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athāsau yuga-sandhyāyāṁ dasyu-prāyeṣu rājasu janitā viṣṇu-yaśaso nāmnā kalkir jagat-patiḥ
atha—thereafter; asau—the same Lord; yuga-sandhyāyām—at the conjunction of the yugas; dasyu—plunderers; prāyeṣu—almost all; rājasu—the governing personalities; janitā—will take His birth; viṣṇu—named Viṣṇu; yaśasaḥ—surnamed Yaśā; nāmnā—in the name of; kalkiḥ—the incarnation of the Lord; jagat-patiḥ—the Lord of the creation.
Thereafter, at the conjunction of two yugas, the Lord of the creation will take His birth as the Kalki incarnation and become the son of Viṣṇu Yaśā. At this time the rulers of the earth will have degenerated into plunderers.
Here is another foretelling of the advent of Lord Kalki, the incarnation of Godhead. He is to appear at the conjunction of the two yugas, namely at the end of Kali-yuga and the beginning of Satya-yuga. The cycle of the four yugas, namely Satya, Tretā, Dvāpara and Kali, rotates like the calendar months. The present Kali-yuga lasts 432,000 years, out of which we have passed only 5,000 years after the Battle of Kurukṣetra and the end of the regime of King Parīkṣit. So there are 427,000 years balance yet to be finished. Therefore at the end of this period, the incarnation of Kalki will take place, as foretold in the Śrīmad-Bhāgavatam. The name of His father, Viṣṇu Yaśā, a learned brāhmaṇa, and the village Śambhala are also mentioned. As above mentioned, all these foretellings will prove to be factual in chronological order. That is the authority of Śrīmad-Bhāgavatam.