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 which pressure or motion may be transmitted from one point to another, and altered both in magnitude and direction."

Goodeve (1860). "A machine may be defined to be an assemblage of moving parts, constructed for the purpose of transmitting motion or force, and of modifying, in various ways, the motion or force so transmitted."

Rankine. "Machines are bodies, or assemblages of bodies, which transmit and modify motion and force. The word 'machine,' in its widest sense, may be applied to every material substance and system, and to the material universe itself; but it is usually restricted to works of human art, and in that restricted sense it is used in this treatise."

Todhunter. "Machines are instruments used for communicating motion to bodies, for changing the motion of bodies, or for preventing the motion of bodies."

Magnus (1875). "A machine is an instrument by means of which a force applied at one point is able to exert, at some other point, a force differing in direction and intensity."

I conclude that the authors, some of them very distinguished men, whom I have cited, can hardly have been satisfied with their own definitions, which, indeed, ought not strictly speaking to receive that name at all, so far as the machine is concerned. Almost without exception the machine is an "instrument," a "contrivance," an "assemblage of bodies," by means of which something is done or can be done. This something is the thing defined in each case, the machine itself is quite left out. It is instructive to note also how completely the idea of the " ," which will be found presently to be of absolutely vital importance, is absent from most of them. Prof. Rankine recognised it, (although it is excluded by his definition, if "a body" can be a machine), but it is expressly or tacitly excluded by most of the other writers.]

The reader must not be surprised that I have placed here beside each other names of such very various degrees of importance, nor that I have omitted others which are so well known, e.g.,, and among the older authors   and others. These authors give no definition of the machine. They consistently avoid it, going at once into classification and description. I have given so many examples in order to show the more clearly that no authoritative definition has ever yet been arrived at.

The older definitions, much more naïve than the modern attempts to grasp a multitude of phenomena, are by no means uninteresting. Leupold, for example, says (Theatr. Mach., 1724):—"A machine or engine is an artificial work, by means of which some advantageous motion can be obtained, and something moved with a saving, either in time or in force, which would not be otherwise possible." [The word, which occurs in this old definition, and which I have represented (I cannot say translated) by engine, continued in use in Germany until well on in the present century. Prof. Reuleaux traces it back to an adaptation by Zeising, 1607, of an old definition of Vitruvius.]