Sutra 39

Devanagari script

छायायामष्टपौरुष्यामष्टादशभागश्छेदः षट्पौरुष्यां चतुर्दशभागः त्रिपौरुष्यामष्टभागः द्विपौरुष्यां षड्भागः पौरुष्यां चतुर्भागः अष्टाङ्गुलायां त्रयो दशभागाः चतुरङ्गुलायां त्रयोऽष्टभागाः अच्छायो मध्याह्न इति ॥ कZ_०२.२०.३९ ॥

Transliteration

chāyāyām aṣṭa-pauruṣyām aṣṭādaśa-bhāgaś chedaḥ ṣaṭ-pauruṣyāṃ caturdaśa-bhāgaḥ tri-pauruṣyām aṣṭa-bhāgaḥ dvi-pauruṣyāṃ ṣaḍ-bhāgaḥ pauruṣyāṃ catur-bhāgaḥ aṣṭāṅgulāyāṃ trayo daśa-bhāgāḥ caturaṅgulāyāṃ trayo ’ṣṭa-bhāgāḥ acchāyaḥ madhyāhna iti

Translation

By the length of a shadow: when it measures eight ‘pauruṣa’ units, the cut-off is 18 parts; at six pauruṣas, 14 parts; at three pauruṣas, 8 parts; at two pauruṣas, 6 parts; at one pauruṣa, 4 parts; at eight aṅgulas, 3/10 parts; at four aṅgulas, 3/8 parts. When there is no shadow, it is midday.

Word by Word

छायायाम्in (the case of) the shadow / in the shadow-measurement

अष्टeight

पौरुष्याम्when (the shadow is) eight man-lengths

अष्टादशeighteen

भागःparts (fractions)

छेदः(is) the divisor / the dividing number

षट्six

पौरुष्याम्when (the shadow is) six man-lengths

चतुर्दशfourteen

भागःparts

त्रिthree

पौरुष्याम्when (the shadow is) three man-lengths

अष्टeight

भागःparts

द्विtwo

पौरुष्याम्when (the shadow is) two man-lengths

षट्six

भागःparts

पौरुष्याम्when (the shadow is) one man-length

चतुर्भागःfour parts

अष्टeight

अङ्गुलायाम्when (the shadow is) eight finger-breadths

त्रयःthree

दशten

भागाःparts

चतुर्four

अङ्गुलायाम्when (the shadow is) four finger-breadths

त्रयःthree

अष्टeight

भागाःparts

अच्छायःshadowless (no shadow)

मध्याह्नः(it is) midday/noon

इतिthus

Entities Mentioned

shadow (chāyā)

pauruṣa

aṅgula

madhyāhna (midday)

FAQs

Why include a shadow-based method when a water-clock exists?

Redundancy and verification: shadow measurement works in the field without instruments and can cross-check clock time to deter tampering.

What is the administrative intent of defining ‘midday’ as shadowless?

It provides an observable, dispute-resistant reference point for deadlines, court sessions, market regulation, and duty changes.