I have a hard copy of the book, written by R. Bruce Jones. He was my uncle and passed away roughly ten years ago. The surname Satterthwaite does not appear in the book's index.
There is an 11-page chapter devoted to the 1827-1854 time period entitled "Separation - the Meeting on School House Lane". It mentions "then in 1832 a lot was purchased, on a portion of which stands the present Penn and Orthodox Meeting. A frame building was erected, according to Caroline Smedley, and first used for Meeting purposes (in the words of Walter Brinton), "on the first First day of the First month, 1833, and meetings have been held there regularly . . . since that date.""
If there are other names from that period that link to your family, I can check the book further. I, myself, have just started researching family ancestry. My ancestry also passes through Philadelphia at that time under the name of Biles.