[ Hancock / Essay on Instinct ]
Hancock (1783 - 1849) was born in Ireland, earned his medical degree in Scotland, and spent much of his adult life in England. Most of his writings were on religious and ethical topics, informed by his devout Quaker faith.
Full title: Essay on Instinct and its Moral and Physical Relations. This book was published in 1824 (London: W. Phillips), and appears not to have been republished.
Hancock mentions Newfoundlands twice in this book. The first comes when he is discussing instances of "kind and affectionate attachment" between animals, including between different species. One illustration of this principle is the story of an injured Newfoundland befriended by a tame raven; Hancock quotes the incident verbatim (with credit) from its original source, Gentleman's Magazine of March 1788, which you can read here at The Cultured Newf.
The second and final mention is also taken from an earlier work (with credit), and involves a Newfoundland dropping into the water, and then rescuing, a smaller dog that had been pestering him. (This anecdote is taken from a series of lectures given by Abell in Scotland; it seems those lectures were never published.)
Dr. Abell, in one of his Lectures on Phrenology, related a very striking anecdote of a Newfoundland dog in Cork. This dog was of a noble and generous disposition; and when he left his master's house was often assailed by a number of little noisy dogs in the street. He usually passed them with apparent unconcern, as if they were beneath his notice. But one little cur was particularly troublesome, and at length carried his petulance so far as to bite the Newfoundland dog in the back of his foot. This proved to be a step in wanton abuse and insult beyond what was to be patiently endured; and he instantly turned round, ran after the offender, and seized him by the skin of the back. In this way he carried him in his mouth to the quay, and holding him some time over the water, at length dropped him into it. He did not seem, however, to design that the culprit should be punished capitally; and he waited a little while till the poor animal, who was unused to that element, was not only well ducked but near sinking, when he plunged in, and brought him out safe to land.
It would be difficult to conceive any punishment more aptly contrived, or more completely in character. Indeed, if it were fully analysed, an ample commentary might be written in order to show what a variety of comparisons, and motives, and generous feelings entered into the composition of this act. It supplies at least a good moral lesson. It shows the difference between magnanimity and meanness, and by what lawful means the former may correct the latter.
This second anecdote is repeated, almost verbatim, in Willliam Youatt's 1839 The Dog and in Edward Jesse's 1858 Anecdotes of Dogs.