He attended local schools at Kellett and Silverdale, but his teachers noticed his abilities and he won a place at Eton College.
[3] It was said by a Peterhouse Fellow that he was unsuited to "any duty which required the exercise of high notions of morality, and a careful regard to what is just, decent, and venerable".
There were four electors for the vacant Professorship: the Vice-Chancellor, the Regius and the Lady Margaret's Professors of Divinity, and the Master of Peterhouse.
There is a popular story that Barnes, as well as being Master of Peterhouse, was Vice-Chancellor; that as Vice-Chancellor, he nominated himself for the Professorship; that as Master of Peterhouse he seconded himself; and that, by two original votes and a casting vote, he elected himself to the Professorship.
As was common for incumbents of the chair in the eighteenth and early nineteenth centuries, he seems to have given no lectures,[6] and did not publish anything.