It is certain that if I can draw any inference at all concerning objects not examined, it must be done on the data afforded by the objects which have been examined. If I judge that a distant star obeys the law of gravity, it must be because all other material objects sufficiently known to me obey that law. If I venture to assert that all ruminant animals have cloven hoofs, it is because all ruminant animals which have come under my notice have cloven hoofs. On the other hand, I cannot safely say that all cryptogamous plants possess a purely cellular structure, because some cryptogamous plants, which have been examined by botanists, have a partially vascular structure. The probability that a new cryptogam will be cellular only can be estimated, if at all, on the ground of the comparative numbers of known cryptogams which are and are not cellular. Thus the first step in every induction will consist in accurately summing up the number of instances of a particular phenomenon which have fallen under our observation. Adams and Leverrier, for instance, must have inferred that the undiscovered planet Neptune would obey Bode’s law, because *all the planets known at that time obeyed it*. On what principles the passage from the known to the apparently unknown is warranted, must be carefully discussed in the next section, and in various parts of this work. It would be a great mistake, however, to suppose that Perfect Induction is in itself useless. Even when the enumeration of objects belonging to any class is complete, and admits of no inference to unexamined objects, the statement of our knowledge in a general proposition is a process of so much importance that we may consider it necessary. In many cases we may render our investigations exhaustive; all the teeth or bones of an animal; all the cells in a minute vegetable organ; all the caves in a mountain side; all the strata in a geological section; all the coins in a newly found hoard, may be so completely scrutinized that we may make some general assertion concerning them without fear of mistake. Every bone might be proved to contain phosphate of lime; every cell to enclose a nucleus; every cave to hide remains of extinct animals; every stratum to exhibit signs of marine origin; every coin to be of Roman manufacture. These are cases where our investigation is limited to a definite portion of matter, or a definite area on the earth’s surface.