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History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38: Concepts and Measures of Length, Weight and Time

History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38

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English

Contents

Concepts and Measures of Length, Weight and Time

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There is no doubt that units of length, weight and time are basic parameters constructed by man. These parameters are considered as sources of all scientific thinking and lie at the root of natural knowledge. Their formulation and standardisation are based on observations and experiences made at different times and are involved without disturbing uniformity in nature or in measurements. The measure of a thing becomes standardised as a unit by general consent by its being compared with another of the same species. The measures of units of these parameters vary from one culture to another. The strength or the uniqueness is discernible when there is acceptance and influence in other cultures.

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In India the units (*māna* or *parimāna*) are of two types, *Laukika* (worldly) and *Lokattara* (para-worldly). The *Laukika* deals with the process of measurement. The *Lokattara* type has theoretical connections with *Laukika* type and deals with length, and weight from smallest unit (atom) to last of the world space, and time from unit to infinite time. The Jain canons give another group, *bhāvamāna* (idea) under *Lokattara* type which deals with knowledge, perceptions, view points and numbers. Original sources have been collected and analysis of both these facets have been made in this paper, ofcourse in a limited manner, in order to find the religio-philosophical and social linkages from a variety of applications.

Length

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The linear units originated mostly from the body measures and were used for the measures of distance or area (*kṣetra* or *varga*), or volume of solid figures (*ghana*). The idea of *varga-* and *ghana-* *māna* are sometimes mentioned or understood from the contexts. The linear units were also connected with the circumferences of the earth from which modern equivalents of different units have been computed.

Primary Sources:

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The Indus Valley has recorded four measuring rods with markings viz. one broken scale made of shell (M.614) from Mohenjo-daro, one broken bronze rod from Harappa, one graduated scale from Kalibangan, and an ivory rod from Lothal. The broken Mohenjo-daro scale shows nine consecutive uniform parallel lines having a circle on one line and a deep dot on sixth line. The distance of these five intervals is equal to 1.32 inches. Mackay (1931) believed this distance as a part of the whole which is ten times bigger i.e. 13.2 inches giving a decimal connection and having linkages with that of the ancient Egypt and Elam. Berriman (1953) described the distance between the circle and the dot as Indus scale, since 25 Indus inches are exactly equal to 33 inches (25 × 1.32 = 33).

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The *Ṛgveda* and other Vedas used the words, *puruṣa*, *aratni*, *pada*, *aṅgula*, *parva*, *muṣṭi*, etc. for linear measures (Macdonell and Keith). The *Puruṣa* is defined in the Vedic literature as the measure of a man with outstretched arms. The *Śulba Sūtras* of Baudhāyana (BSl.1.3) and Āpastamba (ASl.6.5,15.4) used *rajju* or rope with marks and knots and give the units as follows:

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One *puruṣa* (measure of man with out-stretched arms) = one *vyāma* = 5 *aratnis* = 120 *aṅgulas* (or *aṅg*).

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One *vyāyāma* (measure of stretched arms) = 4 *aratnis* = 96 *aṅg*.

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One *śamyā* = one *bāhu* = 36 *aṅg*.

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One *jānu* = 32 *aṅg*;

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One *aratni* = 2 *prādeśas* = 24 *aṅg*.

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One *prādeśa* = one *prakrama* = one *pada* = 12 *aṅg*.

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One big *pada* = 15 *aṅg*; one small *pada* = 10 *aṅg*.

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One *aṅgula* = 12 *aṇus* = 34 *tilas*

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These are body measures. There are three other measures, *akṣa* (axle), *iṣā* (pole) and *yuga* (yoke), often referred to by the *Ṛgveda* and other Vedas in connection to Chariot (*ratha*) measures.

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Baudhāyana (BSl. 1-3) gives that one *akṣa* = 104 *aṅg*; one *iṣā* = 188 *aṅg*; one *yuga* = 86 *aṅg*. These units have also been used in the Kātyāyana and Māṇava Śulbasūtras.

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Buddhist and Jain sources gave emphasis to both practical and theoretical aspects. The *Lalitavistāra* (Datta and Singh, 1, p.187) has mentioned as follows:

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One *yojana* = 4 *krośa*; 1 *krośa* = 1000 *dhaṇus*.

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One *dhaṇu* = 4 *hastas*; 1 *hasta* = 2 *vitastis*

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One *vitasti* = 12 *aṅguli parvas*.

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So 1 *yojana* = 4000 *dhaṇus*;

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1 *dhaṇu* = 96 *aṅg*. and 1 *hasta* = 24 *aṅg*.

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As regards smaller units from *aṅgula*, there are 10 units, each is one-seventh of the former. These are *aṅgula*, *yava*, *sarṣapa*, *likṣā-raja*, *go-raja*, *eḍaka-raja*, *śaśa-raja*, *vātāyana- raja*, *truṭi*, *reṇu* and *paramāṇu*. Obviously 1 *paramāṇu* = 7-10 *aṅgula*.

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The *Kauṭilya Arthaśāstra* (Shyamasastri (ed) 1956, p.117) gives as follows:

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One *yojana* = 4 *goruta* (distance to reach the sound of a cow), 1 goruta = 1000 daṇḍas (or dhanuṣ), since dhanuṣ and daṇḍas are synonymous. 1 daṇḍa = 4 aratnis, 1 aratni = 2 vitasti, 1 vitasti = 12 aṅgulas So 1 yojana = 4000 daṇḍas; 1 daṇḍa = 96 aṅg. and 1 aratni = 24 aṅg

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Daṇḍa of 96 aṅg is equal to the height of the normal man. It was used also for measuring areas. Daṇḍa and puruṣa become synonymous during Kauṭilya’s time (Agrawala, 1953, p.256).

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Kauṭilya also gives four smaller units of aṅgula. These are yuka, likṣā, rathadhuli and paramāṇu, the latter is lesser by eight part than the former.

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Hence one aṅgula = 8⁴ paramāṇu, and 1 paramāṇu = 8⁻⁴ aṅg.

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The Bṛhat Saṃhitā (ch. 58, vs.1-2) of Varāhamihira (505 A.D.) gives as under: One yojana = 4 krośas, 1 krośa = 25 nalvas; 1 nalva = 40 dhanuṣ; 1 dhanu = 4 hastas; 1 hasta = 24 aṅg. So 1 yojana = 4000 dhanuṣ; 1 dhanu = 96 aṅg.

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The smaller units from aṅgula as given by Varāhamihira are yava, yuka, likṣā, vālāgra, ratha raja, paramāṇu, each 8th part smaller than the former.

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Hence 1 aṅg. = 8⁶ paramāṇus or 1 paramāṇu = 8⁻⁶ aṅg.

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Varāhamihira has also mentioned (ch. 68, vs.105). “The height of a tall, normal and short man is 108 aṅgulas, 96 aṅgulas and 84 aṅgulas by his own measure”. The height of the normal man during Varāhamihira’s time was 96 aṅgulas, and height of the normal man with out-stretched arms will obviously become equal to height of the man and one aratni, i.e. 96 aṅgulas + 24 aṅgulas = 120 aṅgulas, which corroborates with Vedic measure. He further pointed out (Bṛhatsaṃhitā, Shamasastry, 1910, p.109), “An army of the lowest standard can march one yojana, that of middle standard one and half yojana, and that of the best standard two yojanas”. So middle standard army can march = 1¹/₂ yojanas = 1¹/₂ × 4000 daṇḍas (or dhanu) = 6000 daṇḍas.

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The Jain work, Aṇuogadvāra Sūtra (Sūtra 131) gives as follows: One yojana = 4 gavyayuties; 1 gavyayuta = 2000 dhanuṣyas; 1 dhanuṣya = 2 kukṣis 1 kukṣi = 2 aratnis; 1 aratni = 2 vitastis, 1 vitasti = 2 padas; 1 pada = 6 aṅg. This shows 1 yojana = 8000 dhanuṣyas 1 dhanuṣya = 96 aṅg. and 1 aratni = 24 aṅg.

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Āryabhaṭa 1 (499 A.D.) used the word nṛ as synonymous to daṇḍa or dhanuṣ which is equal to the height of the average man, i.e. 1 daṇḍa = 1 nṛ = 4 hastas = 96 aṅg, since 1 hasta = 24 aṅgs. But he has used one yojana = 8000 nṛ.

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The Brāhmasphuṭasiddhānta of Brahmagupta (i.37), Sūryasiddhānta, Siddhāntaśekhara of Śrīpati (ii 94) and Siddhāntaśiromaṇi of Bhāskara II (SSI i.43) have the value of the circumference of the earth as 5000 yojanas. All astronomers from Āryabhaṭa I to Bhāskara II (c 1150 A.D.) have used 1 yojana = 8000 *daṇḍas* (*Āryabhaṭīya*, iii.7; *Gaṇitasāra Saṅgraha* of Mahāvīra, i.29-31 1/2, *Vaṭeśvarasiddhānta*, i.7-13).

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Mahāvīra has used smaller units of *aṅgula* as 1 *aṅg* = 8⁸ *paramāṇu*, *aṇu* is added between *paramāṇu* and *trasareṇu*.

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The measure of *aratni* i.e. 1 *aratni* = 24 *aṅg* has been kept as same through out.

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Thus we find the units of *yojana* i.e. 1 *yojana* = 4000 *daṇḍas* from earliest time to the time of Varāhamihira, and 1 *yojana* = 8000 *daṇḍas* were introduced thereafter, the reason for switching over to this bigger value is not clear. Thus double value of *yojanas* or *krośas* are still prevelent in Bengal, Bihar and other States.

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Hiuen Tsang (c.650 A.D) in his historical account on India, has recorded that there were two *krośas* in India, an old one of 1000 *daṇḍas* and new one of 2000 *daṇḍas* reckoning in his time. Since 1 *yojana* = 4 *krośas*. This statement of Hiuen Tsang also corroborates that 1 *yojana* = 4000 *daṇḍas* (old measure) and 8000 *daṇḍas* (new measure) and the historical situation prevalent in his time. Āl- Bīrūni (c.1030 A.O.) studied astronomical data of the Indians and related *yojana* with *farsakh* and yard without any definition (Mainkar, 1975). Vogt (1903), Fleet (1906, 1912), Shamasastry (1913) tried to establish correlation with chinese *li* and units of other countries which have not also of much correlation.

Yojana, Daṇḍa, Aratni and Aṅgula (Values in inches):

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There are many conjectures about the modern equivalent value of the units of *Yojana*, *Daṇḍa*, *Aratni* and *Aṅgula*. These may be summarised as follows:

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Dongre (1994) on the basis of Ṛgvedic Purusa Sukta¹ believes that one *Puruṣa* sphere, and the Earth’s circumference, thus: *Puruṣa* sphere = 1000 × 2000 × 2000 *aṅg*. = 4 × 10⁹ *aṅg*.

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Earth’s circumference, as per this *sukta* remains one *aṅgula* below that of the *Puruṣa* sphere of radius of 1 *aratni*. Hence Earth’s circumference = 24/25 × 4×10⁹ = 96×4×10⁷ *aṅg* = 4×10⁷ *daṇḍas*. The astronomical texts give the circumference of the Earth mostly as 5000 *yojanas*

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= 5000 × 8000 *daṇḍas*

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= 4×10⁷ *daṇḍas*.

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The lesser value of 4000 *daṇḍas* for *yojanas* was possibly not found compatible by the astronomers of 4-5th century. Of course there may be other reasons.

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The present value of the Equatorial circumference of the Earth = 24900 miles (Encyclopadia) = 4×10⁷ metres.

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From this Dongre concludes that 1 *daṇḍa* = 1 metre

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This gives 1 *aṅgula* = 100/96 = 1.04167 cm.

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We find use of *aṅgula*, *parva* and *muṣṭi aṅgula* in Vedic and Post- vedic India.

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Dongre believes that *muṣṭi* (= 4 *aṅg* = 4 × 100/96 = 4.16cm) and *parva* (= 3 *aṅg* = 3 × 100/96 = 3.125 cm) were of great significance.

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For, cube of one muṣṭi aṅg and parva aṅg changed into sphere, the radius becomes: (1 muṣṭi aṅg)³ = (4.16 cms)³ = 4/3π r₁³.

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Thus r₁ = 2.58 cms. = 1.016 inches

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Again, (1 parva aṅg)³ = (3.125 cm)³ = 4/3π r₂³, r₂ = 0.76 inches.

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The muṣṭi aṅg unit was much bigger and has a connection with Indus scale for 4/3π (1.016 inches)³ = (1.32 inches)³. Since value of the Indus scale = 1.32 inches.

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The parva aṅg unit is possibly used from Vedic period onwards. More work will be of interest to know whether the parva aṅg and muṣṭi aṅg units are responsibile for two values of yojana or krośa in later period. However, parva aṅg is possibly followed more or less uniformly in linear measure as follows:-

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1 hasta = 24 aṅg = 24 × 0.76 inches

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= 18.24 inches = 18 inches (approximately),

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1 aṅgula = 0.76 inches

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= 3/4 inches (approximately)

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However Ayurvedic Pharmacopoeia Committee (Ayurvedic Formulary of India, Pt.1) recommended the same parva values for hasta and aṅgula as given above though the basis for selecting the values are not made clear.

Weight

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The units are usually based on natural elements or phenomenon. What about weight? These are mostly represented by the weight of an object like, a seed (māṣa or guñja) or a piece of metal. If the objects are lost, the very basis of a system is lost. The fact was not possibly unknown to the ancient Indians. There is enough hint in the Arthaśāstra that the weight of māṣa (Phraseolus Radiatus) was standardized with volume of one aṅgula of water. Whether this māṣa of ancient India has any connection with mass of CGS system is a matter of great interest and still to be investigated.

Primary sources

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The archaeological sites of Harappa, Mohenjodaro, Chanhudaro and Lothal bear testimony that weighing balances were known. It consisted of a metallic beam (copper or bronze) with two suspending pans from its two ends (Mackey, 1938, pp.976-77; Mackey, 1976, pp.178, 293; Vat, 1940, pt.CXVII and CXVIII; Marshall 1931). Berriman (1953, pp.33-35) has analysed 288 specimens of small cubes available from Mohenjodaro and Harappa and drawn a frequency chart as parts of 1 unicia = 27.2 gms. These weights are 1.7, 3.4, 6.8, 13.6, 27.2, 54.4, 136 (gms) etc. The beams of weighing balance were uniform, sometimes thicker in the middle and tapering at the end. The beam had no fulcrum hole in the centre. A string was perhaps tied at the middle for holding it during weighing. The pans had two or three holes for suspension. Pans with two holes were possibly used for bulky materials which one could hold by touching it, whereas pans with three holes were used for weighing grains and commodities. The Mohenjodaro had two types, one similar to Harappan types and the other is of smaller type (scale pans of copper or bronze). The Chanhudaro and Lothal sites have also small pan and beam types. These smaller types were perhaps used for weighing gold dust and other precious metals, for these could weigh micro-weights (Sharma and Bhardwaj, 1989).

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The Ancient Indian names for balance was *tulā*. The *Vājasaneyī Saṃhitā* (30.17), *Śatapatha Brāhmaṇa* (2.2.7.33), *Vasiṣṭha Dharmasūtra* (19.18.23) and *Aṣṭādhyāyī* of Pāṇini (4.4.51) bear testimony that equal arm balance of different sizes were used (Agrawal, 1953, p.251). The Vedic literature have used measuring units viz. *kṛṣṇala, aṇḍaka, māṣa, śana, suvarṇa* (TS. 2.3.2.1; Mait S. 2.2.2; Kat. Sr. 11.4; *T Br.* 1.3.6.7 etc.). *Māṣa* is a standard kind of seed (*Phraseolus Radiatus*). The weight can vary in different atmospheric conditions. Then how is it that such seed have been used. Dongre believes² that it is possibly standardized to be equal to volume one *angula* of water i.e. 1 *māṣa* = (1.04167 cm)³ = 1.13 gms for it fits very well with other measures. The vedic units are as follows:

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1 *māṣa* = 4 *aṇḍakas* = 5 *kṛṣṇalas* = 1.13 gms ;

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4 *māṣas* = 1 *śana* = 4.52 gms; 4 *śanas* = 1 *suvarṇa* or

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1 *karṣa* = 18.08 gms;

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4 *suvarṇas* = 1 *niṣka* = 72.32 gms.

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Obviously one *aṇḍaka* = 1/4 *māṣa* = 0.28 gms; one *kṛṣṇala* =

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1/5 *māṣa* = 0.226 gms.

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The *kṛṣṇala* (*Guñja, Ratikā*), the black-and-red berry of the shrub (*Abrus Precatorius*) was used as a natural measure (Seal, pp.80- 85).

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The *Arthaśāstra* of Kauṭilya gives a detail description as to the varieties of balances, measures to check the inaccuracy of balances, methods of state control of weights under the superintendent of weights and measures (*Paṇtādhyakṣa*). The coins were also struck in gold, silver and copper in accurate weights besides commercial activities of ornaments and commodities. Strict steps were taken to avoid debasement of currency metals. The dust currency of gold and silver (*cūrṇi* or *cūrṇa*) were also in vouge. The accurate weights were considered important for all these activities.

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Kauṭilya’s *Arthaśāstra* gives a series of weight measures (Shamasastry, Eng. tr. 1956, pp.113-132) as follows:

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*Gold weight:* 5 *guñjās* (*Abrus Precatorius*) = 1 *suvarṇa māṣa* = 1.13 gms;

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16 *suvarṇa māṣas* = 1 *suvarṇa pala* or *karṣa* = 18.08 gms.

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*Suvarṇa* series as given by *Arthaśāstra* are:

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*Ardhamāṣa* (=0.56 gms), 1 *māṣa* (=1.13 gms), 2 *māṣas* (=2.26 gms),

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4 *māṣas* (=4.52 gms), 8 *māṣas* (=9.04 gms), 16 *māṣas* (=1 *suvarṇa pala* = 1 *karṣa* = 1 *bisto* = 1 *akṣa*, = 18.08 gms), 2 *suvarṇa palas* (= 36.16 gms) and so on.

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Kauṭilya states, “The increase in density (*gaurava vṛddhi*) is increase in matter or price (*satva*) for all metals of equal volumes”³. The densities of gold, silver, copper and iron are 19.3, 10.5, 8.96 and 7.86 respectively, obviously for equal volumes of these metals, silver or copper is 2 times of gold weight and iron is 2.5 times or 3 times of gold weight, i.e.

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1 silver pala = 1 copper pala = 2 suvarṇa pala = 2 × 16 = 32 māṣas = 32 × 1.13 gms = 36.16 gms. = 36.00 gms (approx.)

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1 Iron pala = 2.5 suvarṇa pala = 2.5 × 16 māṣa = 40 māṣas = 40 × 1.13 gms = 4520 gms or = 3 suvarṇa pala = 3 × 1.6 māṣas = 48 māṣas = 48 × 1.13 gms = 54.24 gms

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Silver units of Kauṭilya are:

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88 mastered seeds = 1 silver māṣa; 16 silver māṣas or 20 śaiba seeds = 1 dhāraṇa, 10 dhāraṇas = 1 silver pala. 1 silver pala = 36.00 gms, 1 dhāraṇa = 3.600 gms. 1 silver māṣa = 0.225 gms, 1 śaiba seed = 0.18 gms,

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Silver Series: 1 silver māṣa (= 0.225 gms), 2 silver māṣa (= 0.45 gms), 4 silver māṣa (= 0.90 gms), 16 silver māṣas (= 3.60 gms = 1 dhāraṇa), 2 dhāraṇa (7.2 gms), 10 dhāraṇa (36.00 = a silver pala) and so on.

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Similarly, Iron pala = 40 māṣas = 45.20 gms, or = 48 māṣas = 54.24 gms.

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Series of Iron weights (lauhapalas): 1/32, 1/16, 1/8, 1/4, 1/3, 1/2, 1, 2, 3...100 lauhapalas.

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This results in: 1st series: 1.41 gms, 2.82 gms, 5.64 gms, 11.28 gms, 15.7 gms. 22.60 gms, 45.20 gms, 90.40 gms and so on (when 1 pala = 40 māṣas).

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2nd series: 1.69 gms, 3.39 gms, 7.72 gms, 15.44 gms, 18.04 gms, 27.12 gms, 54.24 gms, 108.48 gms. and so on. (when 1 pala = 48 māṣas).

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The second series is comparable with weights of Mohenjo-daro given by Berriman.

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There are bhājanī or division measures. The vyāvahāriki Bhājanī and Antaḥpura Bhājanī systems of Arthaśāstra bear resemblances to Greek, Persian and Roman systems when one masa = 18 Troy grain.

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The Kātyāyanī or Vimśatikā system used: 25 kṛṣṇala = 1 pada = 2.825 gms, 4 padas = 1 śatamāna or 1 paṇitala = 11.30 gms. This gives śatamāna = 100 krsnalas.

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Series for weights of medicine:

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The Caraka Saṃhitā (Kalpasthāna, 12.87-97) gives measures which are used for preparation of medicine. These are:

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6 *dhaṁsis* = 1 *mārici* = .00074 gms; 6 *māricis* = 1 *sarṣapa* = .00444 gms., 8 *sarṣapa* = 1 *taṇḍula* = .035 gms. 2 *taṇḍulas* = 1 *dhānyamāṣa* = .07 gms, 4 *dhānyamāṣas* = 1 *aṇḍikā* = 0.28 gms., 4 *aṇḍikās* = 1 *māṣa* = 1.13 gms; 3 *māṣas* = 1 *śāṇa* = 3.39 gms; 2 *śānas* = 1 *daṅksana* = 6.78 gms. 2 *daṅkṣaṇas* = 1 *karṣa* = 13.56 gms. So 1 *śāṇa* = 1/4 *karṣa*. The *Suśruta saṁhitā* has used the similar units.

v1.c38.s2.t1.33

The word *bhāra* is referred to in Pāṇini Sūtra (VI. 2.38) in connection with *mahābhāra*. It is a *samjñā* word with a definite meaning. *Amarakośa* (II. 9.87) gives 1 *bhāra* = 8000 *karṣas* = 145 kg. Kauṭilya (II.19) records 1 *bhāra* = 20 *tūlās* = 20 × 100 *palas* = 2000 *palas*, 1 *tūlā* = 7.2 kg. *Bhāra* appears to be headload and *Mahābhāra* may be a cart load.

v1.c38.s2.t1.34

Māhāvira (850 A.D.) in his *Gaṇitasāra Saṁgraha* (i. 39-45) gives as under:

v1.c38.s2.t1.35

*Gold weight :*

v1.c38.s2.t1.36

4 *andakas* = 1 *guñja* = 0.226 gms 5 *guñjas*= 1 *paṇa* = 1.13 gms. 8 *paṇas* = 1 (gold) *dhāraṇa* = 9.04 gms. 2 *dhāraṇas* = 1 *karṣa* or *suvarṇa pala* = 18.08 gms

v1.c38.s2.t1.37

*Silver weight :*

v1.c38.s2.t1.38

2 *dhānyas* = 1 *guñja* = 0.113 gms. 2 *guñjas* = 1 *māṣa* = 0.228 gms 16 *māṣas* = 1 (silver) *dhāraṇa* = 3.64 gms. 2 1/4 *dhāraṇas* = 1 *karṣapurāṇa* = 1 silver *māṣa* = 8.04 gms. 4 *karṣa pūrāṇa* = 1 silver *pala* = 32.82 gms. This is less than weight of Kauṭilya’s time.

v1.c38.s2.t1.39

*Iron weights are given as:*

v1.c38.s2.t1.40

*Pāda, kalā, yava, amśa, bhāga, draksuna, dinar* and *sater* which are doubtful as to their correctness. It also gives 1 *bhāra* = 10 *tūlās*, 1 *tula* = 200 *palas*, thereby, *bhāra* = 2000 *palas*, with difference.

v1.c38.s2.t1.41

Śrīdhara’s *Pāṭīgaṇita* (vs. iv) records gold measures, the same as that of Kauṭilya’s *Arthaśāstra* i.e.

v1.c38.s2.t1.42

5 *guñjas* (Alrus seeds) = 1 *suvarṇa māṣa* 16 suvarṇa māṣas = 1 karṣa (of gold).

v1.c38.s2.t1.43

Bhāskara II records Turkish and units introduced by Badshah Alamgir on weight measures as follows:

v1.c38.s2.t1.44

Turkish units : 96 yava = 1 gaḍyanaka

v1.c38.s2.t1.45

72 tanks` = 1 ser

v1.c38.s2.t1.46

40 sers = 1 man (maund)

v1.c38.s2.t1.47

Badshāh Ālamgīr units : 192 dhātakas or tolās = 1 ser

v1.c38.s2.t1.48

5 ser = 1 dhātikā, 8 dhātikās = 1 man (maund)

v1.c38.s2.t1.49

This shows that new units of weight measures have started being introduced during the time of Bhāskara II (1150 AD)and Bādshah Ālamgīr.

Time

v1.c38.s3.1

The ancients realized on the basis of a clearly agreed experience that there is a unique serial order of events (i.e. one dimensional). This was the foundation of a trustworthy system for the dating of events by the use of calendars, dynasties the primitive sundial and water clock. This notion of time is somewhat different from what it is to theoretical Physics or it is to thermodynamics or to evolutionary sciences such as biology. The early notion of time is mostly connected with the natural phenomenon of day and night. The concept of past, present and future has added an additional difficulty of another dimension into it. I am always in my ‘present’ and can experience no other parts of time which is ‘past’ or ‘future’. Only the ‘present’ is real and has the character of a knife-edge which separates non-existant past from a non-existant future. We will first compile sources on the natural phenomenon of time and then analyse its attribute and impact from different perspectives.

v1.c38.s3.2

Primary Sources : The Ṛgveda (2.28.8) mentions three ordinary divisions of time, namely, present, past and future. Time is identified with the Sun and the Viṣṇu and is also divided into divisions like muhūrtas, days, half months, months, seasons, solstices, year, yuga, kalpa, mahākalpa and so on. The whole forms a circle which like a wheel is constantly moving. The word muhūrta appears in the Ṛgveda. The muhūrta as part of a day first appears in the Brāhmaṇas. The Taittirīya Brāhmaṇa (3.10.1. 1-3, 10..9.7) gives the name of each muhūrta. The Śatapatha Brāhmaṇa (12.3.2.5) gives further subdivision of year into muhūrtas as follows: 1 year = 10800 muhūrtas;

v1.c38.s3.3

1 muhūrta = 15 kṣipras;1 kṣipra = 15 etarhis;1 etarhi = 15 idānis 1 idānis = 15 prāṇas (breathings) etc.

v1.c38.s3.4

The Vedāṅga Jyotiṣa gives the smaller units of day the muhūrta, vaidika, kāla, ādaka, kuḍava and pala. The time of these units was measured by water clocks. The units are: 1 day = 30 muhūrtas, 1 muhūrta = 2 nāḍis, 1 nāḍikā = 10 kalās.

v1.c38.s3.5

Sphujidhvaja in his Yavanajātaka (3rd century A.D.) has taken 1 nāḍikā = 10 kalās to avoid fraction or followed Suśruta (Shukla, 1989, p.213).

v1.c38.s3.6

The Jainas and Buddhists used large numbers for measurments of space and time. The Lalitavistāra usèd as big as 1053. The Jaina used the number 10140 (asaṃkhya), measurement of time as pūrvī where one pūrvī = 756 x 10¹¹ years and one śirṣa-prahelikā = (84 x 10⁵)²⁸ pūrvīs. The introductions of such large numbers led to the conception of infinity which is not very precise from practical point of view.

v1.c38.s3.7

The Atharva Jyotiṣa gives the subdivision of day i.e. ahorātra (day and night together) as muhūrta, truṭi, kalā, lava, former being 30 times of the latter.

v1.c38.s3.8

Kauṭilya gives (Shamasastry, 1956, p.118-119), 1 day (day & night) = 30 muhūrtas, 1 muhūrta = 2 nālikā, 1 nālikā = 40 kalās, 1 kalā = 30 kāṣṭhās, 1 kāṣṭhā = 5 nimeṣa, 1 nimeṣa = 2 lavas and 1 lava = 2 truṭis. From days and nights, Kauṭilya goes upto month, ṛtu (season), ayana (solstices), samvatsara (year), and yuga. Udayana’s Kiraṇāvalī and Śrīdhara’s Nyayakandalī give: 1 day (24 hours) = 30 muhūrtas, 1 muhūrta = 30 kāṣṭhās, 1 kāṣṭhā = 18 nimeṣas, 1 nimeṣa = 2 lavas, 1 lava = 2 kṣanas. This makes 1 kṣana = 2/45 seconds, if 1 day is taken as 24 hours, which was possibly determined from diurnal rotation of the earth.

v1.c38.s3.9

Āryabhaṭa I (b.496 A.D.) gives:

v1.c38.s3.10

1 year = 12 months, 1 month = 30 days, 1 day = 60 nāḍis or nāḍikās), 1 nāḍi = 60 viṇāḍis, 1 sidereal viṇāḍi = 60 long syllables or 6 prāṇas (respirations) (Āryabhaṭīya Tr. Shukla, 1976, p.86). The Sūryasiddhānta (i.11) gives the same table.

v1.c38.s3.11

In the Smṛtis as also in the Sūryasiddhānta, the time division are 1 kalpa = 14 manus, 1 manu = 71 yugas and 1 yuga = 4320000 years. A small period preceding and following each Manu called twilight has also been conceived to make one kalpa equivalent to 1000 yugas. A portion is earmarked for the creation of the world, so that world-order starts, plants occupy the same place. Āryabhaṭa I (p. 496 A.D.) does not believe in the theory of creation and annihilation of the world. For him, the time is a continous process, without begining and end (anādi and ananta). The begining of yuga and kalpa, according to him, having nothing to do with terrestrial occurance, they are accordingly based on astronomical phenomena. Āryabhaṭa I rejected the highly artificial time division with the following : 1 kalpa = 14 manus; 1 manu = 72 yugas; 1 yuga = 4320000 years. One yuga was again divided into 4 small yugas viz. kṛta (17,28000 years). Tretā (12,96000 years) Dvāpara (8,64000 years), and Kali (4,32000 years). So the Sūryasiddhānta and Āryabhata I believe that the current Kaliyuga began on Friday 18, 3102 B.C.

v1.c38.s3.12

The Gaṇitasārasamgraha (i. 32-35) of Mahāvīra gives a time division of year as ayana, ṛtu, māsa, pakṣa, dina, the same value as others. Further down he gives:

v1.c38.s3.13

1 dina = 30 muhūrtas; 1 muhūrta = 2 ghaṭis; 1 ghaṭi = 38 lavas; 1 lava = 7 stokas, 1 stoka = 7 ucchvāsas; 1 ucchvāsa = saṅkhyāta avali; 1 avali = asaṃkhyāta samaya.

v1.c38.s3.14

The Vaṭesvarasiddhānta (i. 8-9) gives same for kalpa, yuga, year, month and day. From day to truṭi, the months are as follows: 1 day = 60 ghaṭikās (24 hours); 1 ghaṭikā = 60 palas (24 minutes); 1 sidered pala (vinadi, vighaṭikā or casaka) = 6 asus, 1 asu (respiration) = 2¹/₂ kāṣṭhas = 4 seconds; 1 kāṣṭhā = 4 long syllabus; 1 long syllabus = 4¹/₂ nimeṣas (twinkling of an eye);

v1.c38.s3.15

1 nimeṣa = 100 lavas; 1 lava = 100 truṭis. Similar divisions are also found in the Brāhmasphuṭasiddhānta (i. 5-6) of Brahmagupta, Siddhāntaśekhara of Śrīpati (i.11-15; i.3, see also Makkibhaṭṭa’s commentary).

v1.c38.s3.16

Bhāskara II (1150 A.D.) notes, 1 day (24 hours) = 30 kṣaṇas; 1 kṣaṇa = 2 ghaṭikās (48 minutes); 1 ghaṭikā = 30 kalās (24 minutes); 1 kalā = 30 kāṣṭhās (48 seconds); 1 kāṣṭhā = 18 nimeṣas, 1 nimesa = 30 tatparas, 1 tatpara = 100 truṭis, 1 truṭi (lotus pricking time) = 1/33,750 of a second. Bhāskara II while computing the instantaneous motion of planets compared its successive positions and considered its motion as constant during the interval which cannot be greater than a truṭi of time, though it may be infinitely less.

Concluding Remarks

v1.c38.s4.1

The concepts of length, weight and time, in their origin and ramifications have been an integral part of the Indian religio- philosophical and social system. These concepts attempted to explain the limited material world on one hand and tried to speculate their relationship with unlimited world on the other. For linear measure they have developed a length - measured from aṅgula to yojana for practical purposes, but conceived as small a unit as aṇu and gave the diameter of earth as big as 10⁵ yojanas, associating them with number and extending it from beginning to infinity (ādi and ananta), which is one dimensional. Area and volume were obtained by length and breadth; length, breadth and height respectively by the same scale. Whether the Indian had clear picture of dimension upto 12th century is not known. As regards weight, the words, gaurava (density), gurūtva (gravity or heaviness), bhāra (weight) were used. According to Nyāya Vaiśesika, gravity is one of the attribute of matter and regarded it not as a force but as a causal factor associated with act of falling or rising. There was possibly no correlation with gravity and mass. But to equate māṣa with the volumes of one aṅgula of water is indeed a unique step. The word bhāra for weight was used by later scholars in the same sense as before. The number is also an attribute of matter and there are expressions from insignificant weight to a very large weight. The knowledge, view points, perceptions and numbers give it also some significance but not over practical uses. Time is divided into day and its sub-divisions months, seasons, solstices, year, yuga, kalpa and mahākalpa.

v1.c38.s4.2

Though the division is astronomical and cyclic in nature, the concept of smaller kali yuga (432000 years) and its beginning in 3102 B.C. leaves a terrestrial association in mind. The doctrine of transmigration of soul in Indian heritage i.e. life after death and effect of good and evil deeds in future life created an endless time, though the basic problem revolves round ātman, brahman, nirvāṇa (soul becomes free from the world), and the literature is full of discussion on puruṣa, prakṛti, guṇas, mind reflection of mind (māyā), immortality of mind and confusing conceptions of phenomenal world and various related matter. This is unlike Judaism, Christianity and Islam which had a limited nature of universe commencing from a period of 4000 years B.C.

v1.c38.s4.3

The idea of past, present and future gives us also an idea of linear time which is as if something is moving forward from the moment of creation. The Eurocentric imagination has introduced modernism, progress in place of future and has assimilated what is best of other cultures, first as a philosophical method then as a political method (revolution) and as an artistic method (avant garde). Modernity never looks, towards individual, rather looks towards human race through progress. There are also words like muhūrta (constant), kṣaṇa (moment) as ultimate unit of time. The followers of yoga school of Patañjali imagine that there is an uninterrupted flow of time of these moments. Ilya Prigogine, the Noble Laureate and the eminent theoretical Physicist has explained the idea of instant with a beautiful example with reference to Indian Culture. He says, be it a dancing Śiva or a miniature in temple - in which there appears very clearly the search for a junction between stillness and motion, time arrested and time passing. The instant is just like a window to the other side of time-eternity. The other world can be glimpsed in the flash of its existence. This reconciles among past, present and eternity. Indians had concepts of time but did not try to reconcile them in life with terrestrial activities, possibly because of religio-philosophical orientation in the society.

v1.c38.s4.4

1. The first ṛca (stanza) of Puruṣa - sukta (vs. 1) of the Ṛgveda, arranged in prose form is as follows:

v1.c38.s4.5

Sahasra śīrṣā sahasrākṣah sahasrapat (aṅgulaḥ) saḥ puruṣah vis vatah bhumiṃ vṛtvā (bhukarṇa prati hasta mānāya) daśāṅgulam ati atitisthat.

v1.c38.s4.6

The perimeter of the Puruṣa which remains surrounding the Earth is 1000 × 2000 × 2000 (aṅgulas). It rests one angula away of the earth of radius of one hasta (24 aṅg).

v1.c38.s4.7

2. Kauṭilya gives three sets of iron balances with length of beam and corresponding weight.

v1.c38.s4.8

For first set, length of the beam = 8 aṅg, weight = 1, ironpala = 48 māṣa, and diameter = 1, then density (D) in māṣa per unit anguli is expressed as π (1/2)² . 8 . D = 48
So, D = 24/π = 24x7/22 = 7.64 [taking π = 22/7]

v1.c38.s4.9

So the density of iron = 7.64 māṣa per cubic angula. Similarly density for other sets is calculated by method of average.

v1.c38.s4.10

3. Sarva dhātunām gaurava vṛddhau satvavṛddhiḥ !

v1.c38.s4.11

“The increase in density is increase in matter/price of all metals of equal volumes”.

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v1.c38.s5.1

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v1.c38.s5.3

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