European Hipparion, having one large digit and two small ones on each foot, and the general characters of the fore-arm and leg to which I have referred.  But it is more valuable than the European Hipparion, for the reason that it is devoid of some of the peculiarities of that form—­peculiarities which tend to show that the European Hipparion is rather a member of a collateral branch, than a form in the direct line of succession.  Next, in the backward order in time, is the Miohippus, which corresponds pretty nearly with the Anchitherium of Europe.  It presents three complete toes—­one large median and two smaller lateral ones; and there is a rudiment of that digit, which answers to the little finger of the human hand.

[Illustration:  FIG. 9.]

The European record of the pedigree of the horse stops here; in the American Tertiaries, on the contrary, the series of ancestral equine forms is continued into the Eocene formations.  An older Miocene form, termed Mesohippus, has three toes in front, with a large splint-like rudiment representing the little finger; and three toes behind.  The radius and ulna, the tibia and the fibula, are distinct, and the short crowned molar teeth are anchitherold in pattern.

But the most important discovery of all is the Orohippus, which comes from the Eocene formation, and is the oldest member of the equine series as yet known.  Here we find four complete toes on the front limb, three toes on the hind-limb, a well-developed ulna, a well-developed fibula, and short-crowned grinders of simple pattern.

Thus, thanks to these important researches, it has become evident that, so far as our present knowledge extends, the history of the horse-type is exactly and precisely that which could have been predicted from a knowledge of the principles of evolution.  And the knowledge we now possess justifies us completely in the anticipation, that when the still lower Eocene deposits, and those which belong to the cretaceous epoch, have yielded up their remains of ancestral equine animals, we shall find, first, a form with four complete toes and a rudiment of the innermost or first digit in front, with probably a rudiment of the fifth digit in the hind foot;[4] while, in still older forms, the series of the digits will be more and more complete, until we come to the five-toed animals, in which, if the doctrine of evolution is well founded, the whole series must have taken its orgin.

That is what I mean by demonstrative evidence of evolution.  An inductive hypothesis is said to be demonstrated when the facts are shown to be in entire accordance with it.  If that is not scientific proof, there are no merely inductive conclusions which can be said to be proved.  And the doctrine of evolution, at the present time, rests upon exactly as secure a foundation as the Copernican theory of the motions of the heavenly bodies did at the time of its promulgation.  Its logical basis is precisely of the same character—­the coincidence of the observed facts with theoretical requirements.