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The Thrones (lat. thronus, pl. throni) are a class of celestial beings mentioned by Paul of Tarsus in Colossians 1:16 (New Testament) and related to the throne of God the Father. They are living symbols of God's justice and authority. According to the New Testament, these high celestial beings are among those Orders at the Christ's service.  The Thrones are mentioned again in Revelation 11:16.
The corresponding order of angels in Judaism is called the "abalim" or "arelim"/"erelim". The Ophanim (Wheels or Galgallin) is a different class of higher liberated celestial beings, under many Christian angelic hierarchies, that are also know as the "Thrones", from Daniel 7:9 (Old Testament). They are the carriers of the throne of God, hence the name. They are said to be great wheels covered in eyes.
About the Thrones
Thrones are angels of the Sixth Order (second sphere) and are beings of tremendous power and movement. They are the keepers of higher more expanded energies. They ensure that these energies maintain connections and flows through the realms. They act as the conduits of the physical worlds and tend to be more stationary in their existence.
According to tradition
God's spirit is conveyed in a certain manner to these angels, who in turn pass on the message to men and the inferior angels. Thrones are known in scripture as the bringers of justice, but their status in hierarchy is often confused, sometimes placing them above the Seraphim, and sometimes placing them at the same level as the Cherubim. They do however, come in the second Choir, and are assigned to planets.
This position makes them some of the most powerful angels in service to the Lord. According to St. Thomas Aquinas, the Thrones have the task of pondering the disposition of divine judgments. In other words, they carry out or fulfill the divine justice of the Lord.
They create, channel and collect incoming and outgoing positive energies. Dispensation of justice is important to the Thrones and they send healing energies to victims while shining a light on injustice to bring it's presence to our attention.
Like their counterparts in the second angelic triad, they come the closest of all Angels to spiritual perfection and emanate the light of God with mirror-like goodness. They, despite their greatness, are intensely humble, an attribute that allows them to dispense justice with perfect objectivity and without fear of pride or ambition. Because they are living symbols of God's justice and authority, they are called Thrones and have as one of their symbols the throne.
According to the Western Wisdom Teachings
The Thrones (Gr. thronos) may possibly be equated with the "Lords of Wisdom", a Hierarchy of Elohim astrologically associated to Virgo, presented in The Rosicrucian Cosmo-Conception. They inhabit, in Rosicrucian cosmology, the World of Divine Spirit, which is the home of The Father. However, these teachings direcly present the Thrones (from Old Testament vision) as a higher hierarchy of celestial beings called "Lords of the Flame", already liberated (see Ophanim). According to this source, both these hierarchies have worked together in a far past toward the development of mankind.
1 Colossians 1:14-20
2 1 Peter 3:21-22
3 Bunson, Matthew. Angels A to Z. New York:Crown Trade Paperbacks, 1996. ISBN 0-517-88537-9.