The motto: Auxilio Dei translates traditionally as: “By the help of God.” That is the translation according to Baron Modar Neznanich, on his webpage: Mottoes at the URL address:

  The second word in the motto: Dei is plural, though, and the motto therefore should be read as: “By the help of the gods.”

  The first instance of the motto being associated with the arms of any Muirhead armiger, was in the year 1676. The arms of James Muirhead of Bredisholm bore the motto: Auxilio Deo. [Note that the second word is the singular form translating as “God”.] Subsequent matriculations of the arms of Muirhead bore the motto: Auxilio Deo.

  In 1737, the arms of James Grosset Muirhead were given the motto: Pro patria auxilio Dei, which has been translated as: “For my country with God’s help.” The translation of Dei to ‘gods’ became ‘God’s’. Later, the first part of the motto was dropped, but instead of returning to Auxilio Deo, as in the earliest matriculations, the variation of Auxilio Dei was retained.