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Yojanas

distances - yojanas…

Posted by satyask on October 7, 2008 from http://www.hindudharmaforums.com/showthread.php?t=295

Please note that the orinal author used the phrase “speed of light” in his analysis which I have now substituted with “speed of sun” follwoing his quote of Sayana directly.
तरणिर्विश्वदर्शतो ज्योतिष्कृदसि सूर्य । विश्वमा भासिरोचनम् ॥
taranirviśvadarśato jyotishkridasi sūrya | viśvamā bhāsirocanam ||

Swift and all beautiful art thou, O Surya, maker of the light; illuminating all the radiant realm. [RV: 1.50.4]

Sayana (c.1315-1387 AD) comments: “It is remembered that Sun traverses 2,202 yojanas in half a nimesa; giving light to all things, even to the moon and the planets, by night; for they are of a watery substance from which the rays of the sun are reflected.”

“yojana is a yoking or harnessing, that which is yoked or harnessed, a team or vehicle, or a course or path.

yojanA is a stage or the distance traversed in one harnessing or without unyoking.

1 yojana is said to comprise either 4 or 8 krosha (a cry or shout, or the range of the voice in calling); and 1 krosha (or goruta ~ as far as a cow’s lowing may be heard, or a bull’s roar) may represent either 1000 or 2000 daNDa (a rod or staff).

Sound radiates in all directions, so perhaps there is some confusion in regarding a krosha either as the radius of travel in one direction or as the full diameter of travel.

Man is the traditional measure of all things, and 1 danda represents 1 pauruSa (a man’s length) which equals 1 dhanvantara (bow-string) or dhanu (bow).

1 yojana measures either 4,000 or (more likely) 8,000 dhanus.

Assuming that 1 paurusha is 6 ft long, then 1 yojana must represent a distance of about 14.6 km (or about 9 miles, as suggested by Monier-Williams).

A full range of self-consistent units was anciently devised from the proportions of man’s own frame, although their exact conversion into modern units is unclear.

The basic unit is an angula (digit or finger), and 1 danda was perhaps originally divided into 100 digits, although 108 is the traditional value, and Aryabhatta prefers 96.

Assuming a 6 ft danda, Aryabhatta’s angula is exactly ¾ inch (or about 1.9 cm).

It does appear that 1 angula has always measured around 1.8 to 1.9 cm, with 1 danda or dhanu ranging from 1.83 to 2.05 m, so that 1 yojana must extend somewhere between 14.6 and 16.4 km.

nimeSa means shutting the eye or winking, and as a measure of time it is a wink of the eye or a moment.

Kautilya’s Arthashastra (c.320 BC) defines 1 nimesha as 1/360,000th of a day and night ~ i.e. 0.24 seconds.

2,202 yojanas in half a nimesha.

Given that 1 yojana is between 14.6 and 16.4 km, 2,202 yojanas must represent between 32,149 and 36,113 km.

Half a nimesha is 0.12 seconds.

Sayana thus gives the speed of the sun as between 267,910 and 300,940 km/sec ~ the currently accepted value for the speed of light being 299,792 km/sec.

Assuming that the true speed of light was actually known to Sayana, who presented “2,202 yojanas in half a nimesha” as a verity; and accepting Kautilya’s value for nimesha; then a perfect yojana would be exactly 16,337.4636 m and a perfect paurusha or danda exactly 2.0422 m in length.

And (assuming 108 digits per danda) then 1 angula = 1.89 cm, 1 dhanurgraha = 7.56 cm, 1 dhanurmushti = 15.13 cm, 1 vitasti = 22.69 cm, and 1 hasta (cubit) = 51.05 cm.

All discussion of Sayana’s comment has assumed that one yojana is about 14.6 km, and this is based on the western ideal of a 6 ft man.

The ancient sacred Egyptian cubit measured 28 angulas or 52.92 cm; and the ancient sacred Babylonian cubit measured 51.03 cm ~ i.e. 27 angulas ~ and this cubit was well known in ancient India.

There are 32,000 hasta or cubits in a yojana; and if the Sumerian sacred cubit is assumed, then one yojana is actually 16.33 km.

Therefore, 2,202 yojanas measures 35,958 km, and the speed of the sun is properly calculated to be 299,648 km/sec ~

The ordinary cubit measures 24 angulas (digits) or 6 dhanurgrahas (palms) or about 45 cm.
The old Egyptian royal cubit measured 28 digits (each 1.8710 cm) or 7 palms (each 13.0970 cm) ~ i.e. 52.3881 cm.
A copper bar from Nippur (c. 2650 BC) perhaps defined a Sumerian cubit of about 51.85 cm.
The Persian cubit measured about 50.01 cm.
The Harappan cubit was between 51.562 cm and 52.324 cm in length.

Thus, an ordinary man is about 1.8 m tall, and his travel is measured by stages of about 14.5 km.
The divine Egyptian ruler measured 2.09552 m, and his journey was by stages of 16.7642 km.
The copper man of Nippur would perhaps have stood 2.074 high, with leaps of 16.592 km.
The Persian paurusha was about 2.0004 m long, with stages or yojanas of 16.0032 km.
The Indus standard was between 2.062 and 2.093 m, with yojanas from 16.50 to 16.74 km.

Given the dictum of 2,202 yojanas in half a nimesha, an ordinary man would judge the speed of sun to be 266,075 km/sec; and the pharaoh’s sun would travel at 307,623.07 km/sec, but neither the royal Egyptian cubit of 28 digits nor the mortal human cubit of 24 digits is appropriate for this formula, which traditionally relies on a measure of 108 (i.e. 4 x 27) digits.

The Nippur standard would provide a speed of 304,463.2 km/sec; the Persian standard gives us 293,658.72 km/sec; and the Sarasvati standard gives a figure somewhere between 302,775 km/sec and 307,179 km/sec.

Assuming a perfect yojana, the constant of 2,202 could actually be any number from 2,182 to 2,222,

Very simply, light travels about 2,200 yojanas in half a nimesha; so that the sun travels about 2,200 x 720,000 yojanas in a day. And given a yojana of about 16.5 km, this means that the speed of sun was anciently calculated to be about 302,500 km/sec.”

Written by Satya Sarada Kandula

December 27, 2008 at 7:28 pm

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