Cachinnatory refers to loud or immoderate laughter. Though this may seem to be celebrating boisterous high spirits, it dates from the early nineteenth century, at a time when gentlemen in England did not laugh out loud, at least not in public.
It has about it a sense of the distaste we feel when persons nearby are carousing too loudly for comfort. That master of the second-rate novel, Sir Edward Bulwer-Lytton, was a great user of the word and illustrated its exuberance in his Paul Clifford of 1842: “If Paul’s comrade laughed at first, he now laughed ten times more merrily than ever. He threw his full length of limb upon a neighbouring sofa, and literally rolled with cachinnatory convulsions; nor did his risible emotions subside until the entrance of the hung-beef restored him to recollection”. It also appears in Fan by Henry Harford, published in 1892, in which the heroine is visiting London Zoo: “The laughing jackasses laughed their loudest, almost frightening her with their weird cachinnatory chorus”.
The Romans clearly knew of this unrestrained outpouring of immoderate humour, since the word is from Latin cachinnare with the same sense.