Who is this a portrait of - and what book is he reading?

This is fascinating. There's a painting owned by the National Maritime Museum that they used to think was a portrait of Nevil Maskelyne (the fifth Astronomer Royal) but is now apparently quite firmly regarded as being of someone else. So the question is who is it - though the answer could be someone almost untraceable such as a philanthropist with a passion for astronomy - but also, what book is he holding?

Here's the painting - but the 'Art Detective' website posing the questions is absolutely fascinating for the detective work by visitors to the site.

I forgot to say - I picked up on this via a tweet from the Royal Astronomical Society librarian:

https://twitter.com/astro_librarian/status/496263472154705920