Kautilya's Arthashastra 2.20: Chapter 20 (Section 38): Measures of Space and Time

2.20.1

mānādhyakṣyo deśakālamānaṃ vidyāt //

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 1 likshá. 8 likshás are equal to the middle of a yúka (louse) or a yúka of medium size. 8 yúkas are equal to 1 yava (barley) of middle size. 8 yavas are equal to

2.20.2

aṣṭau paramāṇavo rathacakravipruṭ //

2.20.3

tā aṣṭau likṣā //

2.20.4

tā aṣtau yūkā //

2.20.5

tā aṣṭau yavamadhyaḥ //

2.20.6

aṣṭau yavamadhyā aṅgulam //

1 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. 4 angulas are equal to 1 dhanurgraha. 8 angulas are equal to 1 dhanurmushti. 12 angulas are equal to 1 vitasti, or 1 chháyápaurusha. 14 angulas are equal to 1 sama, sala, pariraya, or pada. 2 vitastis are equal to 1 aratni or 1 prájápatya hasta 2 vitastis plus 1 dhanurgraha are equal to 1 hasta used in measuring balances and cubic measures, and pasture lands. 2 vitastis plus 1 dhanurmusti 1 kishku or 1 kamsa. 42 angulas are equal to

2.20.7

madhyamasya puruṣasya madhyamāyā anugulyā madhyaprakarṣo vāṅgulam //

2.20.8

caturaṅgulo dhanurgrahaḥ //

2.20.9

aṣṭāṅgulā dhanurmuṣṭiḥ //

2.20.10

dvādaśāṅgulā vitastiḥ, chāyāpauruṣaṃ ca //

2.20.11

caturdaśāṅgulaṃ śamaḥ śalaḥ parīrayaḥ padaṃ ca //

2.20.12

dvivitastir aratniḥ prājāpatyo hastaḥ //

2.20.13

sa-dhanurgrahaḥ pautavavivītamānam //

2.20.14

sa-dhanurmuṣṭiḥ kuṣkuḥ kaṃso vā //

2.20.15

dvicatvāriṃśadaṅgulas takṣṇaḥ krākacanikakiṣkuḥ skandhāvāradurgarājaparigrahamānam //

1 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 1 hasta used in measuring timber forests. 84 angulas are equal to 1 vyáma, used in measuring ropes and the depth of digging, in terms of a man's height. 4 aratnis are equal to 1 danda, 1 dhanus, 1 nálika and 1 paurusha. 108 angulas are equal to

2.20.16

catuṣpañcāśadaṅgulaḥ kūpyavanahastaḥ //

2.20.17

caturaśītyaṅgulo vyāmo rajjumānaṃ khātapauruṣaṃ ca //

2.20.18

caturaratnir daṇḍo dhanurnālikā pauruṣaṃ ca gārhapatyam //

1 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 1 paurusha, a measure used in building sacrificial altars. 6 kamsas or 192 angulas are equal to 1 danda, used in measuring such lands as are gifted to Bráhmans. 10 dandas are equal to

2.20.19

aṣṭaśatāṅgulaṃ dhanuḥ pathiprākāramānaṃ pauruṣaṃ cāgnicityānām //

2.20.20

ṣaṭkaṃso daṇḍo brahmadeyātithyamānam //

2.20.21

daśadaṇḍo rajjuḥ //

1 rajju. 2 rajjus are equal to 1 paridesa (square measure). 3 rajjus are equal to 1 nivartana (square measure). The same (3 rajjus) plus 2 dandas on one side only are equal to 1 báhu (arm). 1000 dhanus are equal to 1 goruta (sound of a cow). 4 gorutas are equal to 1 yojana.

2.20.22

dvirajjukaḥ parideśaḥ //

2.20.23

trirajjukaṃ nivartanam ekataḥ //

2.20.24

dvidaṇḍādhiko bāhuḥ //

2.20.25

dvidhanuḥsahasraṃ gorutam //

2.20.26

caturgorutaṃ yojanam //

2.20.27

iti deśamānam //

Thus are the lineal and square measures dealt with.

2.20.28

kālamānam ata ūrdhvam //

Then with regard to the measures of time:---

2.20.29

tuṭo lavo nimeṣaḥ kāṣṭhā kallā nālikā muhūrtaḥ pūrvāparabhāgau divaso rātriḥ pakṣo māsa ṛtur ayanaṃ saṃvatsaro yugam iti kālāḥ //

(The divisions of time are) a truti, lava, nimesha, káshthá, kalá, náliká, muhúrta, forenoon, afternoon, day, night, paksha, month, ritu (season), ayana (solstice); samvatsara (year), and yuga. 2 trutis are equal to 1 lava. 2 lavas are equal to 1 nimesha. 5 nimeshas are equal to 1 káshthá. 30 káshthás are equal to 1 kalá. 40 kalás are equal to 1 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. 2 nálikas are equal to 1 muhúrta. 15 muhúrtas are equal to 1 day or 1 night.

2.20.30

dvau tuṭau lavaḥ //

2.20.31

dvau lavau nimeṣaḥ //

2.20.32

pañcanimeṣāḥ kāṣṭhāḥ //

2.20.33

triṃśatkāṣṭhāḥ kalāḥ //

2.20.34

catvāriṃśatkalāḥ nālikā //

2.20.35

suvarṇamāṣakāś catvāraś caturaṅgulāyāmāḥ kumbhacchidram āḍhakam ambhaso vā nālikā //

2.20.36

dvināliko muhūrtaḥ //

2.20.37

pañcadaśamuhūrto divaso rātriś ca caitre cāśvayuje ca māsi bhavataḥ //

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.

2.20.38

tataḥ paraṃ tribhir muhūrtair anyataraḥ ṣaṇmāsaṃ vardhate hrasate ceti //

2.20.39

chāyāyām aṣṭapauruṣyām aṣṭādaśabhāgaś chedaḥ, ṣaṭpauruṣyāṃ caturdaśabhāgaḥ, tripauruṣyām aṣṭabhāgaḥ, dvipauruṣyāṃ ṣaḍbhāgaḥ, pauruṣyāṃ caturbhāgaḥ, aṣṭāṅgulāyāṃ trayo daśabhāgāḥ, caturaṅgulāyāṃ trayo 'ṣṭabhāgāḥ, acchāyo madhyāhna iti //

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.

2.20.40

parāvṛtte divase śeṣam evaṃ vidyāt //

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

2.20.41

āṣāḍhe māsi naṣṭacchāyo madhyāhno bhavati //

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.

2.20.42

ataḥ paraṃ śrāvaṇādīnāṃ ṣaṇmāsānāṃ dvyaṅgulottarā māghādīnāṃ dvyaṅgulāvarā chāyā iti //

2.20.43

pañcadaśāhorātrāḥ pakṣaḥ //

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

2.20.44

somāpyāyanaḥ śuklaḥ //

2.20.45

somāvacchedano bahulaḥ //

2.20.46

dvipakṣo māsaḥ //

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).

2.20.47

triṃśadahorātraḥ karmamāsaḥ //

2.20.48

sa-ardhaḥ sauraḥ //

2.20.49

ardhanyūnaś cāndramāsaḥ //

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

2.20.50

saptaviṃśatir nākṣatramāsaḥ //

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

2.20.51

dvātriṃśad balamāsaḥ //

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.

2.20.52

pañcatriṃśad aśvavāhāyāḥ //

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

2.20.53

catvāriṃśaddhastivāhāyāḥ //

Once in forty months there comes a malamása for hastiváhas.

2.20.54

dvau māsāv ṛtuḥ //

Two months make one ritu (season).

2.20.55

śrāvaṇaḥ prauṣṭhapadaś ca varṣāḥ //

Srávana and proshthapada make the rainy season (varshá).

2.20.56

āśvayujaḥ kārttikaś ca śarat //

Asvayuja and Kárthíka make the autumn (sarad).

2.20.57

mārgaśīrṣaḥ pauṣaś ca hemantaḥ //

Márgasírsha and Phausha make the winter (hemanta).

2.20.58

māghaḥ phālgunaś ca śiśiraḥ //

Mágha and Phalguna make the dewy season (sisira).

2.20.59

caitro vaiśākhaś ca vasantaḥ //

Chaitra and Vaisákha make the spring (vasanta).

2.20.60

jyeṣṭhāmūlīya āṣāḍhaś ca grīṣmaḥ //

Jyeshthámúlíya and Ashádha make the summer (grishma).

2.20.61

śiśirādy uttarāyaṇam //

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

2.20.62

varṣādi dakṣiṇāyanam //

2.20.63

dvyayanaḥ saṃvatsaraḥ //

2.20.64

pañcasaṃvatsaro yugam / iti //

2.20.65

divasasya haraty arkaḥ ṣaṣṭibhāgam ṛtau tataḥ /
karoty ekam ahaśchedaṃ tathaivaikaṃ ca candramāḥ //

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.

2.20.66

evam ardhatṛtīyānām abdānām adhimāsakam /
grīṣme janayataḥ pūrvaṃ pañcābdānte ca paścimam //E