I am assuming Arran was named for the Earl of Arran then

I was wondering if John Pearson (snr) had been a surgeon too. (With son George following in his footsteps).
If you google "John Pearson, esq" then there are links to a book/journal titled 'Short Notes of the Opinions and Practice of the Late John Pearson Esq., F.R.S., on Syphilitic Disease' published 1848