"The extent of the influence exerted by this one man over the literature and religion of Virginia," says Dr. A.Alexander, (who was one of his students), "cannot be calculated."If this is true, and I assume it has some truth to it, it would be reasonable to conclude that the different Log colleges exerted substantial influence on what their students would teach others later on. Understanding the history of these different log colleges, taken together with John Witherspoon´s influence at Princeton, would have obviously helped in making an informed decision concerning the direction of education at Princeton at the beginning of the 19th century. That is likely the reason Alexander studied the history of both Tennent's log college, the history of the Presbyterians in Ireland, and Robert Smith's Academy at Pequea.
However, it's reasonable to suspect that these schools all had a slightly different educational approach. These slightly different approaches were likely all inspired by educational reforms of John Knox and more recent trends from a variety of origins. For the superficial observer there might have been only two Presbyterian flavors until the reunification of 1758, old lights and new lights. In reality there were all kinds of contradicting developments, tensions and approaches that had to work together at that time.
It's in this context and for precisely this reason that the Princeton trustees had chosen Samuel Davies and Samuel Finley as early presidents before the arrival of John Witherspoon. These presidents aimed and eventually succeeded in bringing together old lights and new lights. But I think we are missing something if we think that that was the only divide they had to bridge. To understand how they were able to bring this diverse crowd together, the sermon Samuel Finley preached after Davies's death is a good starting point.
But to dig deeper into the understanding of the unifying force the two men were able to tap in to, we should also look at Samuel Finley's educational approach at his West Nottingham Academy in Cecil County which, according to Smith Futhey and Gilbert Cope, 'acquired a higher reputation than any other in the middle colonies, so that students from a distance were attracted to it'.