"In the opening lecture of my last year's course I tried to convince you that it is only in the organization of animals that we find the foundation of the natural relations between the different groups, where they diverge and where they approach each other. Finally, I tried to show you that the enormous series of animals which nature has produced presents, from that of its extremities where are placed the most perfect animals, down to that which comprises the most imperfect, or the most simple, an evident modification, though irregularly defined (_nuancé_), in the structure of the organization. "To-day, after having recalled some of the essential considerations which form the base of this great truth; after having shown you the principal means by which nature is enabled to create (_opérer_) her innumerable productions and to vary them infinitely; finally, after having made you see that in the use she has made of her power of generating and multiplying living beings she has necessarily proceeded from the more simple to the more complex, gradually complicating the organization of these bodies, as also the composition of their substance, while also in that which she has done on non-living bodies she has occupied herself unremittingly in the destruction of all preëxistent combinations, I shall undertake to examine under your eyes the great question in natural history--What is a _species_ among organized beings? "When we consider the series of animals, beginning at the end comprising the most perfect and complicated, and passing down through all the degrees of this series to the other end, we see a very evident modification in structure and faculties. On the contrary, if we begin with the end which comprises animals the most simple in organization, the poorest in faculties and in organs--in a word, the most imperfect in all respects--we necessarily remark, as we gradually ascend in the series, a truly progressive complication in the organization of these different animals, and we see the organs and faculties of these beings successively multiplying and diversifying in a most remarkable manner. "These facts once known present truths which are, to some extent, eternal; for nothing here is the product of our imagination or of our arbitrary principles; that which I have just explained rests neither on systems nor on any hypothesis: it is only the very simple result of the observation of nature; hence I do not fear to advance the view that all that one can imagine, from any motives whatever, to contradict these great verities will always be destroyed by the evidence of the facts with which it deals. "To these facts it is necessary to add these very important considerations, which observation has led me to perceive, and the basis of which will always be recognized by those who pay attention to them; they are as follows: