A very good question, and a propos to the ongoing controversy about Darwinian evolution today. Proponents of ID love to push “theistic evolutionists” for clear answers on this very question. That’s fair, as far as it goes, but sometimes IMO it’s not fair to expect too much. I am reminded of what Whewell wrote about divine action in his famous Bridgewater Treatise, in that very same part of the book quoted briefly by Darwin opposite the title page in the Origin of Species. Immediately before the words Darwin famously quoted, we find this:
“We are not to expect that physical investigation can enable us to conceive the manner in which God acts upon the members of the universe. The question, “Canst thou by searching find out God?” must silence the boastings of science as well as the repinings of adversity. Indeed, science shows us, far more clearly than the conceptions of every day reason, at what an immeasurable distance we are from any faculty of conceiving how the universe, material and moral, is the work of the Deity.”
Any theist (at least) who wants to know exactly how guides evolution, IMO, needs first to ask herself what she’s asking, in light of Whewell’s thoughts here.
Does guide need miracles to guide evolution? Compton said NO, and I sense that Asa Gray would have said the same thing, even though Gray unquestionably didn’t question the reality of the Incarnation, Resurrection, and other miracles associated with Jesus. They both understood that God can govern the world by working through natural processes to produce desired results. Now, perhaps that’s not a coherent view; perhaps God must do at least some miracles in natural history in order to govern evolution. I’m not here to argue for or against that notion. I will say simply, that when AHC learned science (prior to 1920), a majority of evolutionists believed in that evolution was in fact goal-directed. Darwin didn’t think so, and therein lies an irony: although Darwin did persuade the next generation of biologists to accept evolution (in the sense of common ancestry), he failed to persuade the next generation to accept “Darwinian” evolution (in which evolution is “unguided” by God or any other mind). That didn’t happen until after the neo-Darwinian synthesis. Julian Huxley later called this historical fact the “eclipse of Darwinism.” Some of the scientists who held teleological views of evolution were orthodox Christians (Gray fit into this category), others were modernist Christians (AHC), and still others were theists of some sort that is even harder to map onto Christianity than modernism (Joseph LeConte). They expressed their belief in teleology in various ways. For Gray, God led evolution “along certain beneficial lines,” apparently by guiding “variations” (mutations and other things producing phenotypical changes). I don’t know if I could pin down Compton even as vaguely as this: like many of his fellow modernist Protestants, he marveled at how life had advanced to produce persons, and he believed that God had devoted so much time and care to that process that God would preserve those persons in existence after death–also without miracles, incredibly (my editorial comment).
Compton was very active in the same Hyde Park church attended by theologian Shailer Mathews, whose definition of God was, basically, the personality-producing process of the universe. Compton’s theism was certainly more robust than Mathews’ theism–I sometimes wonder whether Mathews thought God was any more than a social construction–but, it was certainly also no less than Mathews’ theism. For the modernists, the production of personalities was the ultimate goal of the universe, and (at least for many of them) there had to be personality behind the universe, whether or not we should capitalize the “P”. Compton didn’t hesitate to capitalize it, by praying to “God” regularly and seeking personal guidance from a personal God. For Kirtley Mather (who as a student attended the same church), on the other hand, “God” was not necessarily the best word for what he preferred to call “the administration of the universe,” and he explicitly declined to capitalize the “a.”
Sorry for a long, rambling answer, but I don’t think a simple one is possible, either for Compton or many other scientists of his generation or Gray’s.