Sir David Brewster, in a somewhat similar manner, succeeded in measuring the refractive indices of irregular fragments of transparent minerals. It was a troublesome, and sometimes impracticable work to grind the minerals into prisms, so that the power of refracting light could be directly observed; but he fell upon the ingenious device of compounding a liquid possessing the same refractive power as the transparent fragment under examination. The moment when this equality was attained could be known by the fragments ceasing to reflect or refract light when immersed in the liquid, so that they became almost invisible in it. The refractive power of the liquid being then measured gave that of the solid. A more beautiful instance of representative measurement, depending immediately upon the principle of inference, could not be found.[29] [29] Brewster, *Treatise on New Philosophical Instruments*, p. 273. Concerning this method see also Whewell, *Philosophy of the Inductive Sciences*, vol. ii. p. 355; Tomlinson, *Philosophical Magazine*, Fourth Series, vol. xl. p. 328; Tyndall, in Youmans’ *Modern Culture*, p. 16. Throughout the various logical processes which we are about to consider--Deduction, Induction, Generalisation, Analogy, Classification, Quantitative Reasoning--we shall find the one same principle operating in a more or less disguised form. *Deduction and Induction.* The processes of inference always depend on the one same principle of substitution; but they may nevertheless be distinguished according as the results are inductive or deductive. As generally stated, deduction consists in passing from more general to less general truths; induction is the contrary process from less to more general truths. We may however describe the difference in another manner. In deduction we are engaged in developing the consequences of a law. We learn the meaning, contents, results or inferences, which attach to any given proposition. Induction is the exactly inverse process. Given certain results or consequences, we are required to discover the general law from which they flow. In a certain sense all knowledge is inductive. We can only learn the laws and relations of things in nature by observing those things. But the knowledge gained from the senses is knowledge only of particular facts, and we require some process of reasoning by which we may collect out of the facts the laws obeyed by them. Experience gives us the materials of knowledge: induction digests those materials, and yields us general knowledge. When we possess such knowledge, in the form of general propositions and natural laws, we can usefully apply the reverse process of deduction to ascertain the exact information required at any moment. In its ultimate foundation, then, all knowledge is inductive--in the sense that it is derived by a certain inductive reasoning from the facts of experience.