and certain methods, all the forms and arrangements that are applicable to the desired purpose, from which he may select at pleasure. At present, questions of this kind can only be solved by that species of intuition which long familiarity with a subject usually confers upon experienced persons, but which they are totally unable to communicate

to others.

When the mind of a mechanician is occupied with the contrivance of a machine, he must wait until, in the midst of his meditations, some happy combination presents itself to his mind which may answer his purpose. Yet upon analysing the mental operations by which the nascent contrivance is gradually made to assume form and consistency, it will generally be observed, that the motions of the machine are the principal subject of contemplation, rather than the forces applied to it, or the work it has to do. For every machine will be found to consist of a train of pieces connected together in various ways, so that if one be made to move they all receive a motion, the relation of which to that of the first is governed by the nature of the connexion. The work which the machine has to do will require that the pieces appropriated to this work shall move with respect to each other in some given manner, and the forces applied to the machine to set it in motion must also move the piece which receives them in some other manner. Thus the question of contriving a machine by which a given kind of power may be made to perform given work, is reduced to a problem of mere motion,-to a question of connecting the pieces which receive the power and

those which do the work; so that when the first move according to the law required by the economy of the power, the last shall necessarily receive the motion which will enable them to do the work. There are, of course, many essential considerations of force and arrangement which must be entered into before the machine can be completed, but they admit of being abstracted in the first instance; and it is only by so doing that we can hope to create a science of mechanism. Yet this view seems to have presented itself but lately, with due clearness, to the minds of writers on this subject; and it may be interesting to trace the history of its rise and progress.

Apart from the writings on the science of Mechanics, the history of which is well known, a number of books have been produced from time to time, having for their subject Machinery. At first, however, the leading principle of classification in these is derived from the purpose for which each machine is designed, and accordingly these books are either confined to machines destined for one particular kind of work, as in the early treatises of Valturius (1472) and Agricola (1550) on warlike and mining machinery respectively; or else they are collections of machines classed and described with reference to the objects for which they are constructed; divided, for example, into machines for raising water, for grinding flour, sawing timber, and so on. The earliest of these collections are the treatises of Besson (1569), Ramelli (1580), Strada (1618), Zonca (1621), Branca (1629), Bockler (1662); and the list might be continued without interruption to the present

day*. The voluminous "Theatrum Machinarum" (1724) of Leupold, although it falls under the same description, yet in its first volume contains the first attempt to consider the parts of machinery separated from their work, and referred to the modifications of motion. And although these parts are made to follow the usual mechanical powers, and are mixed up with considerations of force, yet we find chapters on the crank, on cams, on machines for converting a circular motion into a rectilinear, or a back and forwards motion, and for converting a back and forwards motion into a continued circular motion; and so on. This must, in fact, be considered as the first attempt to produce a systematic treatise on Mechanism. The next step appears to have been made in 1794, by Monge, who, in planning the organization of the Ecole Polytechnique, proposed to devote two months of the first year of study to the elements of machines. "By these elements are to be understood the means by which the directions of motion are changed; those by which progressive motion in a right line, rotative motion, and reciprocating motion, are made each to produce the others. The most complicated machines being merely the result of a combination of some of these elements, it is necessary that a complete enumeration of them should be drawn upt." This enumeration formed the subject of part of his lectures, and was the basis of the two similar systems of Hachette, and of Lanz and Betancourt. The latter was finally

This list might be preceded by Vitruvius, Book x., the works of Hero and other Greek mechanists, &c. Vide Veterum Mathematicorum Opera. Par. 1693. + Vide Essai sur la Composition des Machines, par MM. Lanz and Betancourt, Par. 1808. p. 1.

adopted for the Ecole Polytechnique, and printed in 1808, under the title of "An Essay on the Composition of Machines." It was subsequently translated into English. Postponing for the moment the discussion of the system, we may observe, that Monge, in the above programme, distinctly proposes to study machines by treating them merely as contrivances for changing one kind of motion into another, apart from any considerations of force. We shall see presently, however, that this plan did not extend beyond the mere enumeration and description of the elements, without containing a provision for the calculation of the laws of the motion, or changes of motion produced. Ampère, however, appears to have contemplated the formation of a system that would also include these latter objects; for in his Essay on the Philosophy of the Sciences, published in 1834, we find it distinctly asserted, "that there exist certain considerations which if sufficiently developed would constitute a complete science, but which have been hitherto neglected, or have formed only the subject of memoirs or special essays. This science, (which he terms Kinematics,) ought to include all that can be said with respect to motion in its different kinds, independently of the forces by which it is produced. It should treat in the first place of spaces passed over, and of times employed in different motions, and of the determination of velocities according to the different relations which may exist between those spaces and times.

"It ought then to develope the different instruments by the help of which one motion may be converted into another,

so that, calling these instruments by the usual name of machines, this science will define a machine to be, not as usual, an instrument by means of which we may change the direction and intensity of a given force; but, an instrument by means of which we may change the direction and velocity of a given motion. The definition is thus freed from the consideration of the forces which act on the machine; a consideration which merely distracts the attention of those who endeavour to unravel the mechanism.

"To understand, for example, the wheel-work by means of which the minute-hand of a watch makes twelve turns while the hour-hand makes but one, why need we trouble ourselves with the force that sets the watch in motion? The effect of the wheel-work, so far as it governs the relative velocity of the hands, is the same, by whatever cause the motion may be produced, as, for example, when the minutehand is turned by the finger.

"After these general considerations relating to motion and velocity, this new science might pass on to the determination of the ratios that exist between the velocities of the different points of a machine, or generally of any system of material points, in all the movements of which the machine or system is susceptible; in a word, to the determination, independently of the forces applied to the material points, of what are called virtual velocities; a determination which is infinitely more comprehensible when thus separated from considerations of Force*."

* Vide Ampère, Essai sur la Philosophie des Sciences, 1835, p. 50.