The Root of the Powers of Air is the Ace of Swords in the Tarot, representing the primal, unformed essence of the element Air. In Crowley's system, it is attributed to the Hebrew letter Vau and the Path 31 on the Tree of Life, connecting Binah (Understanding) to Tiphereth (Beauty). This path is associated with the element Air and the letter Vau, embodying the formative power of air. The card symbolizes the pure intellectual force, the beginning of all air-related powers in the Tarot.

On the Tree of Life, the Ace of Swords occupies Path 31, which runs from Binah (the sphere of Saturn and Understanding) to Tiphereth (the sphere of the Sun and Beauty). It represents the channel through which the understanding of Binah flows into the beauty of Tiphereth, manifesting as clear thought and communication.

Astrologically, the Ace of Swords corresponds to the planet Mercury and the Air signs Aquarius, Gemini, and Libra. It embodies the qualities of intellect, communication, and clarity, reflecting the swift, adaptable nature of air.

In Tarot history, the Ace of Swords has been interpreted as a card of victory, justice, and mental power. In the Rider-Waite-Smith deck, it depicts a hand holding a sword aloft, crowned with laurel, symbolizing triumph and authority. In Crowley's Thoth deck, it is shown as a sword with a blue background, emphasizing its airy nature and the element's purity. It is the root card of the Swords suit, which governs thoughts, words, and conflicts.

In Liber 777, at scale step 31 bis (The Court Cards of the Tarot, with the Spheres of their Celestial Dominion—Swords), the entry for 'The Root of the Powers of Air' appears as a foundational element. It is listed alongside the court cards (Prince, Queen, King, Princess) but stands as the pure Air force from which those cards derive their powers. This placement underscores its role as the origin of the Swords suit's energies.