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$$ 15-17 1 सटीको वृत्तजातिसमुच्चयः
xix tions of that Vștta taken together. As the commentator says, even this has been shown under the Pātāla Prastāra.32 Virahānka, therefore, gives one more method for the same in vv. 42-44. It is this:--In the permutations of a Vștta with 1 letter in its Pāda the number of short and long letters will be 1 each; in those of a Vrtta with 2 letters in its Päda, it will be 4 each. In those of a Vștta with 3 letters in a Pāda it will be twice as much, i.e., 8, but with the addition of 4 to it; thus 12. So in the permutations of a Vịtta with 3 letters in its Pāda the total number of short and long letters will be 12 each. Hereafter, for getting the required number, the number of the immediately preceding Vịtta is to be doubled; to this then is to be added the figure that is to be obtained by doubling the figure that was added in the case of the last Vịtta. Thus in the permutations of a metre with 4 letters in its Pāda, we have 12 multiplied by 2, equal to 24; to this is to be added 4 multiplied by 2, i.e., 8. Thus we get 32 as the number required. Similarly in the permutations of a Vrtta with 5 letters in its Pāda we shall have 32X2=64 plus 8X2=16; thus 80 short and 80 long letters in all. In the case of a Vrtta with 6 letters in a Pāda, the number will be 80X2=160 plus 16X2=32; thus 192 short and 192 long letters in all. The process is to be continued until we reach the Utkrti Vrttas which have each of them 26 letters in their Pāda. The method of knowing the short and long letters in a given Mātrā Vrtta is given by Virahānka in v. 45. Count the number of letters and deduct them from the total number of Mātrās that are possible in that Mātrā Vștta : the resulting number is the number of long letters in it, while the rest are short ones.
17. The fifth Pratyaya is Samkhyā. This too has been already explained under the Suci and the Meru Prastāras.33 In vv. 46-48, therefore,
rahänka gives only an additional method of arriving at the Samkhyā, i.e., the total number of the permutations of a given metre. It is this :The Samkhyā for a Vștta with 1 letter in its Pāda is 2; this is to be doubled continuously for Vșttas having an additional letter in their Pādas. Thus the Samkhyā for a Vịtta with 2 letters in a Pāda will be 4, that for a Vrtta with 3 letters in a Pāda will be 8; that for a Vrtta with 4 letters in a Pada will be 16 and so on, until we reach the Utkrti Vịtta having 26 letters in their Pāda. The Samkhya in this last case is 67,108,864 (v. 48). For the Mātrā Vrttas the rule is slightly different. The Samkhyā for a metre with only 1 Mātrā is 1; that for a metre with 2
32. See para 11 above. 33. See para & above.
