beyond a generalization, or classification, and nothing is gained by using two terms for the same thing, when there are two notions to be distinguished from each other. (See Appendix I, § 233, Nos. 4, 5, and 7. Also Appendix J, § 234.)

54. Another point should be clearly outlined: The mere Repetition of examples, substantially identical, does not increase the force and certitude, nor extend the range, of an inference. One example covers the whole territory, and it, together with all others of the kind, does no more than illustrate the original principle established directly or indirectly by definition. In arithmetic, for example, repetition of examples adds nothing to the elements of which the rule" is made it simply serves to impress the way, the procedure, upon the mind of a learner, similarly to the repetition in the finger exercises upon the piano. (See §§ 204-7.)

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It should be observed that there is a great variety of opinions among authors concerning the nature of Induction. The citations in the Appendix exhibit some of the views.

55. (ƒ) If a scholar assume the possession of generals or universals, furnished either by Induction, by Definition, or by Intuition, and then use them with which to compare individual facts or truths, and by this means establish individual truths of like kind as an end of the process, the way of proceeding is known as Deduction. (See Appendix K, § 235.)

56. III. Consider the way in which the

individual student addresses himself to his tasks. He may be proceeding by any of the abovenamed modes, or ways, usually called Methods, and his own characteristics of disposition, habits, eccentricities, may be prominent. These may or may not be aids in securing valuable results of his labors. In any case, these are simply and solely individualities-they belong exclusively to the investigator-they are no necessary part of the mode or Method he is following-they are his Manner.

Critical discrimination should be made between what is necessary to a way, and what is purely incidental to the individual who is proceeding over that way. Indifference to this discrimination is followed by the pedantic assertion that each man can have a method of his own. Methods are ways which are independent of this or that man, and which are determined by the nature of the mind of man, or by the nature of the object-matter to be investigated. But Manner is his individuality when proceeding in a Method. (See § 123.)

57. When one's Manner is well ordered in its System, it is designated by the term Mode. (See 123.)

I.

ON THE THEORY OF METHODS OF TEACHING.

58. “I am afraid it must be allowed, that no art, of equal importance to mankind, has been so little investigated scientifically as the art of teaching. No art is in the hands of practitioners who are so apt to follow so blindly in the old paths. I say this with the full recollection that there has been great improvement in England lately, and that the books of teaching, most in use, have been purged of many gross errors both of statement and of method. But one line of enquiry there is which has never been sufficiently followed, though one would have thought it antecedently the most promising of all,—the study of the human mind through actual observation, and the study of the expedients by which its capacity for receiving and retaining knowledge may be enlarged. The field of investigation has been almost wholly neglected, and therefore it may just be that we are on the eve of great discoveries in education, and that the processes of these teachers are only a rough anticipation of the future. The fact that the methods of teaching followed in England are almost wholly empirical, that