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TWO:Beginning at the tool there is, first, a clamped joint between the tool and the swing block; second, a movable pivoted joint between the block and shoe piece; third, a clamped joint between the shoe piece and the front saddle; fourth, a moving joint [131] where the front saddle is gibed to the swing or quadrant plate; fifth, a clamp joint between the quadrant plate and the main saddle; sixth, a moving joint between the main saddle and the cross head; seventh, a clamp joint between the cross head and standards; and eighth, bolted joints between the standards and the main frame; making in all eight distinct joints between the tool and the frame proper, three moving, four clamped, and one bolted joint.The next step was to create a method for determining the particular configuration on which any given property of matter depends. If such a problem could be solved at all, it would be by some new system of practical analysis. Bacon did not see this because he was a Schoolman, emancipated, indeed,377 from ecclesiastical authority, but retaining a blind faith in the power of logic. Aristotle��s Organon had been the great storehouse of aids to verbal disputation; it should now be turned into an instrument for the more successful prosecution of physical researches. What definitions were to the one, that Forms should be to the other; and both were to be determined by much the same process. Now Aristotle himself had emphatically declared that the concepts out of which propositions are constructed were discoverable by induction and by induction alone. With him, induction meant comparing a number of instances, and abstracting the one circumstance, if any, in which they agreed. When the object is to establish a proposition inductively, he has recourse to a method of elimination, and bids us search for instances which, differing in everything else, agree in the association of two particular marks.541 In the Topics he goes still further and supplies us with a variety of tests for ascertaining the relation between a given predicate and a given subject. Among these, Mill��s Methods of Difference, Residues, and Concomitant Variations are very clearly stated.542 But he does not call such modes of reasoning Induction. So far as he has any general name for them at all, it is Dialectic, that is, Syllogism of which the premises are not absolutely certain; and, as a matter of nomenclature, he seems to be right. There is, undoubtedly, a process by which we arrive at general conclusions from the comparison of particular instances; but this process in its purity is nothing more nor less than induction by simple enumeration. All other reasoning requires the aid of universal propositions, and is therefore, to that extent, deductive. The methods of elimination or, as they are now called, of experiment, involve at every step the assumption of378 general principles duly specified in the chapter of Mill��s Logic where they are analysed. And wherever we can rise immediately from, a single instance to a general law, it is because the examination of that single instance has been preceded by a chain of deductive reasoning.