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The Catholic Encyclopedia
(Greek aer, "the air").
The largest and outer-most covering of the chalice and paten in the Greek church, corresponding to the veil in the Latin rite. It is slightly larger than the veil used to cover the chalice and paten in the Latin rite, and is beautifully embroidered in the same style and colour as the vestments of the officiating priest. It takes its name either from the lightness of the material of which it was formerly made or from the fact that the priest during the time of the recital of the Nicene Creed in the Mass holds it high in the air and waves it slowly towards the chalice. Its use, like that of the veil, was originally to cover the chalice and to prevent anything from falling therein before the consecration and before the sacred vessels were brought to the altar. It is first mentioned by name in an explanation of the liturgy (Mass) by a writer of the sixth century, and is also alluded to as "the so-called aër" in the Acts of the Council of Constantinople. In the Greek Orthodox church the veil is put on the shoulders of the deacon who brings the paten to the altar at the great entrance, and the same rite is preserved in the Greek Catholic church, where the aër usually has a couple of short strings to secure it over the shoulders. A similar ceremony is still preserved in the Roman rite, where the deacon at high Mass brings the chalice and paten to the altar and places a special veil over his shoulders.
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Obstat, Nihil. Lafort, Remy, Censor. Entry for 'Aër'. The Catholic Encyclopedia. https://www.studylight.org/encyclopedias/eng/tce/a/aandeumlr.html. Robert Appleton Company. New York. 1914.