In a manner that is free from clouds; with a clear, unclouded sky.
From 'cloudless' (adjective meaning without clouds, from 'cloud' + '-less') plus '-ly' (adverb suffix). The adverbial form emerged in the 17th-18th centuries in literary and descriptive writing.
Poets loved the word 'cloudlessly' because it sounds beautiful and creates a vivid picture of a perfectly clear sky—it's the kind of word that appears in Romantic poetry but almost never in casual conversation!
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