Posted: 14.11.2014

As suggested before, let us interpret *kṣaṇa *as *samaya *which is the ultimate indivisible unit of time.^{[1]} Now, for calculating the number of *samayas *in 6 months, first we have to find out the number of *samayas *in 1 *āvalikā*. This number is equal to ^{[2]}-

*Jaghanya-Yukta-Asa**ṃkhyāta *(i.e., *J. Y. A.*)

This number is described as ^{[3]}-(*Jaghnya Parita Asaṃkhyāta*) raised to (*Jaghnya-Parita-Asaṃkhyāta*), which we can write as (*J. P. A.*) (*J. P. A.*). where *J. P. A. *is equal to-*Utkṛṣṭa Asaṃkhyāta *+ 1 (i.e., the highest numerable number + 1).^{[4]}

Now, again it is very difficult to compute the value of this number.^{[5]} However, we can replace the *Utkṛṣṭa asaṃkhyāta *by the number -

*x *= Śīrṣaprahelikā

Which is the highest numerable unit of time.^{[6]}

As mentioned above,

| = |

Now, | = ( |

| = ( |

There are two variants in Shvetambara traditions which give differently the value of *x*.

The value given by the Synod at Māthurī is - (84,00,000^{28})

= 758,263,253,073,010,241,157,963,569,975,696,406,218,966,808,080,183,296 x 10

^{40}= 7.58 x 10

^{193}approximately.

According to the version of the Synod at Vallabhī, this number is - (84,00,000^{28})

= 187,957,179,550,112,795,419,009,699,813,430,770,797,465,494,261,977,747,657,257,345,718,681,6 x 10

^{180}= 1.87 x 10

^{249}approximately.

We may use the lower value (as we are trying to find out the lower limit of the value of one *rajju*), i.e., that given by Māthurī synod.

Again, neglecting one which is much much less than *Śīrṣaprahelikā*, and substituting the value of *Śīrṣaprahelikā *in equation no. 1 we get,

J. Y. A. = (7.58 x 10

^{193})^{(7.58 x 10193)}.

Using the table of the units of time, we find that

1

Muhūrta(= 48 minutes) = 1,57,77,216Āvalikās6 months = 5,400

muhūrtas.

Then a *rajju*, which is the distance travelled in six months at the speed of 20,57,152 *yojanas *per *samaya*, will be

= 5,400 x 1,67,77,216 x (7.58 x 10^{193})^{(7.58 x 10193}) x 20,57,152 yojanas.

The approximate calculations of the above multiplication is given

1

rajju= 1.86 x 10^{{(1.47 x 10196}) + 17} yojanas.

Now 1 *yojana *= 8,000 miles

∴ 1

rajju= 14.88 x 10^{{(1.47 x 10196) + 20}}miles-----(1-A)

or, in terms of light-years, since,

1 light-year = 5.88 x 10

^{12}miles1

rajju= 2.91 x 10^{{(1.47 x 10196) + 8}}light years-----(1-B).

Then, the volume of the universe, which is 343 cubic *rajjus*, will be

= 11.35 x 10{(4.41 x 10196) + 65} cubic miles, if the first value (1-A) is taken.

In the terms of cubic light-years, the volume will be

= 8.45 x 10

^{{(4.41 x 10196) + 27}}cubic light years according to (1-B).

In the above calculations, we have taken

1

yojana= 8,000 miles.

However, according to the Digambara tradition,

1

yojana= 4,000 miles.^{[7]}

If we take this value, then the above values will be -

1

rajju= 7.44 x 10^{{(1.47x10196)+20}}miles1

rajju= 1.45 x 7.44 x 10^{{(1.47x10196)+8}}light years

Volume of *loka *will be

1.42 x 10 {(4.41x10^{196})+65} cubic miles

1.05 x 10 {(4.41x10

^{196})+27} cubic light years

Footnotes: | |

[1] | See Table of Time-units in Appendix II, infra pp. 341-343. |

[2] | jahaṇṇayaṃ juttāsaṃkhejjayaṃ kettiyaṃ hoi? jahaṇṇayaṃ parittāsaṃkhejjayaṃ |

[3] | For detail, see Appendix III, infra p. 373 |

[4] | See, Ibid., p. 373 |

[5] | See, Ibid., p. 372. |

[6] | See, Appendix II, infra p. 344; although this will not be able to give us the exact value of rajju, because the actual value of Utkṛṣṭa saṃkhyāta is much higher than Śīrṣaprahelikā, yet at least we shall be able to find out the lower limit of the value of one rajju. |

[7] | See Appendix I, infra p. |