Chapter 20 - Measurement of Space and Time

[Sanskrit text for this chapter is available]

The superintendent of lineral measure shall possess the knowledge of measuring space and time.

8 atoms (paramāṇava) are equal to 1 particle thrown off by the wheel of a chariot.
8 particles are equal to 1 likṣā.
8 likṣās are equal to the middle of a yūka (louse) or a yūka of medium size.
8 yūkas are equal to 1 yava (barley) of middle size.
8 yavas are equal to 1 aṅgula (three-fourths of an English inch). [Or the middlemost joint of the middle^[1] finger of a man of medium size may be taken to be equal to an aṅgula.]
4 aṅgulas are equal to 1 dhanurgraha.
8 aṅgulas are equal to 1 dhanurmuṣṭi
12 aṅgulas are equal to 1 vitasti, or 1 chāyāpauruṣa.^[2]
14 aṅgulas are equal to 1 śama, śala, pariraya, or pada.
2 vitastis are equal to 1 aratni or 1 prājāpatya 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 dhanurmuṣṭi are equal to = 1 kiṣku or 1 kaṃsa.
42 aṅgulas are equal to 1 kiṣku according to sawyers and black smiths, and used in measuring the grounds for the encampment of the army, for forts and palaces.
54 aṅgulas are equal to 1 hasta used in measuring timber forests.
84 aṅgulas are equal to 1 vyāma, used in measuring ropes and the depth of digging, in terms of a man’s height.
4 aratnis are equal to 1 daṇḍa, 1 dhanus, 1 nālikā and 1 pauruṣa.^[3]
108 aṅgulas are equal to 1 gārhapatya dhanus (i.e. a measure used by carpenters called gṛhapati). This measure is used in measuring roads and fort walls.

The same (108 aṅgulas) are equal to 1 pauruṣa, a measure used in building sacrificial altars.
6 kaṃsas or 192 aṅgulas are equal to 1 daṇḍa, used in measuring such lands as are gifted to Brāhmans.^[4]
10 daṇḍas^[5] are equal to 1 rajju.
2 rajjus are equal to 1 parideśa (square measure).
3 rajjus are equal to 1 nivartana (square measure).^[6]
The same (3 rajjus) plus 2 daṇḍas on one side only [=] are equal to 1 bahu (arm).
1000 dhanus^[7] are equal to 1 goruta (sound of a cow).
4 gorutas^[8] are equal to 1 yojana.^[9]

Thus are the lineal and square measures dealt with.

Then with regard to the measures of time:

(The divisions of time are) a truṭi, lava, nimeṣa, kāṣṭhā, kalā, nālikā, muhūrta, forenoon, afternoon, day, night, pakṣa, month, ṛtu (season), ayana (solstice), saṃvatsara (year), and yuga.

2 truṭis are equal to 1 lava,
2 lavas are equal to 1 nimeṣa.
5 nimeṣas are equal to 1 kāṣṭhā.
30 kaṣṭhās are equal to 1 kalā.
40 kalās are equal to 1 nālikā, or the times during which one āḍhaka of water passes out of a pot through an aperture of the same diameter as that of a wire of 4 aṅgulas in length and made of 4 māṣas of gold.
2 nālikās are equal to 1 muhūrta.
15 muhūrtas are equal to 1 day or 1 night.

Such a day and night happen in the months of Caitra and Āśvayuja. Then after the period of six months it increases or diminishes by three muhūrtas.

When the length of shadow is eight pauruṣas (96 aṅgulas), it is 1/15th part of the day.^[10]

When it is 6 pauruṣas (72 aṅgulas), it is 1/14th part of the day; when 4 pauruṣas, ⅛th part; when 2 pauruṣas, ⅙th part; when 1 pauruṣa, ¼th part; when it is 8 aṅgulas, 8/15th part (trayodaśabhāga); when 4 aṅgulas, ⅜th part; and when no shadow is cast, it is to be considered midday.

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

It is in the month of Āṣāḍha that no shadow is cast at midday. After Āṣāḍha, during the six months from Śrāvana upwards, the length of shadow successively increases by two aṅgulas, and during the next six months, from Māgha upwards, it successively decreases by two aṅgulas.

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

Two pakṣas make one month (māsa). Thirty days and nights together make one work-a-month (prakarmamāsa).^[11] 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 (candramāsa).

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

Once in thirty-two months there comes^[12] one malamāsa, 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 malamāsa for aśvavāhas.

Once in forty months there comes a malamāsa for hastivāhas.^[13]

Two months make one ṛtu (season).
Śrāvaṇa and Proṣṭhapada make the rainy season (varṣā).
Āśvayuja and Kārtika make the autumn (śarad).
Mārgaśīrṣa and Pauṣamake the winter (hemanta).
Māgha and Phālguṇa make the dewy season (śīśira).
Caitra and Vaiśākha make the spring (vasanta).
Jyeṣṭhāmūlīya and Āṣāḍha make the summer (grīṣma).

Seasons from śiśira [śīśira?] and upwards are the summer solstice (uttarāyaṇa), and (those) from varṣā and upwards are the winter solstice (dakṣiṇāyana). Two solstices (ayanas) make one year (saṃvatsara). 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 (ṛtau). Likewise the moon (falls behind by 1/65th of a whole day every day and falls behind one day in every two months). Thus in the middle of every third year,^[14] they (the sun and the moon) make one adhimāsa, additional month, first in the summer season and second at the end of five years.^[15]

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

Footnotes and references:

[1]:

For an aṅgula of 6 yavas, see J.R.A S., 1913, pp. 153 to 155; or the Saṅgītaratnākara of Saraṅgadeva, Chap. IV, verses 526-27.

[2]:

The length of the shadow cast by a Saṅku or gnomon, twelve aṅgulas high. See below.

[3]:

Catasrassaṃjñā, four designations are meant here.—Com.

Chāyāpauruṣa is to be distinguished from pauruṣa: the latter is used to measure the standard height of a man as four aratnis or 96 aṅgulas = 96 x ¾ X 1/12 = 6 English feet, while the former word is used to designate the shadow of 12 aṅgulas cast by a gnomon of twelve aṅgulas in height. In other words, one pauruṣa is equal to 6 feet; and one chāyāpauruṣa is the shadow of 12 aṅgulas in length and cast by a gnomon of 12 añgulas in height. The word, pauruṣa, is also used to mean 108 aṅgulas when used in measuring the height of a sacrificial altar. Vide below.—Trans.

[4]:

brahmadeyātithyamānam, brahmadeyānāmṛtvigādideyakṣetrānāmātithyānām ca satrādidharmanimittadharmādhikārikṣetrānām mānam

—“A measure used in measuring the lands gifted to priests and others, also such lands as are given to the officials entrusted with the management of an almshouse and other ca rities”.—Com.

[5]:

A daṇḍa of 4 hastas.—Com.

[6]:

This is used in measuring squares.—Com.

[7]:

Dvidhanussahasram, 2,000 dhanus (so reads the commentator) are equal to one goruta.

[8]:

Gorutam krośam, a goruta means a krośa.—Com.

[9]:

Taking the ordinary dhanus of 96 aṅgulas, one goruta or krośa will be equal to 96 x 1,000 x 3 / 12 x 3 x 4 = 2,000 yards, and one yojana to 2,000 X 4 yards = 4.54 British miles, or say, 4½ for general purposes. See J.R.A.S., 1912, pp. 234, 237.

[10]:

1/18th part of the day shall be considered as having been elapsed and 17/[??]ths remaining.—Com.

[11]:

“sāvanaḥ triṃśadahorātraḥ”.—Sāvana month consists of 30 days and nights.—Com.

[12]:

Dvātriṃśanmalamāsaḥ, thirty-two a malamāsa. This sentence is ambiguous: it may mean 32 days and nights make a malamāsa or once in thirty-two months, as is customary among the Hindu astronomers, there comes a malamāsa. The commentator has omitted to explain this passage. Dr. J. F. Fleet writes: “I retain my opinion that malamāsa is a corrupt reading for mallamāsa, and that the passage means that wrestlers were hired by a month of 32 days, horse-carriages by a month of 35 days, and elephant-carriages by a month of 40 days.”

[13]:

“aśvavāhāyāḥ (aśvavāhana) āśvayavasaghāsakādīnām catvāriṃsadahorātraḥ hastivāhāyāma (vāhana) hastipakādīnām vetanamāsaḥ”

—“aśvavāha means those who procure meadow grass for horses; forty days and nights make up for elephant-drivers and others a wage-earning month”.—Com.

By taking forty in the sense of a month of forty days and nights, the commentator seems to take the words thirty-two and thirty-five in the sense of months of thirty-two days and nights and of thirty-five days and nights also. But I think it better to take the above passages as referring to the intercalation of an additional month once in thirty-two months or once in thirty-five months, or once in forty months. For the custom of adding an intercalary month once in 37 or 38 months, see my Vedic Calendar, published in the Indian Antiquary, 1912.

[14]:

I.e. once in thirty months.—Com.

[15]:

In śloka-metre.