In Chapter 6 we are told Isabella appears concerned about possible attentions by two odious young men ;) in the Pump Room She suggests they go and look at the new arrivals.

They walked to the book, where Isabella examined the names.

Might this be the Subscription book kept by an employee of the Bath Corp ?

I was wondering if Isabella was examining the book because she was interested in who the two young men might be.

Or if she had any notion of John arriving in Bath, if he had already visited the Pump Room and siged his name.
Just a thought !