In a manner that is acceptable to one's conscience; in an ethically sound way.
From 'conscionable' + the adverbial suffix '-ly'. This follows the standard English pattern of converting adjectives to adverbs by adding '-ly'.
This adverb is so rare that it's essentially extinct in modern usage, yet it once represented an important distinction—the difference between acting in a merely 'conscientious' way versus acting in a 'conscionably' defensible way.
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