The ESTC record for the Theosophical transactions by the Philadelphian Society (ESTC P2702) has the following note:
"Essays on philosophy and religion, some in dialogue form. Each issue concludes with lyrics and music for a hymn. The first two numbers of the proceedings of the first Quaker society in America; the idea to publish them apparently originated with Christopher Marshall (cf. Huntington Library note on endpaper of their copy)"
I do find this difficult to believe. I would not have thought that they would have reprinted Quaker material.
Can anyone say for sure?
I have already notified ESTC that the Transactions went up to No. 5 (Nov 1697).
I accept that JL & the Philadelphians were part of that general nexus and certainly kinship in some areas, but I am still not sure about a straight reprint of Quaker material.
The Google book reference does seem to make it clear that they wanted to distinguish themselves from the Quakers.