The Collaborative International Dictionary of English v.0.48:

Cucking stool \Cuck"ing stool`\ (k?k"?ng st??l`). [Cf. AS.
   scealfingst[=o]l, a word of similar meaning, allied to
   scealfor a diver, mergus avis; or possibly from F. coquine a
   hussy, slut, jade, f. of coquin, OE. cokin, a rascal; or cf.
   Icel. k?ka to dung, k?kr dung, the name being given as to a
   disgracing or infamous punishment.]
   A kind of chair formerly used for punishing scolds, and also
   dishonest tradesmen, by fastening them in it, usually in
   front of their doors, to be pelted and hooted at by the mob,
   but sometimes to be taken to the water and ducked; -- called
   also a castigatory, a tumbrel, and a trebuchet; and
   often, but not so correctly, a ducking stool. --Sir. W.
   Scott.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Castigatory \Cas`ti*ga*to*ry\, a. [L. castigatorius.]
   Punitive in order to amendment; corrective.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Castigatory \Cas"ti*ga*to*ry\, n.
   An instrument formerly used to punish and correct arrant
   scolds; -- called also a ducking stool, or trebucket.
   --Blacktone.
   [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

CASTIGATORY, punishments. An engine used to punish women who have been
convicted of being common scolds it is sometimes called the trebucket,
tumbrel,  ducking stool, or cucking stool. This barbarous punishment has
perhaps never been inflicted in the United States. 12 S. & It. 225. Vide
Common Scold.