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Measurements : Kautilya

Reference: Kautilya Arthasastra : Translation by Shama Shastry



THE Superintendent of lineal measure shall possess the knowledge of measuring space and time.

8 atoms (paramánavah) are equal to 1 particle thrown off by the wheel of a chariot.
8 particles are equal to likshá.
likshás are equal to the middle of a yúka (louse) or a yúka of medium size.
yúkas are equal to yava (barley) of middle size.
yavas are equal to angula (¾ of an English inch) or the middlemost joint of the middle finger of a man of medium size may be taken to be equal to an angula.
angulas are equal to dhanurgraha.
angulas are equal to dhanurmushti.
12 angulas are equal to vitasti, or 1 chháyápaurusha.
14 angulas are equal to samasalapariraya, or pada.
vitastis are equal to aratni or 1 prájápatya hasta
vitastis plus dhanurgraha are equal to hasta used in measuring balances and cubic measures, and pasture lands.
vitastis plusdhanurmusti kishku or 1 kamsa.
42 angulas are equal to kishku according to sawyers and blacksmiths and used in measuring the grounds for the encampment of the army, for forts and palaces.
54 angulas are equal to hasta used in measuring timber forests.
84 angulas are equal to vyáma, used in measuring ropes and the depth of digging, in terms of a man’s height.
aratnis are equal to danda, 1 dhanus, 1 nálika and 1 paurusha.
108 angulas are equal to garhapatya dhanus (i.e., a measure used by carpenters called grihapati). This measure is used in measuring roads and fort-walls.
The same (108 angulas) are equal to paurusha, a measure used in building sacrificial altars.
kamsas or 192 angulas are equal to danda, used in measuring such lands as are gifted to Bráhmans.
10 dandas are equal to rajju.
rajjus are equal to paridesa (square measure).
rajjus are equal to nivartana (square measure).
The same (3 rajjusplusdandas on one side only are equal to báhu (arm).
1000 dhanus are equal to goruta (sound of a cow).
gorutas are equal to yojana.

Thus are the lineal and square measures dealt with.

Then with regard to the measures of time:—

(The divisions of time are) a trutilavanimeshakáshthákalánálikámuhúrta, forenoon, afternoon, day, night, paksha, month, ritu (season), ayana (solstice); samvatsara (year), and yuga.

trutis are equal to lava.
lavas are equal to nimesha.
nimeshas are equal to káshthá.
30 káshthás are equal to kalá.
40 kalás are equal to náliká, or the time during which one ádhaka of water passes out of a pot through an aperture of the same diameter as that of a wire of 4 angulas in length and made of 4 máshas of gold.
nálikas are equal to muhúrta.
15 muhúrtas are equal to 1 day or 1 night.

Such a day and night happen in the months of Chaitra and Asvayuja. Then after the period of six months it increases or diminishes by three muhúrtas.

When the length of shadow is eight paurushas (96 angulas), it is 1/18th part of the day.

When it is 6 paurushas (72 angulas), it is 1/14th part of the day; when 4 paurushas, 1/8th part; when 2 paurushas, 1/6th part; when 1 paurusha, ¼th part; when it is 8 angulas, 3/10th part (trayodasabhágah); when 4 angulas, 3/8th part; and when no shadow is cast, it is to be considered midday.

Likewise when the day declines, the same process in reverse order shall be observed.

It is in the month of Ashádha that no shadow is cast in midday. After Ashádha, during the six months from Srávana upwards, the length of shadow successively increases by two angulas and during the next six months from Mágha upwards, it successively decreases by two angulas.

Fifteen days and nights together make up one paksha. That paksha during which the moon waxes is white (sukla) and thatpaksha during which the moon wanes is bahula.

Two pakshas make one month (mása). Thirty days and nights together make one work-a-month (prakarmamásah). The same (30 days and nights) with an additional half a day makes one solar month (saura).

The same (30) less by half a day makes one lunar month (chandramása).

Twenty-seven (days and nights) make a sidereal month (nakshatramása).

Once in thirty-two months there comes one malamása profane month, i.e., an extra month added to lunar year to harmonise it with the solar.

Once in thirty-five months there comes a malamása for Asvaváhas.

Once in forty months there comes a malamása for hastiváhas.

Two months make one ritu (season).

Srávana and proshthapada make the rainy season (varshá).

Asvayuja and Kárthíka make the autumn (sarad).

Márgasírsha and Phausha make the winter (hemanta).

Mágha and Phalguna make the dewy season (sisira).

Chaitra and Vaisákha make the spring (vasanta).

Jyeshthámúlíya and Ashádha make the summer (grishma).

Seasons from sisira and upwards are uttaráyana, and (those) from varshá and upwards are the winter solstice dakshináyana. Two ayanas make one year (samvatsara). Five years make one yuga.

The sun carries off (harati) 1/60th of a whole day every day and thus makes one complete day in every two months (ritau). Likewise the moon (falls behind by 1/60th of a whole day every day and falls behind one day in every two months). Thus in the middle of every third year, they (the sun and the moon) make one adhimása, additional month, first in the summer season and second at the end of five years.

[Thus ends Chapter XX, “Measurement of Space and Time” in Book II, “The Duties of Government Superintendents” of theArthasástra of Kautilya. End of the forty-first chapter from the beginning.]

The above calculations give us about half a mile to a yojana.


Written by 1 2 Next Change!

June 5, 2009 at 12:45 pm

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