17. When we have established Natural Classes of objects, we seek for Characters of our classes; and these Characters may, to a certain extent, be called the _Definitions_ of our classes. This is to be understood, however, only in a limited sense: for these Definitions are not absolute and permanent. They are liable to be modified and superseded. If we find a case which manifestly belongs to our Natural Class, though violating our Definition, we do not shut out the case, but alter our definition. Thus, when we have made it part of our Definition of the _Rose_ family, that they have _alternate stipulate leaves_, we do not, therefore, exclude from the family the genus _Lowæa_, which has _no stipulæ_. In Natural Classifications, our Definitions are to be considered as temporary and provisional only. When Sir C. Lyell established the distinctions of the tertiary strata, which he termed _Eocene_, _Miocene_, and _Pliocene_, he took a numerical criterion {232} (the proportion of recent species of shells contained in those strata) as the basis of his division. But now that those kinds of strata have become, by their application to a great variety of cases, a series of Natural Classes, we must, in our researches, keep in view the natural connexion of the formations themselves in different places; and must by no means allow ourselves to be governed by the numerical proportions which were originally contemplated; or even by any amended numerical criterion equally arbitrary; for however amended, Definitions in natural history are never immortal. The etymologies of _Pliocene_ and _Miocene_ may, hereafter, come to have merely an historical interest; and such a state of things will be no more inconvenient, provided the natural connexions of each class are retained, than it is to call a rock _oolite_ or _porphyry_, when it has no roelike structure and no fiery spots. The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us to _Laws of Phenomena_ only. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. But before we speak of these, we shall say a few words respecting the way in which inductive propositions, once obtained, may be verified and carried into effect by their application. {{233}} CHAPTER IX. OF THE APPLICATION OF INDUCTIVE TRUTHS. APHORISM LIII. _When the theory of any subject is established, the observations and experiments which are made in applying the science to use and to instruction, supply a perpetual_ verification _of the theory._ APHORISM LIV. _Such observations and experiments, when numerous and accurate, supply also_ corrections _of the_ constants _involved in the theory; and sometimes_, (_by the Method of Residues_,) additions _to the theory._