Thanks, both of you. I've been doing some research in the newspaper database at FindMyPast, and it would seem the school was situated on Castlereagh Street. I also found a Durham University e-thesis about education for working class children in Barnsley, detailing Barnsley's endowed grammar schools in the 19th century, and this shows that it was not the Holgate school, which was vastly bigger and better funded. It describes Barnsley Grammar School as being rather run-down. The Locke Scholarships founded in 1861 seem to have breathed a bit of life into it, though not immediately. In 1865, a return by the Assistant Commissioner for Yorkshire to the Taunton Commission described it as "languid, the numbers low and the teaching inefficient." Apparently the headmaster did not welcome Locke scholars, because in his opinion, their presence prevented the presence of boys from "homes of a superior class." It's a fascinating thesis!