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Krṣṇa, the Supreme Personality of Godhead
Śiva is the greatest of all great souls,  mahātmās , he keeps on his head the purifying water of the Ganges, which emanates from a hole in this material universe made by the toe of Lord Viṣṇu. Lord Śiva is in charge of the material quality of ignorance, and in order to keep himself in a transcendental position, he always meditates on Lord Viṣṇu. Therefore Rukmiṇī knew very well that obtaining the favor of Krṣṇa was not an easy job. If even Lord Śiva must purify himself for this purpose, surely it would be difficult for Rukmiṇī, who was only the daughter of a  kṣatriya  king. Thus she desired to dedicate her life to observing severe austerities and penances, such as fasting and going without bodily comforts. If it were not possible in this lifetime to gain Krṣṇa's favor by these activities, she was prepared to do the same lifetime after lifetime. In the  Bhagavad-gītā  it is said that pure devotees of the Lord execute devotional service with great determination. Such determination, as exhibited by Rukmiṇīdevī, is the only price for purchasing Krṣṇa's favor and is the way to ultimate success in Krṣṇa consciousness.
After explaining Rukmiṇīdevī's statement to Krṣṇa, the  brāhmaṇa  said: "My dear Krṣṇa, chief of the Yadu dynasty, I have brought this confidential message for You from Rukmiṇī; now it is placed before You for Your consideration. After due deliberation You can act as You please, but if You want to do something, You must do it immediately. There is not much time left for action."
Thus ends the Bhaktivedanta purport of the Fifty-first Chapter of Krṣṇa, "Krṣṇa, the Ranchor."