inexactness in a number of ways makes its appearance. It may be noticed too that this first problem of the fixed pulley, so far as concerns the theory of the motions involved in it, is already a very complicated one, as I shall show in the text later on.
The ideas by which alone the nature of a simple mechanism can be arrived at may be very complex, or in certain circumstances may be quite the reverse. But equally whether these ideas be simple or complex, if it be desired to examine and understand the simple apparatus scientifically, it is necessary to work through the whole succession of them, passing from each one to the next higher from which it was developed, until really general principles are arrived at. However difficult this may be, and however little use it may appear to have, it must be done; its omission by kinematists hitherto has caused the wreck of all their theories. What they have done is what I have already indicated as incorrect,—they have accepted the simple or apparently simple mechanism as it came from the hand of the inventor, whether he were a well-known person, or nameless in the traditions of the dawn of national history.
An examination of these hazy traditions gives the kinematist much subject for remark. Denying myself here the prosecution of this attractive subject, upon which I shall enter in some detail further on, I must dismiss it with one remark. Following back machines to the earliest forms in which they have been used in historic times, we find in different places contrivances of various kinds in use,—from somewhat complicated machines to the very simplest arrangements,—all of which must be called "machine." We are not yet in a position to discuss the criterion of the comparative difficulty of their invention; we require here only to note that they appear in various places independently of each other. The rollers upon which the Assyrian as well as the Egyptian builders moved their enormous stones are among these primitive machines; carriages of wood and metal, both for war and for transport, were possessed by the Egyptians, Babylonians and Indians in the remotest antiquity; water-wheels were in use in old Mesopotamia and in Egypt, as well as in China, India and Central Asia; toothed wheels were known to the Greeks, as were also the screw, the pulley, certain systems of levers, &c. Some of these arrangements have come down to us unaltered; others, however
