The two possible modes of verification are recourse to experience and appeal to reason; or _empirical_ proofs and _rational_ proofs. In the former the hypothesis is compared with facts by means of further observation and experiment. M. Romanes’ experience with the bees is a fair illustration of this form. Possibly the student has already noted that Romanes’ mode of procedure conforms to the “joint method of agreement and difference.” In the case of rational proofs the hypothesis is subjected to deductive demonstration, either of the form of syllogistic argument or mathematical calculation. A fair sample of this kind of verification is Newton’s discovery of universal gravitation. When he decided that the moon and the apple might be controlled by the same universal force, he undertook to establish his hypothesis by mathematical calculation. At first his figures seemed to disprove his theory, but after a wait of ten years, new data relative to the diameter of the earth, removed the apparent discrepancy. In the case of the discovery of Neptune, the verification was both rational and empirical. Mathematical (rational) calculation led to the assumption that the new planet must be at such a point. With this knowledge the observer was enabled to turn his telescope to the spot indicated and there, true to the calculations, was Neptune (empirical). To summarize: The method of the discoverer involves a knowledge of certain fundamental facts; the observation of crucial facts; a mental unrest; the constructing of an hypothesis through analogy; and finally verification by either appeal to experience, or mathematical demonstration. =6. THE REAL INDUCTIVE METHOD OR DISCOVERER’S METHOD NOT IN VOGUE IN CLASS ROOM WORK.=