You are very welcome. I'm not sure that the term "non-subscribing" as it was adopted by certain Irish Presbyterian congregations in the 18th century is at all synonymous with the 19th century term "New School." "Non-subscriber" Presbyterians were unique to Ireland. The term came from their refusal to "subscribe" to the Westminister Confession of Faith. Part of what made non-subscribers unique was their unorthodox beliefs concerning the Trinity. In this respect, they were more Arian or Unitarian in their doctrine than other Presbyterians. As far as I know, most New School Presbyterians had traditional Calvinist beliefs about the Trinity.