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Returning to our more immediate subject, we must observe that the Pythagoreans did not maintain, in anticipation of modern quantitative science, that all things are determined by number, but that all things are numbers, or are made out of numbers, two propositions not easily distinguished by unpractised thinkers. Numbers, in a word, were to them precisely what water had been to Thales, what air was to Anaximenes, the absolute principle of existence; only with them the idea of a limit, the leading inspiration of Greek thought, had reached a higher degree of abstraction. Number was, as it were, the exterior limit of the finite, and the interior limit of the infinite. Add to this that mathematical studies, cultivated in Egypt and Phoenicia for their practical utility alone, were being pursued in Hellas with ever-increasing ardour for the sake of their own delightfulness, for the intellectual discipline that they supplied��a discipline even12 more valuable then than now, and for the insight which they bestowed, or were believed to bestow, into the secret constitution of Nature; and that the more complicated arithmetical operations were habitually conducted with the aid of geometrical diagrams, thus suggesting the possibility of applying a similar treatment to every order of relations. Consider the lively emotions excited among an intelligent people at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine art, and tactics, were just as strange and wonderful as electrical phenomena are to us; consider also the magical influence still commonly attributed to particular numbers, and the intense eagerness to obtain exact numerical statements, even when they are of no practical value, exhibited by all who are thrown back on primitive ways of living, as, for example, in Alpine travelling, or on board an Atlantic steamer, and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem, the cause of all existence; or that these speculations were more than once revived in after ages, and perished only with Greek philosophy itself.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.

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THREE:"Are you? There is a well in that courtyard. And if perchance anything valuable got into that well, I should say that a rope would be the best way of getting it out. Now do you understand."Water-wheels, or water-power, as a mechanical subject, is apparently quite disconnected with shop manipulation, but will serve as an example for conveying general ideas of force and motion, and, on these grounds, will warrant a more extended notice than the seeming connection with the general subject calls for.

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THREE:In the centre of the town I was detained by three sailors, who called out an angry "Halt!" seized my bicycle, and made me a prisoner, "because I was an Englishman." Happily I could prove the contrary by my papers; and the permit of the Bruges commander to go about on a bicycle made them return it.

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"It's about that business of Dr. Gordon Bruce," Isidore said curtly. "Now, my friend Wolffman, you know me and I know you. I don't want to ruin you body and bones, but I shall do so unless you listen to reason. You are going to write to Dr. Bruce, and tell him the matter shall stand over for the present----"409"Are you quite sure," he asked, "that Mamie is her own child?"

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