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svārājyaṁ bhaujyam apy uta
vairājyaṁ pārameṣṭhyaṁ ca
ānantyaṁ vā hareḥ padam
mūrdhnā voḍhuṁ gadā-bhṛtaḥ
The verb rāj means “to rule,” and from it are derived the words sāmrājyam, meaning “rulership over the entire earth,” and svārājyam, meaning “rulership over heaven.” Bhaujyam comes from the verb bhuj, “to enjoy,” and thus refers to the capacity of enjoying whatever one desires. Virāṭ is explained by Śrīla Viśvanātha Cakravartī as representing the phrase vividhaṁ virājate (“one enjoys many kinds of opulence”) and specifically indicating the eight mystic perfections of aṇimā and so on.
An alternative explanation of these terms is given by Śrīla Śrīdhara Svāmī, who says that according to the Bahv-ṛca Brāhmaṇa, these four terms designate the power of sovereignty over each of the four cardinal directions: sāmrājya for the East, bhaujya for the South, svārājya for the West, and vairājya for the North.
Lord Kṛṣṇa’s queens clearly state that they do not desire any of these powers, or even the position of Brahmā, liberation or entrance into the kingdom of God. They simply want the dust from Śrī Kṛṣṇa’s feet, which Goddess Śrī herself worships. Śrīla Viśvanātha Cakravartī tells us that the goddess of fortune mentioned here is not Lakṣmī, the consort of Nārāyaṇa. After all, the ācārya explains, Goddess Lakṣmī could not attain the direct association of Kṛṣṇa even after performing extended austerities, as Uddhava states: nāyaṁ śrīyo ’ṅga u nitānta-rateḥ prasādaḥ (Bhāg. 10.47.60). Rather, the Śrī referred to here is the supreme goddess of fortune identified by the Bṛhad-gautamīya-tantra:
devī kṛṣṇa-mayī proktā
kāntiḥ sammohinī parā
“The transcendental goddess Śrīmatī Rādhārāṇī is the direct counterpart of Lord Śrī Kṛṣṇa. She is the central figure for all the goddesses of fortune. She possesses all the attractiveness to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord.”