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History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38.s1: Length

History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38.s1

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English

Contents

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.

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