In the school room with classes addicted to careless, inaccurate work, to accept nothing but a perfectly induced generalization, when this is feasible, is a most valuable lesson. For example, the teacher may not accept the generalization that all of the “first class” cities of the U. S. are located on navigable waterways, until the pupils have investigated the waterway conditions of every city belonging to the class. On the other hand, there may be individual cases of “cocksureness” which need attention. The teacher can do little for the “know-it-all youngster” until he pricks the bubble of conceit. This may be accomplished by allowing the youth to draw a generalization, which seems to meet all the requirements of truth arrived at by means of an _imperfect induction_; then without warning let the teacher give an instance which will show the generalization to be _false_. This involves what Socrates termed the “torpedo’s shock.” To illustrate: Consider the “prime number” formula given by Jevons. In deriving this, direct the class to add 2 to its square, and to this sum add 41. Give similar directions relative to numbers 3, 4, 7 and 10. Indicating the work as directed, would give the following: (1) 2 + 2² + 41 = 47 (2) 3 + 3² + 41 = 53 (3) 4 + 4² + 41 = 61 (4) 7 + 7² + 41 = 97 (5) 10 + 10² + 41 = 151 A question or two will make apparent the fact that all the results are prime numbers, and then the generalization may be drawn; namely, X + X² + 41 = prime number. Now without warning, but under the assumption that you desire to test deductively the general formula, let X = 40. This gives (40 + 40² + 41) 1681, which is the square of 41 and is, therefore, not a prime number. =15. TRADUCTION.= It may have been noted by the student that “perfect induction” is not induction at all according to the definition; viz.: Inductive reasoning is reasoning from less general premises to a more general conclusion. Referring to the first illustration of the previous section it is apparent that the conclusion is no broader than the premises. Ostensibly, the conclusion is a mere summary, or a generalization of the facts mentioned in the premises. Moreover perfect induction does not readily conform to the definition of deductive reasoning, as in this the movement must be from the more general to the less. We are thus forced to the conclusion that perfect induction is a form of a third type of reasoning which is known under the cognomen of _traduction_. This is from the Latin _trans_, and _ducere_ meaning to lead across. Definition: _Traductive reasoning is reasoning to a conclusion which is neither less general nor more general than the premises._ Aside from the case of perfect induction there are other types which well illustrate traduction. These are: First. _Reasoning from particular_ (_or individuals_) to _particular_ (or individuals). ILLUSTRATION: