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-: 442 :
Bhagavai 6:7:133-134 1 uddhāra palyopama = (4.13 x 1044 x a, x a, x 10?) samayas, but
a, = one year.
So,
1 uddhāra palyopama = (4.13 x 1044 x 10' x a.) years
= (109 x a.) vyavahāra palyopamas. 3. Addhā Palyopama
Each hair-piece, as described in uddhāra palyopama, is cut into a number of pieces equivalent to the number of samayas in uncountable years. The cylindrical pit is made cram-full with these pieces. Every samaya, a single piece is removed from it. The total period of time that elapses for emptying it completely is called addhā palyopama. In this way, the number of hair-pieces filled in the pit
= (4.13 x 1044 x a,xa, x 10') x (number of samayas of uncountable
years). If we consider uncountable years = a,, then
1 addhā palyopama = (4.13 x 1044 x a, xa, x 10'x a,) samayas
= (4.13 x 104 x a,a,a, x 10') years
= (4.13 x 109) a,a,a, years
= 10 a, a, a, vyavahāra palyopama. If we consider a, = a, then 1 addhā palyopama = 10% a, (a.)2 vyavahāra palyopama
= a, a, uddhāra palyopama Table of Time-units of Palyopama (1 vyavahāra palyopama = 4.13 x 1046 years) 1 uddhāra palyopama = (109 x a.) vyavahāra palyopama
1 addhā palyopama = a, a, uddhāra palyopama. Relationships between Time-units and Space-units
We get two equations in the Digambara tradition which indicate relations between time-units and space-units. In these equations, log, is used. Modern name of Chedaganita is logarithms.20
In the first equation, the relationship between sūcī angula ( a linear space-unit) and addhā palyopama is described as follows:21 sūcī angula is equal to addhā palyopama raised to the power logarithm to the base, addhā palyopama.
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