An archaic or dialectal term meaning awkwardly, clumsily, or in an ungainly manner.
From ad- + -ward (toward, in the direction of). The word combines a prefix meaning toward with a directional suffix, though the exact formation is obscure. It may be related to 'awkward' or an independent formation.
Adward is virtually extinct, swallowed up by 'awkwardly'—it's a word that lost out in competition with other synonyms, a common fate for archaic adverbs.
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