The famous short poem “Elegy on the Death of a Mad Dog”
appears in which one of the following Eighteenth Century
novels?

The correct option is: The Vicar of Wakefield by Oliver Goldsmith.

Detailed Explanation:
"An Elegy on the Death of a Mad Dog" is a famous comic poem written by the Irish author Oliver Goldsmith. It was first published within his celebrated 1766 novel, The Vicar of Wakefield, specifically appearing in Chapter 17.
In the context of the novel, the poem is sung by the Vicar's youngest son, Bill, to entertain the family. The poem tells a humorous, ironic story of a seemingly pious man in Islington and a dog that he befriends. The dog eventually loses its mind and bites the man. The neighbors predict that the man will die of rabies; however, in a satirical twist, the man recovers, and it is the dog that dies. This subversion of expectation is a classic example of Goldsmith's playful irony and his critique of superficial sentimentality.

Why other options are incorrect:
- Roderick Random (1748) by Tobias Smollett is a picaresque novel about the adventures of a young man, Roderick Random, and does not contain this poem.
- Tristram Shandy (1759–1767) by Laurence Sterne is a highly experimental, metafictional novel famous for its digressions and humor, but it does not feature Goldsmith's elegy.
- The Castle of Otranto (1764) by Horace Walpole is widely regarded as the first Gothic novel and deals with supernatural occurrences in a medieval castle, which is entirely different in tone and content.