The speaker is mispronouncing the word "animalculum" (singular,) "animalcula" (plural,) or "animalcule" (another form of the singular). The style of the passage sounds old-fashioned, perhaps from the early 1900s. The speakers are using informal, colloquial, slangy, spoken English. Dan has said something about using the microscope to look at a animalcula. Animalcula is an old-fashioned word, no longer used, for microscopic animals like protozoa, or other tiny animals that live in water like daphnia and copepods (pinhead-sized creatures). The -culus suffix means miniature or tiny. Either Jack really did not hear the word correctly and is mispronouncing it, or, possibly is bored and impatient and is deliberately teasing Dan by mispronouncing the name, to show that he isn't really interested in learning the name correctly. He probably knows, or ought to know, that the instrument is a microscope, not a "spy-glass." The writer is trying to give the impression of real, colloquial talk... but at the same time is holding back. Jack probably would not have said "hurts so confoundedly" but something like "hurts so damn much!" But at the time it was written, it would have been considered improper to put it in a book or admit that boys used such bad language. Anton van Leeuwenhoek, the pioneering microscopist, used the word "animalcule." In "The Pirates of Penzance," one of Gilbert and Sullivan's operettas, produced in 1879, a character intentionally misuses the name for comic effect (and to make an intentionally clumsy rhyme): "I'm very good at integral and differential calculus; I know the scientific names of beings animalculous." Here, he is pretending that "animalculous" is an adjective; "beings animalculous" is a pompous way of saying "animals."

This is no ordinary existing word, but the writer of this novel has twisted the word animalculism into annymalculism to make a point about how the speaker speaks. It is a biological term, you can look it up, I suspect most English native speakers would not know this word but you get a good idea of approximate meaning in the context. Hope that helps. Happy New Year.