or c and d marks of one another, without any thing to connect a or b with c or d; we have a science of detached and mutually independent generalizations, such as these, that acids redden vegetable blues, and that alkalies color them green; from neither of which propositions could we, directly or indirectly, infer the other: and a science, so far as it is composed of such propositions, is purely experimental. Chemistry, in the present state of our knowledge, has not yet thrown off this character. There are other sciences, however, of which the propositions are of this kind: a a mark of b, b a mark of c, c of d, d of e, etc. In these sciences we can mount the ladder from a to e by a process of ratiocination; we can conclude that a is a mark of e, and that every object which has the mark a has the property e, although, perhaps, we never were able to observe a and e together, and although even d, our only direct mark of e, may not be perceptible in those objects, but only inferable. Or, varying the first metaphor, we may be said to get from a to e underground: the marks b, c, d, which indicate the route, must all be possessed somewhere by the objects concerning which we are inquiring; but they are below the surface: a is the only mark that is visible, and by it we are able to trace in succession all the rest.
§ 6. We can now understand how an experimental may transform itself into a deductive science by the mere progress of experiment. In an experimental science, the inductions, as we have said, lie detached, as, a a mark of b, c a mark of d, e a mark of f, and so on: now, a new set of instances, and a consequent new induction, may at any time bridge over the interval between two of these unconnected arches; b, for example, may be ascertained to be a mark of c, which enables us thenceforth to prove deductively that a is a mark of c. Or, as sometimes happens, some comprehensive induction may raise an arch high in the air, which bridges over hosts of them at once; b, d, f, and all the rest, turning out to be marks of some one thing, or of things between which a connection has already been traced. As when Newton discovered that the motions, whether regular or apparently anomalous, of all the