In the Jain canonical works as well as the post-canonical works, we get a long list of the various space-units used to measure the spatial dimensions. Right from the *paramāṇu *in the microcosmic measurement up to the *rajju *in the macroscopic (astrophysical) ones, we get the names and measures of these units.

As we have already seen, the ultimate indivisible unit of *pudgala *is called *paramāṇu *and the space occupied by one *paramāṇu *is called one *ākāśa-pradeśa *(the indivisible space-unit).Thus, the *ākāśa-pradeśa *can be considered equivalent to the geometrical point.

The ancient canonical works like *Bhagavatī *and *Anuogadārāiṃ *are the primary sources dealing in detail this topic. We describe it here. Occasionally, however, we shall also refer to other works^{[1]} like *Tiloyapaṇṇatti*, *Jambuddīvapaṇṇatti*, *Lokaprakāśa*, etc..

The starting point of the description of the space-units is the *paramāṇu *(the ultimate atom) of *pudgala*. The *paramāṇu *of *pudgala *is of two kinds: *sukṣma *(subtle) and *vyāvahārika *(empirical). In the present context, the subtle *paramāṇu *is not intended to be described. An infinite number of subtle *paramāṇus *make one empirical atom.^{[2]} It cannot be cut or pierced even by the sharpest weapon. For detailed description of such atom, see *Anuogadārāiṃ*, *sūtras *396-399. Abhayadevasūri says that the impossibility of cutting and piercing by any weapon is applicable also to the ultimate (transcendental) atom (*naiścayika paramāṇu*). Here, however, in the context of the topic of measurement, it is the empirical atom that is intended.^{[3]}

In the *Bhagavatī Sūtra*, we get the reading of the text as *aṇaṃtāṇaṃ paramāṇupoggalāṇaṃ*, whereas in the *Aṇuogadārāiṃ*, the reading of the text is-"*aṇaṃtāṇaṃ vavahāriya paramāṇupoggalāṇaṃ"*. Abhayadevasūri explains *paramāṇu *(given in *Bhagavatī's *reading*s*) as an empirical atom. The following table provides a comparison of the *Bhagavatī *and *Aṇuogadārāiṃ *texts on the topic:

Bhagavatī, 6/134 | Aṇūogadārāi ṃ, Sūtras 399, 400 |

Infinite material atoms = 1 utślakṣṇaślakṣṇikā[4] | Infinite number of empirical (practical) atoms = 1 utślakṣṇaślakṣṇikā |

8 utślakṣṇaślakṣṇikās = 1 ślakṣṇāślakṣṇikā[5] | 8 utślakṣṇaślakṣṇikās = 1 ślakṣṇāślakṣṇikā |

8 ślakṣṇāślakṣṇikās = 1 ūrdhvareṇu[6] | 8 ślakṣṇāślakṣṇikās= 1 ūrdhvareṇu |

8 ūrdhvareṇus = 1 trasareṇu | 8 ūrdhvareṇus = 1 trasareṇu |

8 trasareṇus = 1 rathareṇu | 8 trasareṇus= 1 rathareṇu |

8 rathareṇus = 1 bālāgra of theDevakuru and Uttarakuru humans[7] | 8 rathareṇus = 1 bālāgra of theDevakuru and Uttarakuru humans |

8 bālāgras of the Devakuru andUttarakuru humans = 1 bālāgraof Harivarṣa-Ramyakvarṣa humans[8] | 8 bālāgras of the Devakuru and Uttarakuru humans = 1 bālāgra of Harivarṣa-Ramyakvarṣa humans |

8 bālāgras of the Harivarṣa-Ramyakvarṣa humans = 1 bālāgra of Haimavata-Hairaṇyavata humans[9] | 8 bālāgras of the Harivarṣa-Ramyakvarṣa humans = 1 bālāgra of Haimavata-Hairaṇyavata humans |

8 bālāgras of the Haimavata- Hairanyavarta[10]humans = 1 bālāgra of the Pūrvavideha-Aparavideha[11] humans | 8 bālāgras of the Haimavata-Hairanyavarta humans = 1 bālāgra of the Pūrvavideha- Aparavideha humans |

8 bālāgra of the Pūrvavideha-Aparavideha humans[12] = 1 likṣā | 8 bālāgras of the Pūrvavideha-Aparavideha humans = 1 bālāgra of the Bharata-Airāvata[13] humans |

8 bālāgras of the Bharata-Airāvata humans = 1 likṣā | |

8 likṣās = 1 yūkā | 8 likṣās = 1 yūkā |

8 yūkās = 1 yavamadhya [14] | 8 yūkās = 1 yavamadhya |

8 yavamadhyas = 1 aṅgula | 8 yavamadhyas = 1 utsedha aṅgula |

6 aṅgulas = 1 pāda | 6 aṅgulas = 1 pāda |

12 aṅgulas = 1 vitasti | 12 aṅgulas = 1 vitasti |

24 four aṅgulas = 1 ratni | 24 four aṅgulas = 1 ratni |

48 aṅgulas = 1kukṣi | 48 aṅgulas = 1kukṣi |

96 aṅgulas = 1 daṇḍa, dhaṇūṣa, yuga, | 96 aṅgulas = 1 daṇḍa, dhaṇūṣa, yuga, |

nālika, akṣa, musala | nālika, akṣa, musala |

2000 dhaṇūṣas = 1 gavyūta | 2000 dhaṇūṣas = 1 gavyūta |

4 gavyūtas = 1 yojana | 4 gavyūtas = 1 yojana |

Further,

asaṃkhya yojanas = 1 rajju (see, supra pp. 159-167).

7 *rajjus* = 1 *jagaśreṇī*.^{[15]}

It may be useful to know the space-units as mentioned in other ancient traditions and also to compare the Jain space-units with them as well as modern space-units.

In the Buddhist work named *Lalitavistara,*^{[16]} we get the following space-units:

7 Paramāṇu-raja 7 Reṇu 7 Truṭi 7 Vātāyana-raja 7 Śaśā-raja 7 Eḍaka-raja 7 Go-raja 7 Likṣā-raja 7 Sarśapa 7 Yava 12 Aṅguli-parva 1 Vitasti 4 Hasta 1000 Dhanu 4 Krośa | 1 Reṇu 1 Truṭi 1 Vātāyana-raja 1 Śaśā-raja 1 Eḍaka-raja 1 Go-raja 1 Likṣā-raja 1 Sarśapa 1 Yava 1 Aṅguli-parva 1 Vitasti 1 Hasta 1 Dhanu 1 Krośa (Kośa) 1 Yojana |

Now, when we compare these space-units with the Jain space units, we find that there is complete agreement between those units which are between *aṅgulī-parva and dhanu*, except that we get the name *aṅgula* in the Jain units. Again, whereas 2000 dhanuṣas are equal to 1 *kośa* (gavyuta) in the Jain units, we get 1000 dhanuṣas=1 kośa in the Buddhist units

It means that

1 yojana = 7,68,000 *aṅgulas* in the Jain tradition.

1 yojana = 3,84,000 *aṅgulīparvas* in the Buddhist tradition.

Thus, 1 *aṅgula* (in the Jain tradition) = 2 *aṅgulīparvas* (in the Buddhist tradition).

The Buddhist space-units have been converted into the modern space-units.^{[17]}According to Dr. Bibhuti Bhushana Datta,

1 *paramāṇu* -rajja = 1.3 x 7-10inches

Now, since 1 *aṅgulīparva* = 710 *paramāṇus*

1 *aṅgulīparva* = 1.3 inches

Thus, 1 *aṅgula* = 0.65 inches

*aṅgulas*

= 7,68,000 x 0.65 inches

= 499200 inches

and... 1 mile = 63360 inches, we get

1 *yojana *= 499200/63360 miles

= 7.8787 miles approximately.

If we take 1 aṅgulīparva to be 1.32 inches, then we get 1 yojana to be 8.00 miles.

This is corroborated by the traditional belief which considers1 *kośa* = 2 miles.^{[18]} We can thus consider the yojana based on *utṣedhāṅgula* to be equal to 8 miles.

In the Śvetāmbara tradition, the *yojana *based on the *paramāṇaṅgula *is used to measure astrophysical distances like the diameters of the oceans, continents etc., where

1 *paramāṇaṅgula *= 1000 *utṣedhāṅgula*

whereas in the Digambara tradition

1 *paramāṇaṅgula *= 500 *utṣedhāṅgula*.^{[19]}

Thus, in Śvetāmbara tradition,

1 *yojana *= 8000 miles

In Digambar tradition,

1 *yojana *= 4000 miles.

In the next appendix, we shall discuss about the time-units in the Jain tradition. There we shall see how the units like *utṣedhāṅgula *and *bālāgras *(hair-tips) of the humans of *Devakuru *and *Uttarakuru *regions are used to calculate the time-units. Here also there is difference in the values of *utṣedhāṅgula*.

In the Shvetambara tradition,^{[20]}

1 *utṣedhāṅgula *= 8^{7} *bālāgras *of the *Uttarakuru *and *Devakuru *humans.

In the Digambara tradition,

1 *utṣedhāṅgula *= 8^{7} *bālāgras *of the *Uttama Bhogabhūmi *humans.

We have considered in the above list the space-units of one dimensional extension. Now we consider the two dimensional space-units.

There are two space-units of two-dimensional measurements:^{[21]}

1 *pratarāngula *= (*suci-aṅgula*)^{2}

1 *jagapratara *= (*jaga-śreṇī*)^{2}

There are four space-units of three-dimensional measurements:^{[22]}

(1) *khaṇḍuka:* The cube (solid body having six equal square sides) with all sides measuring ¼ *rajju *is called a *khaṇḍuka *(See figure). Thus,

1 *khaṇḍuka* = 1/64 cubic *rajju*

(2) *Sucī rajju *: Four *khaṇḍukas *placed in a straight line is called *sucī rajju*. (See figure).

Its dimensions are 1 *rajju*, ¼ *rajju *and ¼ *rajju *respectively. Thus,

1 *sucī rajju *= 4 *khaṇḍukas*

= 1 x ¼ x ¼ cubic *rajju*

= 1/16 cubic *rajju*.

(3) *Pratara rajju *: the four *sucī rajjus *placed in a single plane forming a cuboid having dimensions of 1 *rajju*, 1 *rajju *and ¼ *rajju *respectively. (See figure)

1 *pratara rajju *= 4 *sucī rajjus*

= 16 *khaṇḍukas*

= 1 x 1 x ¼ cubic *rajju*

= ¼ cubic *rajju*.

(4) *Ghana rajju *: The four *pratara rajjus *placed to form a cube fo dimension of 1 *rajju *each. (See figure)

1 *ghana rajju *= 4 *pratara rajjus*

= 16 *sucī rajjus*

= 64 *khaṇḍukas *

= 1 cubic *rajju*.

In the Digambara tradition, we get the following two space units in three dimensional measurements:^{[23]}

1 *ghanāṅgula *= (*suci- aṅgula) ^{3}*

1 *ghanaloka *= (*jagaśreṇī*)^{3}

*Bhagavatī*, 6.134; *Aṇuogadārāiṃ*, *sūtras *388-400; *Jambuddīvapaṇṇatti*, 2.6;

*Lokaprakāśa*, 1.21-67; *Tiloyapaṇṇatti*, 1.95-116.

*Bha. Vṛ*. 6.134-*yadyapi ca naiścayikaparamāṇorapīdameva lakṣaṇaṃ*

*Tathā'pīha pramāṇādhikārādvyāvahārikaparamāṇulakṣaṇamidamavaseyam*.

In its place, in *Tiloyapaṇṇatti*, we get '*uvasannāsana skandha*' and in *Jambuddīvapaṇṇatti *we get '*ussaṇha saṇhiāi*'.

In its place, in *Tiloyapaṇṇattiī*, we get '*sannāsana skandha*' and in *Jambuddīvapaṇṇatti we* get '*saṇhasaṇhiyāi*'.

A*ṇ*u. sū. 418-432.-In the original text of Bha., we get the reading *eraṇṇavayāṇaṃ*, but in *Ṭhāṇaṃ *and *Anu*., we get *heraṇṇavayāṇaṃ*

In the original text of *Bha*., we do not get the reading *aparavideha*, which, it seems, is erroneously omitted.

In the Śvetāmbara tradition, the term *jagaśreṇī *is not mentioned. However, at some places the term *abhrāṃśaśreṇī *is found. (See, *Lokaprakāśa*, 12.136)

See *Hindu Gaṇita-śāstra Kā Itihāsa*, by Dr. Bibhuti Bhusana Datta and Dr.

Avadhesa Narayana Singh, Hindi Edition, p. 177.