It's always helpful to hear another side of the story but I wonder about the connection with Eton Public School?

If a school in England is called a public school, it is in fact a private school. However, in Scotland a school that is called a public school is run by the state. I thought it worth stating the difference for the sake of readers who haven't heard of Eton Public School.

However, a public library in both countries is state-run, for use by the general public.