As used in paragraph 10, what does the word “smarting” mean?

I would not have it imagined, however, that he was one of those cruel potentates of the school who joy in the smart of their subjects; on the contrary, he administered justice with discrimination rather than severity; taking the burden off the backs of the weak, and laying it on those of the strong. Your mere puny stripling, that winced at the least flourish of the rod, was passed by with indulgence; but the claims of justice were satisfied by inflicting a double portion on some little tough wrong-headed, broad-skirted Dutch urchin, who sulked and swelled and grew dogged and sullen beneath the birch. All this he called “doing his duty by their parents;” and he never inflicted a chastisement without following it by the assurance, so consolatory to the smarting urchin, that “he would remember it and thank him for it the longest day he had to live.”