Sec. 4, — The Recording Secretary shall keep the minutes of the Scientific proceedings of the Academy, and shall issue notices for special Scientific meetings. He shall also keep a register in which he shall cause to be entered the names of all visitors to the Academy.
The position shows up in both the 1854 charter no less than the 1859 charter. Apparently "R S" is the standard acronym for recording secretary. To this end when, in Depuydt's article ends with the reference that members can come see the Secretary to check out the fragment it might help explain why J R Walker refers to himself as "Dr R(ecording) S(ecretary) Walker.". In other words, Walker is not presenting a paper in his field of expertise, he's just the secretary making an announcement as to the fragment on display in the office.