possibility which it opens of asking and answering questions by the deductive method. It might be supposed that a theory without a mathematical basis would exhibit comparatively little power of prediction, although its validity might never be questioned. Quantity of effect can not be measured, much less predicted, by deduction from theories susceptible only of historical treatment. All that can be expected is the power to indicate the presence or absence of things that are still unknown. But the laws of heredity, variation, correlation, etc., although still undefined and perhaps undefinable, furnish peculiar opportunities for brilliant deduction.
Paleontology would be a sorry science without the power of restoration afforded by the principle of correlation. Its fragments of bones and teeth and stumps and leaves would be almost absolutely worthless. But from the standpoint of logic this is as truly prediction by deduction from known laws as the minute predictions for the nautical almanac. Perfect heredity would place the principle on a basis of certainty. Any one character of ruminants indicated to Cuvier the presence of all the rest. But the generalized types of paleontology are transitional forms possessing combinations of ruminant characters, with others belonging to the carnivora, such as he never dreamed of. But the recognition of secular change in the correlations of organs, instead of weakening, has strengthened the possibility of anticipating unknown facts.
In recent years the progress from deduction to verification has been so rapid that frequently the latter has followed at the heels of the former, so that the element of time has hardly entered between them to make them both more striking. Many of the deductions from the theory of descent, afterward verified, are commonplaces to the scientist, but their logical force is not sufficiently emphasized when the nature of the evidence is considered.
The doctrine of descent required the belief that ruminants once had upper incisors and canines. The belief was made almost a certainty by the presence of partially developed fœtal teeth where they are absent after birth. The confident expectation was justified by the discovery of generalized ruminants with full sets of teeth. If man were descended from lower forms, an explanation was required for the absence of the os centrale as an independent bone from the human wrist, for it is almost constantly present in amphibians, reptiles, and mammals. Rosenberg looked for it in the human embryo and found it. Wiedersheim was moved to declare that this was one of the greatest triumphs that morphology, based on the theory of descent, had yet won. The
- Wiedersheim, Lehrbuch der vergleichenden Anatomie der Wirbelthiere, p. 223.