Definition: in a covert manner
Under the table may mean either “in a covert manner” or “into a stupor,” as in “We accepted the bet, for who could have guessed that a marmoset would drink us all under the table?” The “covert” sense is fairly recent, dating in use to the early 20th century. We have been drinking each other under tables for far longer than this, as evidence of this use goes back to at least the beginning of the 17th century.
And also in an other kinde of vnfaithfulnesse is in riotous seruants, that can rid of no worke, but meat and drinke, to carowse and drinke healths, and drinke one an other vnder the table; let them alone they be men of proofe, for such matters, but if it be to doe any thing of good seruice to the familie, that the master should be the better for it, yet can doe nothing.
— John Dod, The Bright Star Which Leadeth Wise Men to our Lord, 1603