O wise Nārada, what has been given thus far is but a summary; now, let the detailed explanation be unfolded, drawn from various places as needed. Among the roots ending in the letter ‘a’, all are generally set aside except for ‘vṛṅ’ and ‘vṛñ’. The roots to be considered include: ‘bhañj’, ‘bhuj’, ‘bhrasj’, ‘mat’, ‘ji’, ‘yaj’, ‘yuj’, ‘ruj’, ‘rañj’, ‘avi’, ‘jir’, ‘svañj’, ‘isañj’, and ‘sṛja’. Along with these, there are others such as śad, sadī, svidyatiḥ, skandir, hadī, krudh, kṣudhi, and budhyatī; as well as manyah, annā, pkṣip, chupita, ptipa, stṛpyati, and dṛpyatī. Further, the roots kruśi, daṃśi, diśī, dṛś, mṛśi, ruś, liś, viś, spṛśaḥ, and kṛṣiḥ are included. Then come vasati, dahati, hiduho, nahmih, ruhli, and hvahi, and others of their kind. There are also the indeclinables known as cādyā and gavayaḥ, and the prādyā, which arise from direction, place, and time. The practice of reciting groups, aphorisms, and roots is taught, and with these, words established in the Vedas and in worldly use, O Nārada, are to be known. Through concise methods, the proper words are determined—by means of base, suffix, substitution, elision, and addition. Yet, because of their vastness and infinitude, no one can speak them all, O Nārada. Now, listen further: By the mere knowledge of these matters, the accomplishment of dharma arises for people. This includes calculation, the casting of horoscopes, O Brāhmaṇa, and the collections known as Skandha. There is inquiry into matters such as lunar and solar eclipses, and also the Udāsya. Within the horoscope are the divisions of signs, the origins of planets, and the matters relating to birth. One must also know of actions, the span of life, the eight groups, royal yogas, and celestial yogas. The results of planetary positions, the mixed yogas of support, and the determination of lost birth are all to be understood, as are the characteristics of the Dreṣkāṇa. There are the conjunctions of lunar day, day, star, and the periods known as half-tithi. The waxing and waning of the moon, and the seasons associated with all the lunar mansions, are to be considered. In the course of life, there are rites such as the first cutting of hair, the piercing of the ears, the tonsure, and the tying of the knife, and so on. There is the beginning of a journey, entering a place, sudden rain, and actions of special significance. In calculation, one must understand the numbers: one, ten, a hundred, a thousand, ten thousand, and a hundred thousand. There are also the ‘niravara’, the ‘mahāpadma’, the ‘shaṅku’, and even the ocean itself, each representing particular measures. Whether in order or out of order, combinations are to be made according to the result required. When the divisor is pure, O sage, the quotient is to be multiplied by the last remainder to yield the result. But if the last number is odd, the odd portion should be set aside, and the root taken separately. That product, O Brāhmaṇa, should then be abandoned, and the division repeated with the root. This is known as the ‘samatra’ operation; the rule for the solid is given in its place. Wealth, too, must be purified by the odd from the last; this is called the root. By that product, one should purify what has been diminished, as well as the ‘nighnī’. In the mutual taking and striking down, the shares must be exactly cut off. The proportion among the shares should be understood, O sage, by those who reflect on the science’s meaning. By removing the shares from the total, one should assign to each its own increased portion. When the shares are equal, the combination is to be made at the end, O sage. The result emerges from the operation of subtracting, cutting, striking, and multiplying the differing shares. The remainder must be taken in the division of shares, and the rule of multiplication applied. Finally, for the accomplishment of each step, a sound should be produced at every stage, and likewise a sound should resound everywhere, marking the progress and completion of each act.