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THREE:We have seen how Greek thought had arrived at a perfectly just conception of the process by which all physical transformations are effected. The whole extended universe is an aggregate of bodies, while each single body is formed by a combination of everlasting elements, and is destroyed by their separation. But if Empedocles was right, if these primary substances were no other than the fire, air, water, and earth of everyday experience, what became of the Heracleitean law, confirmed by common observation, that, so far from remaining unaltered, they were continually passing into one another? To this question the atomic theory gave an answer so conclusive, that, although ignored or contemned by later schools, it was revived with the great revival of science in the sixteenth century, was successfully employed in the explanation of every order of phenomena, and still remains the basis of all physical enquiry. The undulatory theory of light, the law of universal gravitation, and the laws of chemical combination can only be expressed in terms implying the existence of atoms; the laws of gaseous diffusion, and of thermodynamics generally, can only be understood with their help; and the latest develop34ments of chemistry have tended still further to establish their reality, as well as to elucidate their remarkable properties. In the absence of sufficient information, it is difficult to determine by what steps this admirable hypothesis was evolved. Yet, even without external evidence, we may fairly conjecture that, sooner or later, some philosopher, possessed of a high generalising faculty, would infer that if bodies are continually throwing off a flux of infinitesimal particles from their surfaces, they must be similarly subdivided all through; and that if the organs of sense are honeycombed with imperceptible pores, such may also be the universal constitution of matter.26 Now, according to Aristotle, Leucippus, the founder of atomism, did actually use the second of these arguments, and employed it in particular to prove the existence of indivisible solids.27 Other considerations equally obvious suggested themselves from another quarter. If all change was expressible in terms of matter and motion, then gradual change implied interstitial motion, which again involved the necessity of fine pores to serve as channels for the incoming and outgoing molecular streams. Nor, as was supposed, could motion of any kind be conceived without a vacuum, the second great postulate of the atomic theory. Here its advocates directly joined issue with Parmenides. The chief of the Eleatic school had, as we have seen, presented being under the form of a homogeneous sphere, absolutely continuous but limited in extent. Space dissociated from matter was to him, as afterwards to Aristotle, non-existent and impossible. It was, he exclaimed, inconceivable, nonsensical. Unhappily inconceivability is about the worst negative criterion of truth ever yet invented. His challenge was now35 taken up by the Atomists, who boldly affirmed that if non-being meant empty space, it was just as conceivable and just as necessary as being. A further stimulus may have been received from the Pythagorean school, whose doctrines had, just at this time, been systematised and committed to writing by Philolaus, its most eminent disciple. The hard saying that all things were made out of number might be explained and confirmed if the integers were interpreted as material atoms.

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THREE:After determining the ultimate objects of an improvement, and laying down the general principles which should be followed in the preparation of a design, there is nothing connected with constructive engineering that can be more nearly brought within general rules than arranging details. I am well aware of how far this statement is at variance with popular opinion among mechanics, and of the very thorough knowledge of machine application and machine operation required in making designs, and mean that there are certain principles and rules which may determine the arrangement and distribution of material, the position and relation of moving parts, bearings, and so on, and that a machine may be built up with no more risk of mistakes than in erecting a permanent structure.

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