I ask for clarity of reference because he wrote more than one book. Not asking for a full quote, just something more specific than 'the book.'
Okay, I looked through the first one credited to Rowbotham in the library, Experimental Proofs, that reviews the wager about the Bedford canal. He addresses refraction in a paragraph at the top of page 20, after quoting a Britannica article on levelling. Unsurprisingly, he says it can be ignored.
It's clear he did not, in fact, take refraction into account. Quite the opposite; he claims he didn't need to.
Did you not read this?