History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38.s1.t2: Yojana, Daṇḍa, Aratni and Aṅgula (Values in inches):

History of Technology in India, Vol. I: From Antiquity to c. 1200 A.D. v1.c38.s1.t2

Language: English

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*.

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:-

Linked texts (1)

Ṛgvedasaṃhitā — Sanskrit