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Darwin is quoting two acknowledged authorities on the meaning and role of scientific investigation.
Bacon was considered, especially for English readers, the "father of experimental science." Whewell was the great Cambridge scholar of the history and philosophy of science. These references serve to justify Darwin's investigation as properly inductive and within the bounds of good Newtonian science. This is also a sly campaign: Whewell opposed evolutionism, and the "Bridgewater Treatise" series included some of the masterworks of the argument from design, which Darwin is about to demolish.
Darwin continued the rhetoric of justification on his opening page, where in the Introduction he starts the book with
"When on board H.M.S. 'Beagle,' as naturalist, I was much struck with certain facts in the distribution of the inhabitants of South America, and in the geological relations of the present to the past inhabitants of that continent. These facts seemed to me to throw some light on the origin of species -- that mystery of mysteries, as it has been called by one of our greatest philosophers. On my return home, it occurred to me, in 1837, that something might perhaps be made out on this question by patiently accumulating and reflecting on all sorts of facts which could possibly have any bearing on it. After five years' work I allowed myself to speculate on the subject, and drew up some short notes; these I enlarged in 1844 into a sketch of the conclusions, which then seemed to me probable: from that period to the present day I have steadily pursued the same object. I hope that I may be excused for entering on these personal details, as I give them to show that have not been hasty in coming to a decision."
In this short masterpiece of rhetoric, Darwin reminds us of his prestige as a naturalist, his experience, and his priority. He gives a fairly misleading account of his process of theorizing, in fact masking his skill as a theoretician, but this version does fit the prevailing image of good science as inductive and not hasty to theorize.
The detailed Table of Contents provides a nice overview of the structure of the book:
The facts of variation, familiar to any naturalist or gentleman farmer
The less familiar context of variation in nature, obvious once pointed out
Introducing the familiar vision of the balanced "economy of nature", with its tendency and limitation of increase
Natural selection derived from the previous elements, and explained as a cause of evolutionary change
Back to variation, to show that at least there are some understood patterns and rules
Confronting the potential objections to his argument and refuting them, which also provides a model of selectionist reasoning
Here Darwin begins to cover the various subjects that should be reconsidered under an evolutionary theory, to show how the ability to account for these phenomena support the validity of his theory. After a few chapters on geology, he returns to biological phenomena in Chapter XIII.
Summarizing, while making a rhetorical appeal for reasonable consideration and appreciation of the power of this new idea
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