: 5 264:22 141:48 173:32 205:31 235:52 264:14

7:39 112:56 142:24 174:17 206:41 237: 2 265:11 142:29 174:19 206:29 236:49 265: 3 142:34 174:20 206:18 236:35 264:55

7:42 113:38 143:10 175: 6 207:28 237:46 265:52 143:15 175: 7 207:16 237:32 265:44 143:20 175: 9 207: 5 237:18 265:36

7:45 114:21 143:56 175:55 208:15 238:29 266:34 144: 1 175:56 208: 3 238:16 266:26 144: 6 175:57 207:52 238: 2 266:18

7:48 115: 3 144:43 176:44 209: 3 239:13 267:15 144:47 176:45 208:50 238:59 267: 7 144:52 176:46 208:38 238:45 266:59

7:51 115:46 145:29 177:33 209:50 239:56 267:56 145:34 177:34 209:37 239:42 267:48 145:39 177:34 209:25 239:28 267:40

7:54 116:29 146:16 178:22 210:37 240:39 268:37 146:20 178:22 210:24 240:25 268:29 146:25 178:23 210:11 240:11 268:22

7:57 117:12 147: 2 179:11 211:24 241:22 269:19 147: 7 179:11 211:11 241: 8 269:11 147:12 179:11 210:58 240:54 269: 3

8: 0 117:55 147:49 180: 0 212:11 242: 5 269:60 147:54 180: 0 211:57 241:51 269:52 147:58 180: 0 211:44 241:37 269:44

8: 3 118:38 148:36 180:49 212:58 242:48 270:41 148:40 180:49 212:44 242:34 270:33 148:45 180:49 212:30 242:20 270:25

8: 6 119:21 149:23 181:38 213:44 243:31 271:23 149:27 181:38 213:30 243:17 271:15 149:32 181:37 213:17 243: 2 271: 7

8: 9 120: 4 150:10 182:27 214:31 244:14 272: 4 150:14 182:26 214:17 243:59 271:56 150:19 182:26 214: 3 243:45 271:48

8:12 120:47 150:57 183:16 215:17 244:57 272:45 151: 1 183:15 215: 3 244:42 272:37 151: 6 183:14 214:49 244:27 272:29

8:15 121:31 151:45 184: 5 216: 4 245:39 273:26 151:49 184: 4 215:49 245:25 273:19 151:53 184: 3 215:34 245:10 273:11

8:18 122:14 152:32 184:54 216:50 246:22 274: 8 152:36 184:53 216:35 246: 7 273:60 152:40 184:51 216:20 245:52 273:52

8:21 122:58 153:19 185:43 217:36 247: 4 274:49 153:23 185:41 217:21 246:50 274:41 153:27 185:40 217: 6 246:35 274:33

8:24 123:41 154: 7 186:32 218:22 247:47 275:30 154:11 186:30 218: 7 247:32 275:23 154:14 186:28 217:52 247:17 275:15

8:27 124:25 154:54 187:21 219: 9 248:29 276:12 154:58 187:19 218:53 248:14 276: 4 155: 2 187:17 218:37 247:59 275:56

8:30 125: 9 155:42 188:10 219:54 249:11 276:53 155:46 188: 7 219:38 248:56 276:45 155:49 188: 5 219:22 248:41 276:37

8:33 125:53 156:30 188:59 220:40 249:54 277:35 156:33 188:56 220:24 249:39 277:27 156:37 188:53 220: 8 249:24 277:19

8:36 126:37 157:18 189:48 221:26 250:36 278:16 157:21 189:45 221: 9 250:21 278: 8 157:24 189:42 220:53 250: 6 278: 0

8:39 127:21 158: 6 190:36 222:12 251:18 278:58 158: 9 190:33 221:55 251: 3 278:50 158:12 190:30 221:38 250:48 278:42

8:42 128: 5 158:54 191:25 222:57 252: 0 279:39 158:57 191:22 222:40 251:45 279:31 158:60 191:18 222:23 251:30 279:23

8:45 128:49 159:42 192:14 223:42 252:42 280:21 159:45 192:10 223:25 252:27 280:13 159:48 192: 7 223: 8 252:11 280: 5

8:48 129:34 160:30 193: 3 224:28 253:24 281: 2 160:33 192:59 224:10 253: 9 280:54 160:36 192:55 223:53 252:53 280:46

8:51 130:18 161:18 193:51 225:13 254: 6 281:44 161:21 193:47 224:55 253:51 281:36 161:24 193:43 224:38 253:35 281:28

8:54 131: 3 162: 6 194:40 225:58 254:48 282:25 162: 9 194:35 225:40 254:32 282:18 162:12 194:31 225:22 254:17 282:10

8:57 131:47 162:55 195:28 226:43 255:30 283: 7 162:57 195:24 226:25 255:14 282:59 162:60 195:19 226: 7 254:59 282:51

9: 0 132:32 163:43 196:17 227:28 256:11 283:49 163:46 196:12 227:10 255:56 283:41 163:48 196: 7 226:52 255:40 283:33

9: 3 133:17 164:32 197: 5 228:13 256:53 284:30 164:34 197: 0 227:54 256:37 284:23 164:36 196:55 227:36 256:22 284:15

9: 6 134: 2 165:20 197:54 228:57 257:35 285:12 165:22 197:48 228:39 257:19 285: 5 165:25 197:43 228:20 257: 4 284:57

9: 9 134:47 166: 9 198:42 229:42 258:16 285:54 166:11 198:36 229:23 258: 1 285:46 166:13 198:31 229: 4 257:45 285:39

9:12 135:32 166:57 199:30 230:26 258:58 286:36 166:59 199:24 230: 7 258:42 286:28 167: 1 199:19 229:49 258:27 286:21

9:15 136:18 167:46 200:18 231:11 259:39 287:18 167:48 200:12 230:52 259:24 287:10 167:50 200: 6 230:33 259: 8 287: 3

9:18 137: 3 168:35 201: 6 231:55 260:21 287:60 168:36 201: 0 231:36 260: 5 287:52 168:38 200:54 231:16 259:50 287:45

9:21 137:48 169:24 201:54 232:39 261: 2 288:42 169:25 201:48 232:20 260:47 288:34 169:27 201:42 232: 0 260:31 288:27

9:24 138:34 170:12 202:42 233:23 261:44 289:24 170:14 202:36 233: 4 261:28 289:17 170:15 202:29 232:44 261:12 289: 9

9:27 139:20 171: 1 203:30 234: 7 262:25 290: 6 171: 3 203:23 233:47 262:10 289:59 171: 4 203:17 233:28 261:54 289:51

9:30 140: 6 171:50 204:18 234:51 263: 7 290:49 171:51 204:11 234:31 262:51 290:41 171:53 204: 4 234:11 262:35 290:33

9:33 140:51 172:39 205: 6 235:35 263:48 291:31 172:40 204:58 235:15 263:32 291:23 172:41 204:51 234:55 263:16 291:16

9:36 141:38 173:28 205:53 236:19 264:30 292:13 173:29 205:46 235:58 264:14 292: 6 173:30 205:38 235:38 263:58 291:58

9:39 142:24 174:17 206:41 237: 2 265:11 292:56 174:18 206:33 236:42 264:55 292:48 174:19 206:25 236:22 264:39 292:41

9:42 143:10 175: 6 207:28 237:46 265:52 293:38 175: 7 207:20 237:25 265:36 293:31 175: 7 207:13 237: 5 265:20 293:23

9:45 143:56 175:55 208:15 238:29 266:34 294:21 175:55 208: 7 238: 9 266:18 294:13 175:56 207:59 237:48 266: 2 294: 6

9:48 144:43 176:44 209: 3 239:13 267:15 295: 3 176:44 208:54 238:52 266:59 294:56 176:45 208:46 238:31 266:43 294:49

9:51 145:29 177:33 209:50 239:56 267:56 295:46 177:33 209:41 239:35 267:40 295:39 177:34 209:33 239:14 267:24 295:31

9:54 146:16 178:22 210:37 240:39 268:37 296:29 178:22 210:28 240:18 268:22 296:22 178:22 210:20 239:57 268: 6 296:14

9:57 147: 2 179:11 211:24 241:22 269:19 297:12 179:11 211:15 241: 1 269: 3 297: 4 179:11 211: 6 240:40 268:47 296:57

10: 0 147:49 180: 0 212:11 242: 5 269:60 297:55 180: 0 212: 2 241:44 269:44 297:47 180: 0 211:53 241:23 269:29 297:40

10: 3 148:36 180:49 212:58 242:48 270:41 298:38 180:49 212:48 242:27 270:25 298:31 180:49 212:39 242: 5 270: 9 298:23

10: 6 149:23 181:38 213:44 243:31 271:23 299:21 181:38 213:35 243: 9 271: 7 299:14 181:38 213:26 242:48 270:51 299: 7

10: 9 150:10 182:27 214:31 244:14 272: 4 300: 4 182:27 214:21 243:52 271:48 299:57 182:26 214:12 243:30 271:32 299:50

10:12 150:57 183:16 215:17 244:57 272:45 300:47 183:16 215: 8 244:35 272:29 300:40 183:15 214:58 244:13 272:13 300:33

10:15 151:45 184: 5 216: 4 245:39 273:26 301:31 184: 5 215:54 245:17 273:11 301:24 184: 4 215:44 244:55 272:55 301:17

10:18 152:32 184:54 216:50 246:22 274: 8 302:14 184:53 216:40 245:60 273:52 302: 7 184:53 216:30 245:38 273:36 302: 0

10:21 153:19 185:43 217:36 247: 4 274:49 302:58 185:42 217:26 246:42 274:33 302:51 185:41 217:16 246:20 274:17 302:44

10:24 154: 7 186:32 218:22 247:47 275:30 303:41 186:31 218:12 247:24 275:15 303:34 186:30 218: 2 247: 2 274:59 303:28

10:27 154:54 187:21 219: 9 248:29 276:12 304:25 187:20 218:58 248: 7 275:56 304:18 187:19 218:47 247:44 275:40 304:11

10:30 155:42 188:10 219:54 249:11 276:53 305: 9 188: 9 219:44 248:49 276:37 305: 2 188: 7 219:33 248:27 276:22 304:55

10:33 156:30 188:59 220:40 249:54 277:35 305:53 188:57 220:29 249:31 277:19 305:46 188:56 220:19 249: 9 277: 3 305:39

10:36 157:18 189:48 221:26 250:36 278:16 306:37 189:46 221:15 250:13 278: 0 306:30 189:45 221: 4 249:51 277:44 306:23

10:39 158: 6 190:36 222:12 251:18 278:58 307:21 190:35 222: 0 250:55 278:42 307:14 190:33 221:49 250:33 278:26 307: 8

10:42 158:54 191:25 222:57 252: 0 279:39 308: 5 191:24 222:46 251:37 279:23 307:58 191:22 222:34 251:14 279: 8 307:52

10:45 159:42 192:14 223:42 252:42 280:21 308:49 192:12 223:31 252:19 280: 5 308:43 192:10 223:20 251:56 279:49 308:36

10:48 160:30 193: 3 224:28 253:24 281: 2 309:34 193: 1 224:16 253: 1 280:46 309:27 192:59 224: 5 252:38 280:31 309:21

10:51 161:18 193:51 225:13 254: 6 281:44 310:18 193:49 225: 1 253:43 281:28 310:12 193:47 224:49 253:20 281:12 310: 5


22/95



0


RAMCH:M



10:54 162: 6 194:40 225:58 254:48 282:25 311: 3 194:38 225:46 254:25 282:10 310:56 194:35 225:34 254: 2 281:54 310:50

10:57 162:55 195:28 226:43 255:30 283: 7 311:47 195:26 226:31 255: 6 282:51 311:41 195:24 226:19 254:43 282:36 311:35

11: 0 163:43 196:17 227:28 256:11 283:49 312:32 196:14 227:16 255:48 283:33 312:26 196:12 227: 4 255:25 283:18 312:20

11: 3 164:32 197: 5 228:13 256:53 284:30 313:17 197: 3 228: 0 256:30 284:15 313:11 197: 0 227:48 256: 6 283:59 313: 5

11: 6 165:20 197:54 228:57 257:35 285:12 314: 2 197:51 228:45 257:11 284:57 313:56 197:48 228:32 256:48 284:41 313:50

11: 9 166: 9 198:42 229:42 258:16 285:54 314:47 198:39 229:29 257:53 285:39 314:41 198:36 229:17 257:29 285:23 314:35

11:12 166:57 199:30 230:26 258:58 286:36 315:32 199:27 230:14 258:34 286:21 315:26 199:24 230: 1 258:11 286: 5 315:21

11:15 167:46 200:18 231:11 259:39 287:18 316:18 200:15 230:58 259:16 287: 3 316:12 200:12 230:45 258:52 286:47 316: 6

11:18 168:35 201: 6 231:55 260:21 287:60 317: 3 201: 3 231:42 259:57 287:45 316:57 201: 0 231:29 259:34 287:29 316:52

11:21 169:24 201:54 232:39 261: 2 288:42 317:48 201:51 232:26 260:39 288:27 317:43 201:48 232:13 260:15 288:11 317:37

11:24 170:12 202:42 233:23 261:44 289:24 318:34 202:39 233:10 261:20 289: 9 318:29 202:36 232:57 260:57 288:54 318:23

11:27 171: 1 203:30 234: 7 262:25 290: 6 319:20 203:27 233:54 262: 2 289:51 319:14 203:23 233:41 261:38 289:36 319: 9

11:30 171:50 204:18 234:51 263: 7 290:49 320: 6 204:14 234:38 262:43 290:33 320: 0 204:11 234:25 262:19 290:18 319:55

11:33 172:39 205: 6 235:35 263:48 291:31 320:51 205: 2 235:22 263:24 291:16 320:46 204:58 235: 8 263: 1 291: 1 320:41

11:36 173:28 205:53 236:19 264:30 292:13 321:38 205:49 236: 5 264: 6 291:58 321:32 205:46 235:52 263:42 291:43 321:27

11:39 174:17 206:41 237: 2 265:11 292:56 322:24 206:37 236:49 264:47 292:41 322:18 206:33 236:35 264:23 292:26 322:13

11:42 175: 6 207:28 237:46 265:52 293:38 323:10 207:24 237:32 265:28 293:23 323: 5 207:20 237:18 265: 5 293: 8 322:60

11:45 175:55 208:15 238:29 266:34 294:21 323:56 208:11 238:16 266:10 294: 6 323:51 208: 7 238: 2 265:46 293:51 323:46

11:48 176:44 209: 3 239:13 267:15 295: 3 324:43 208:59 238:59 266:51 294:49 324:38 208:54 238:45 266:27 294:34 324:33

11:51 177:33 209:50 239:56 267:56 295:46 325:29 209:46 239:42 267:32 295:31 325:24 209:41 239:28 267: 8 295:17 325:19

11:54 178:22 210:37 240:39 268:37 296:29 326:16 210:33 240:25 268:14 296:14 326:11 210:28 240:11 267:50 295:60 326: 6

11:57 179:11 211:24 241:22 269:19 297:12 327: 2 211:20 241: 8 268:55 296:57 326:58 211:15 240:54 268:31 296:43 326:53

12: 0 180: 0 212:11 242: 5 269:60 297:55 327:49 212: 6 241:51 269:37 297:40 327:45 212: 2 241:37 269:14 297:26 327:40

12: 3 180:49 212:58 242:48 270:41 298:38 328:36 212:53 242:34 270:17 298:23 328:32 212:48 242:20 269:54 298: 9 328:27

12: 6 181:38 213:44 243:31 271:23 299:21 329:23 213:40 243:17 270:59 299: 7 329:19 213:35 243: 2 270:35 298:52 329:14

12: 9 182:27 214:31 244:14 272: 4 300: 4 330:10 214:26 243:59 271:40 299:50 330: 6 214:21 243:45 271:16 299:36 330: 2

12:12 183:16 215:17 244:57 272:45 300:47 330:57 215:13 244:42 272:21 300:33 330:53 215: 8 244:27 271:57 300:19 330:49

12:15 184: 5 216: 4 245:39 273:26 301:31 331:45 215:59 245:25 273: 3 301:17 331:40 215:54 245:10 272:39 301: 3 331:36

12:18 184:54 216:50 246:22 274: 8 302:14 332:32 216:45 246: 7 273:44 302: 0 332:28 216:40 245:52 273:20 301:46 332:24

12:21 185:43 217:36 247: 4 274:49 302:58 333:19 217:31 246:50 274:25 302:44 333:15 217:26 246:35 274: 1 302:30 333:12

12:24 186:32 218:22 247:47 275:30 303:41 334: 7 218:17 247:32 275: 7 303:28 334: 3 218:12 247:17 274:43 303:14 333:59

12:27 187:21 219: 9 248:29 276:12 304:25 334:54 219: 3 248:14 275:48 304:11 334:51 218:58 247:59 275:24 303:58 334:47

12:30 188:10 219:54 249:11 276:53 305: 9 335:42 219:49 248:56 276:29 304:55 335:39 219:44 248:41 276: 6 304:42 335:35

12:33 188:59 220:40 249:54 277:35 305:53 336:30 220:35 249:39 277:11 305:39 336:27 220:29 249:24 276:47 305:26 336:23

12:36 189:48 221:26 250:36 278:16 306:37 337:18 221:20 250:21 277:52 306:23 337:14 221:15 250: 6 277:29 306:10 337:11

12:39 190:36 222:12 251:18 278:58 307:21 338: 6 222: 6 251: 3 278:34 307: 8 338: 3 222: 0 250:48 278:10 306:54 337:59

12:42 191:25 222:57 252: 0 279:39 308: 5 338:54 222:51 251:45 279:15 307:52 338:51 222:46 251:30 278:52 307:39 338:48

12:45 192:14 223:42 252:42 280:21 308:49 339:42 223:37 252:27 279:57 308:36 339:39 223:31 252:11 279:33 308:23 339:36

12:48 193: 3 224:28 253:24 281: 2 309:34 340:30 224:22 253: 9 280:39 309:21 340:27 224:16 252:53 280:15 309: 8 340:24

12:51 193:51 225:13 254: 6 281:44 310:18 341:18 225: 7 253:51 281:20 310: 5 341:15 225: 1 253:35 280:57 309:53 341:13

12:54 194:40 225:58 254:48 282:25 311: 3 342: 6 225:52 254:32 282: 2 310:50 342: 4 225:46 254:17 281:38 310:38 342: 1

12:57 195:28 226:43 255:30 283: 7 311:47 342:55 226:37 255:14 282:44 311:35 342:52 226:31 254:59 282:20 311:23 342:50

13: 0 196:17 227:28 256:11 283:49 312:32 343:43 227:22 255:56 283:25 312:20 343:41 227:16 255:40 283: 2 312: 8 343:38

13: 3 197: 5 228:13 256:53 284:30 313:17 344:32 228: 6 256:37 284: 7 313: 5 344:29 228: 0 256:22 283:44 312:53 344:27

13: 6 197:54 228:57 257:35 285:12 314: 2 345:20 228:51 257:19 284:49 313:50 345:18 228:45 257: 4 284:26 313:38 345:16

13: 9 198:42 229:42 258:16 285:54 314:47 346: 9 229:36 258: 1 285:31 314:35 346: 7 229:29 257:45 285: 8 314:23 346: 5

13:12 199:30 230:26 258:58 286:36 315:32 346:57 230:20 258:42 286:13 315:21 346:55 230:14 258:27 285:50 315: 9 346:53

13:15 200:18 231:11 259:39 287:18 316:18 347:46 231: 4 259:24 286:55 316: 6 347:44 230:58 259: 8 286:32 315:54 347:42

13:18 201: 6 231:55 260:21 287:60 317: 3 348:35 231:49 260: 5 287:37 316:52 348:33 231:42 259:50 287:14 316:40 348:31

13:21 201:54 232:39 261: 2 288:42 317:48 349:24 232:33 260:47 288:19 317:37 349:22 232:26 260:31 287:56 317:26 349:20

13:24 202:42 233:23 261:44 289:24 318:34 350:12 233:17 261:28 289: 1 318:23 350:11 233:10 261:12 288:38 318:12 350: 9

13:27 203:30 234: 7 262:25 290: 6 319:20 351: 1 234: 1 262:10 289:44 319: 9 350:60 233:54 261:54 289:21 318:58 350:58

13:30 204:18 234:51 263: 7 290:49 320: 6 351:50 234:45 262:51 290:26 319:55 351:49 234:38 262:35 290: 3 319:44 351:48

13:33 205: 6 235:35 263:48 291:31 320:51 352:39 235:28 263:32 291: 8 320:41 352:38 235:22 263:16 290:46 320:30 352:37

13:36 205:53 236:19 264:30 292:13 321:38 353:28 236:12 264:14 291:51 321:27 353:27 236: 5 263:58 291:28 321:16 353:26

13:39 206:41 237: 2 265:11 292:56 322:24 354:17 236:56 264:55 292:33 322:13 354:16 236:49 264:39 292:11 322: 3 354:15

13:42 207:28 237:46 265:52 293:38 323:10 355: 6 237:39 265:36 293:16 322:60 355: 5 237:32 265:20 292:53 322:49 355: 4

13:45 208:15 238:29 266:34 294:21 323:56 355:55 238:22 266:18 293:59 323:46 355:54 238:16 266: 2 293:36 323:36 355:54

13:48 209: 3 239:13 267:15 295: 3 324:43 356:44 239: 6 266:59 294:41 324:33 356:43 238:59 266:43 294:19 324:23 356:43

13:51 209:50 239:56 267:56 295:46 325:29 357:33 239:49 267:40 295:24 325:19 357:33 239:42 267:24 295: 2 325:10 357:32

13:54 210:37 240:39 268:37 296:29 326:16 358:22 240:32 268:22 296: 7 326: 6 358:22 240:25 268: 6 295:45 325:57 358:21

13:57 211:24 241:22 269:19 297:12 327: 2 359:11 241:15 269: 3 296:50 326:53 359:11 241: 8 268:47 296:28 326:44 359:11

14: 0 212:11 242: 5 269:60 297:55 327:49 0: 0 241:58 269:44 297:33 327:40 0: 0 241:51 269:29 297:11 327:31 0: 0

14: 3 212:58 242:48 270:41 298:38 328:36 0:49 242:41 270:25 298:16 328:27 0:49 242:34 270: 9 297:55 328:18 0:49

14: 6 213:44 243:31 271:23 299:21 329:23 1:38 243:24 271: 7 298:59 329:14 1:38 243:17 270:51 298:38 329: 6 1:39

14: 9 214:31 244:14 272: 4 300: 4 330:10 2:2 7 244: 7 271:48 299:43 330: 2 2:27 243:59 271:32 299:21 329:53 2:28

14:12 215:17 244:57 272:45 300:47 330:57 3:16 244:49 272:29 300:26 330:49 3:17 244:42 272:13 300: 5 330:41 3:17

14:15 216: 4 245:39 273:26 301:31 331:45 4: 5 245:32 273:11 301:10 331:36 4: 6 245:25 272:55 300:49 331:28 4: 6

14:18 216:50 246:22 274: 8 302:14 332:32 4:54 246:14 273:52 301:53 332:24 4:5 5 246: 7 273:36 301:32 332:16 4:56

14:21 217:36 247: 4 274:49 302:58 333:19 5:43 246:57 274:33 302:37 333:12 5:44 246:50 274:17 302:16 333: 4 5:45

14:24 218:22 247:47 275:30 303:41 334: 7 6:32 247:39 275:15 303:21 333:59 6:33 247:32 274:59 303: 0 333:52 6:34

14:27 219: 9 248:29 276:12 304:25 334:54 7:21 248:22 275:56 304: 5 334:47 7:22 248:14 275:40 303:44 334:40 7:23

14:30 219:54 249:11 276:53 305: 9 335:42 8:1 0 249: 4 276:37 304:49 335:35 8:11 248:56 276:22 304:28 335:28 8:12

14:33 220:40 249:54 277:35 305:53 336:30 8:59 249:46 277:19 305:33 336:23 9: 0 249:39 277: 3 305:12 336:16 9: 2


23/95



0


RAMCH:M



14:36 221:26 250:36 278:16 306:37 337:18 9:48 250:28 278: 0 306:17 337:11 9:49 250:21 277:44 305:57 337: 4 9:51

14:39 222:12 251:18 278:58 307:21 338: 6 10:36 251:10 278:42 307: 1 337:59 10:38 251: 3 278:26 306:41 337:53 10:40

14:42 222:57 252: 0 279:39 308: 5 338:54 11:25 251:52 279:23 307:45 338:48 11:27 251:45 279: 8 307:26 338:41 11:29

14:45 223:42 252:42 280:21 308:49 339:42 12:14 252:34 280: 5 308:30 339:36 12:16 252:27 279:49 308:10 339:30 12:18

14:48 224:28 253:24 281: 2 309:34 340:30 13: 3 253:16 280:46 309:14 340:24 13: 5 253: 9 280:31 308:55 340:18 13: 7

14:51 225:13 254: 6 281:44 310:18 341:18 13:51 253:58 281:28 309:59 341:13 13:53 253:51 281:12 309:40 341: 7 13:55

14:54 225:58 254:48 282:25 311: 3 342: 6 14:40 254:40 282:10 310:44 342: 1 14:42 254:32 281:54 310:25 341:56 14:44

14:57 226:43 255:30 283: 7 311:47 342:55 15:28 255:22 282:51 311:29 342:50 15:31 255:14 282:36 311:10 342:45 15:33

15: 0 227:28 256:11 283:49 312:32 343:43 16:17 256: 4 283:33 312:14 343:38 16:19 255:56 283:18 311:55 343:33 16:22

15: 3 228:13 256:53 284:30 313:17 344:32 17: 5 256:45 284:15 312:59 344:27 17: 8 256:37 283:59 312:40 344:22 17:10

15: 6 228:57 257:35 285:12 314: 2 345:20 17:54 257:27 284:57 313:44 345:16 17:56 257:19 284:41 313:26 345:11 17:59

15: 9 229:42 258:16 285:54 314:47 346: 9 18:42 258: 8 285:39 314:29 346: 5 18:45 258: 1 285:23 314:11 346: 0 18:47

15:12 230:26 258:58 286:36 315:32 346:57 19:30 258:50 286:21 315:15 346:53 19:33 258:42 286: 5 314:57 346:50 19:36

15:15 231:11 259:39 287:18 316:18 347:46 20:18 259:32 287: 3 316: 0 347:42 20:21 259:24 286:47 315:43 347:39 20:24

15:18 231:55 260:21 287:60 317: 3 348:35 21: 6 260:13 287:45 316:46 348:31 21: 9 260: 5 287:29 316:28 348:28 21:12

15:21 232:39 261: 2 288:42 317:48 349:24 21:54 260:55 288:27 317:32 349:20 21:57 260:47 288:11 317:14 349:17 22: 1

15:24 233:23 261:44 289:24 318:34 350:12 22:42 261:36 289: 9 318:17 350: 9 22:46 261:28 288:54 318: 1 350: 6 22:49

15:27 234: 7 262:25 290: 6 319:20 351: 1 23:30 262:17 289:51 319: 3 350:58 23:33 262:10 289:36 318:47 350:56 23:37

15:30 234:51 263: 7 290:49 320: 6 351:50 24:18 262:59 290:33 319:49 351:48 24:21 262:51 290:18 319:33 351:45 24:25

15:33 235:35 263:48 291:31 320:51 352:39 25: 6 263:40 291:16 320:36 352:37 25: 9 263:32 291: 1 320:19 352:34 25:13

15:36 236:19 264:30 292:13 321:38 353:28 25:53 264:22 291:58 321:22 353:26 25:57 264:14 291:43 321: 6 353:24 26: 1

15:39 237: 2 265:11 292:56 322:24 354:17 26:41 265: 3 292:41 322: 8 354:15 26:45 264:55 292:26 321:52 354:13 26:48

15:42 237:46 265:52 293:38 323:10 355: 6 27:28 265:44 293:23 322:55 355: 4 27:32 265:36 293: 8 322:39 355: 3 27:36

15:45 238:29 266:34 294:21 323:56 355:55 28:15 266:26 294: 6 323:41 355:54 28:20 266:18 293:51 323:26 355:52 28:24

15:48 239:13 267:15 295: 3 324:43 356:44 29: 3 267: 7 294:49 324:28 356:43 29: 7 266:59 294:34 324:13 356:42 29:11

15:51 239:56 267:56 295:46 325:29 357:33 29:50 267:48 295:31 325:15 357:32 29:54 267:40 295:17 324:60 357:31 29:58

15:54 240:39 268:37 296:29 326:16 358:22 30:37 268:29 296:14 326: 1 358:21 30:41 268:22 295:60 325:47 358:21 30:46

15:57 241:22 269:19 297:12 327: 2 359:11 31:24 269:11 296:57 326:48 359:11 31:28 269: 3 296:43 326:34 359:10 31:33

16: 0 242: 5 269:60 297:55 327:49 0: 0 32:11 269:52 297:40 327:36 0: 0 32:15 269:44 297:26 327:22 0: 0 32:20

16: 3 242:48 270:41 298:38 328:36 0:49 32:58 270:33 298:23 328:23 0:49 33: 2 270:25 298: 9 328: 9 0:5 0 33: 7

16: 6 243:31 271:23 299:21 329:23 1:38 33:44 271:15 299: 7 329:10 1:3 9 33:49 271: 7 298:52 328:57 1:39 33:54

16: 9 244:14 272: 4 300: 4 330:10 2:27 34:31 271:56 299:50 329:57 2:28 34:36 271:48 299:36 329:44 2:29 34:41

16:12 244:57 272:45 300:47 330:57 3:16 35:17 272:37 300:33 330:45 3:17 35:22 272:29 300:19 330:32 3:18 35:27

16:15 245:39 273:26 301:31 331:45 4: 5 36: 4 273:19 301:17 331:32 4: 6 36: 9 273:11 301: 3 331:20 4: 8 36:14

16:18 246:22 274: 8 302:14 332:32 4:54 36:50 273:60 302: 0 332:20 4:56 36:55 273:52 301:46 332: 8 4:57 37: 0

16:21 247: 4 274:49 302:58 333:19 5:43 37:36 274:41 302:44 333: 8 5:4 5 37:42 274:33 302:30 332:56 5:47 37:47

16:24 247:47 275:30 303:41 334: 7 6:3 2 38:22 275:23 303:28 333:56 6:34 38:28 275:15 303:14 333:44 6:36 38:33

16:27 248:29 276:12 304:25 334:54 7:21 39: 9 276: 4 304:11 334:44 7:23 39:14 275:56 303:58 334:32 7:26 39:19

16:30 249:11 276:53 305: 9 335:42 8:10 39:54 276:45 304:55 335:32 8:12 39:60 276:37 304:42 335:21 8:15 40: 5

16:33 249:54 277:35 305:53 336:30 8:59 40:40 277:27 305:39 336:20 9: 2 40:46 277:19 305:26 336: 9 9: 4 40:51

16:36 250:36 278:16 306:37 337:18 9:4 8 41:26 278: 8 306:23 337: 8 9:5 1 41:31 278: 0 306:10 336:58 9:54 41:37

16:39 251:18 278:58 307:21 338: 6 10:36 42:12 278:50 307: 8 337:56 10:40 42:17 278:42 306:54 337:46 10:43 42:23

16:42 252: 0 279:39 308: 5 338:54 11:25 42:57 279:31 307:52 338:44 11:29 43: 3 279:23 307:39 338:35 11:32 43: 8

16:45 252:42 280:21 308:49 339:42 12:14 43:42 280:13 308:36 339:33 12:18 43:48 280: 5 308:23 339:24 12:21 43:54

16:48 253:24 281: 2 309:34 340:30 13: 3 44:28 280:54 309:21 340:21 13: 7 44:34 280:46 309: 8 340:12 13:10 44:39

16:51 254: 6 281:44 310:18 341:18 13:51 45:13 281:36 310: 5 341:10 13:55 45:19 281:28 309:53 341: 1 13:60 45:25

16:54 254:48 282:25 311: 3 342: 6 14:40 45:58 282:18 310:50 341:58 14:44 46: 4 282:10 310:38 341:50 14:49 46:10

16:57 255:30 283: 7 311:47 342:55 15:28 46:43 282:59 311:35 342:47 15:33 46:49 282:51 311:23 342:39 15:38 46:55

17: 0 256:11 283:49 312:32 343:43 16:17 47:28 283:41 312:20 343:36 16:22 47:34 283:33 312: 8 343:28 16:27 47:40

17: 3 256:53 284:30 313:17 344:32 17: 5 48:13 284:23 313: 5 344:25 17:10 48:19 284:15 312:53 344:18 17:15 48:25

17: 6 257:35 285:12 314: 2 345:20 17:54 48:57 285: 5 313:50 345:14 17:59 49: 4 284:57 313:38 345: 7 18: 4 49:10

17: 9 258:16 285:54 314:47 346: 9 18:42 49:42 285:46 314:35 346: 3 18:47 49:48 285:39 314:23 345:56 18:53 49:55

17:12 258:58 286:36 315:32 346:57 19:30 50:26 286:28 315:21 346:51 19:36 50:33 286:21 315: 9 346:46 19:42 50:39

17:15 259:3

caliculation of hora cusp

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