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The Collaborative International Dictionary
Searchingness

Searching \Search"ing\, a. Exploring thoroughly; scrutinizing; penetrating; trying; as, a searching discourse; a searching eye. ``Piercing, searching, biting, cold.''
--Dickens. [1913 Webster] -- Search"ing*ly, adv. -- Search"ing*ness, n.

Wiktionary
searchingness

n. The state or quality of being searching.