At Cambridge, between 1876 and 1888, Muir lead the research on bismuth compounds, resulting in 18 papers published by him alone or together with his students in the Journal of the Chemical Society. His coauthors were all young graduates, because there were no postgraduate students in chemistry at Cambridge then. He became better known as a writer than researcher though, through his numerous textbooks and history of chemistry treatises. The most successful textbook of Muir was his Principles of Chemistry, which he first published in 1884, and as a second edition in 1889.
In the long running water controversy (19th century to early 20th century), Muir's books Heroes of Science: Chemists (1883) and History of Chemical Theories and Laws (1907) have been noted among the few British books to properly credit Lavoisier (as opposed to Henry Cavendish) for proposing that water was a chemical compound rather than an element. In a 1993 book, historian of science Mary Jo Nye described Muir's chapter on affinity from his History of Chemical Theories and Laws as "still valuable treatment of the topic".