As this isn't any relation to me, or anyone on the thread I doubt if anyone is going to spend money on it!
To my mind, and several others on here, Adelaide Harling and Adelade Springett are one and the same. However if you want to send for the certificate and prove us wrong, I would be the first to admit I've made a mistake. Can you come up with any better proof?
Added: Just thought, as she was on the Bona Vacantia list her death can't have been registered by a relative or anyone who knew her well, so the certificate may not help much.