He would spend half a day in these preparations without ever working out a problem or having the faintest conception of the use of lines or logarithms. And when he had finished, he had the most cheerful confidence that he had done a good day’s work.
This passage stood out to me because it shows how Harry is more focused on looking like he is doing serious work than actually understanding what he is doing. He goes through all the motions of studying engineering by setting up his books, tools, and papers, but he never actually solves anything. The detail about him having “cheerful confidence” that he worked hard makes the moment even more ironic. Twain and Warner seem to be poking fun at people who care more about looking productive or knowledgeable than actually knowing what they are doing.