The double-headed eagle is the emblem of the thirty second and thirty-third (and highest) degrees of Scottish Rite Freemasonry. There exist a multitude explanations of the meaning of the two-headed eagle, from the mundane (it's a heraldic device) to the fantastic (it's the devil, I tell you!). In fact, the eagle is a symbol of the theurgic process undertaken by the Masonic initiate - a symbol of a completed alchemical process.
In the Hermetic Alchemical doctrine on which many Masonic symbols are based, the eagle is a sign of Scorpio, and is emblematic of transformation - the lowly, crawling scorpion remade into the soaring creature of air. Alchemically, the eagle was a symbol of purified sulfur, and was used in alchemical images to portray the ascending spirit. The double heads are often emblematic of the reconciliation of matter and spirit. Other elements in the Masonic eagle reinforce the alchemical symbolism - a sword representing heavenly fire, and the crown of spiritual attainment.
The Masonic eagle is often referred to as the "Eagle of Lagash," after one of the oldest uses of the emblem, in the ancient Sumerian city of Lagash. The two faced eagle was popularized in Europe by the Emperor Charlemagne, and the symbol was adopted formally into Freemasonry in the mid-eighteenth century, by the Council of Emperors of the East and West. At that time, the device was commonly used to depict the uniting of two bodies into one; this was probably a factor in the decision to use the eagle symbol.
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This page is adapted from the Glossary at Phoenixmasonry — Used with permission.