30 PLANETARY PULVERISER A rule for solving a pulveriser, when the dividend is smaller than the divisor: 42-44. Set down the dividend above and the divisor below that. Divide them mutually, and write down the quotients of divi- sion one below the other (in the form of a chain). (When an even number of quotients are obtained) think out by what number the (last) remainder be multiplied so that the product being diminish- ed by the (given) residue be exactly divisible (by the divisor corres- ponding to that remainder). Put down the chosen number (call- ed mati) below the chain and then the new quotient underneath it. Then by the chosen number multiply the number which stands just above it, and to the product add the quotient (written below the chosen number). (Replace the upper number by the resulting sum and cancel the number below). Proceed afterwards also in the same way (until only two numbers remain). Divide the upper number (called "the multiplier") by the divisor by the usual process and the lower one (called "the quotient") by the dividend: the remainders (thus obtained) will respectively be the ahargana and the revolutions, etc., or what one wants to know. We explain this rule by means of an example.¹ Example. The residue of the revolutions of Saturn is 24, find the ahargana and the revolutions performed by Saturn.² The revolution-number of Saturn is 146564, and the number of civil days in a yuga is 1577917500. In the present problem these are respectively the dividend and the divisor. Their H.C.F. is 4, so that dividing them out by 4 we get 36641 and 394479375 as the abraded dividend and the abraded divisor respectively. We have, therefore, to solve the pulveriser 36641x-24 394479375 where x denotes the ahargana and y the revolutions made by Saturn.³ ¹ For other details, the reader is referred to B. Datta and A. N. Singh, History of Hindu Mathematics, Part II, P. 87 ff. 2 Based on Bhaskara I's problem given in LBh, viii. 17. 3 We have not divided the given residue 24 by 4, because it is already computed for the abraded dividend and abraded divisor.
