Alice here:

"rheumatic wheels"

Pneumatic tires were relatively new.  But this is a malapropism. Joyce is having a great time writing this, you can tell.

From Wikipedia, the free encyclopedia.

A malapropism (from French mal à propos, "ill to purpose") is an incorrect usage of a word, usually with comic effect. The term comes from the name of Mrs. Malaprop, a character in Richard Brinsley Sheridan's comedy, The Rivals (1775), whose name was in turn derived from the existing English word malapropos, meaning 'inappropriately'. Here are some examples from her dialogue:

• "He's as headstrong as an allegory on the banks of the Nile." (i.e., alligator)
   
• "He is the very pineapple of politeness". (i.e., pinnacle)
   
• "If I reprehend any thing in this world, it is the use of my oracular tongue, and a nice derangement of epitaphs!" (i.e., apprehend; vernacular; arrangement; epithets).