CM MECHANICS. 



\ag from the object to the spot to which the Utter U to be raised be 

 formed, and the object am be pUced on it* foot, the force of gravity in 

 the vertical direction being resolved into two forces, one of which U 

 destroyed by the reaction of the plane, the other may be overcome by 



motive power less In intensity than that which would be required if 

 a direct application of force were made ; in fact, the force which will 

 lufflce for the attainment of the end diminiahea in proportion aa the 

 length of the plane U greater. 



The manlier of overcoming a resistance, which is specified in this 

 example, will serve also to illustrate the well known fact that in every 

 application of a mechanical contrivance to overcome a resistance, as 

 much advantage is lost in respect of time or space as is gained in 

 respect of power. For it is evident that, in order to raise the object 

 vertically through a space equal to the height of the plane, it would be 

 necessary to move it over a space equal to the length of the plane ; that 

 is, through a space which bears the same ratio to the vertical height as 

 the weight of the object bears to the power required to move it up the 

 plane. 



An account of the applications of the mechanical powers in the con- 

 struction of complex machines would involve descriptions of most of 

 the engines by which human labour is abridged or dispensed with ; 

 some of the most typical of these are referred to under MACHINE, 

 where the reader will also find a reference to works of authority on 

 the subject. 



In determining the efficacy of the mechanical powers it is evidently 

 necessary to consider their parts aa mathematical lines, to assume that 

 the axles are without friction and cords without rigidity, so that a 

 perfect equilibrium may subsist in the machine itself before the moving 

 power is applied. TJie most simple lever, for example, of a physical 

 kind, is a rod of wood or a bar of iron, the arms of which, on opposite 

 aides of the fulcrum, are of unequal weights ; and, in order to reduce 

 such a lever to a state from which the exact relation between the 

 opposing powers may be found, the weight of each arm must be com- 

 puted, and being, in imagination, applied at the centre of gravity of 

 the arm, the product of the weight multiplied by the distance of the 

 centre of gravity from the fulcrum is to be added to the momentum of 

 the weight actually applied to the same arm of the lever. The sums 

 of these momenta, when the actual machine is in equilibrio, serve to 

 determine the correct relation between the opposing powers. The 

 conditions of equilibrium being determined, any excess of the motive 

 power above that which enters into those conditions will evidently 

 overcome the resistance, or produce motion in the machine. 



MECHANICS is the science in which are investigated the actions of 

 bodies on one another, either directly or by means of machinery. 



These actions may be simple pressures without motion, as when one 

 body being supported in any manner, another is placed upon it, either 

 vertically or in some oblique position ; or they may be such as are 

 accompanied by motion, and these may arise either from the mutual 

 attractions which all bodies in nature exercise upon each other, or 

 from the collisions of bodies in motion with others which may be 

 previously in motion or at rest. 



The term is particularly applied to the mutual actions of solid 

 bodies : the actions of fluids on solids form, in part, the subjects of 

 HYDROSTATICS and HYDRODYNAMICS ; but these, as well as pneumatic*, 

 are now frequently included under the general name mechanic!. Wh< n 

 bodies an at rest, and the actions are such as to maintain them in that 

 state, the laws of the actions constitute that branch which is called 

 STATICS ; but when motion is concerned, the laws and phenomena 

 constitute what is called DYNAMICS. 



In all the branches of general mechanics the investigations are 

 founded on experiment and are conducted by geometrical or alge- 

 braical processes : hence the science forms one of. the departments of 

 experimental philosophy, and also of mixed mathematics. This last 

 denomination is applied to mechanics because in the latter are involved 

 several qualities of bodies which do not enter into the researches of 

 pure science, such as matt or quantity of material, inertia, hardntM, 

 tlattialy, lime, tjiace, and power or force. The last-mentioned term is 

 used to ex proas the cause of the actions of bodies on one another ; but 

 we have no other conception of it than that it is productive of motion 

 or of a tendency to motion, or that it arrests an actual motion or renders 



tendency to motion ineffectual. When opposing force* act on a body 

 so as to destroy each other's effects and keep the body unmoved, that 

 body is said to be in a state of equilibrium ; and this state is distin- 

 guished from that of mere rest, since the latter implies the absence of 

 any cause by which the body might change its place. 



The invention of simple machines for moving masses of any material 

 which it might be beyond the unaided power of man to transport to a 

 distance, must have taken place in the earliest ages of the world. 

 Human ingenuity would readily suggest the application of a rod or bar 

 of wood or iron, for the purpose of lifting a heavy body from the 

 ground ; and very little experience would suffice to show that rolling 

 or pushing a block of stone up sloping ground was a much easier ope- 

 ration than that of raising it vertically by the strength of men's arms. 

 Thus may have ariwn the employment of the lecer and incltnfd plane; 

 and from these, subsequently, the tclictl and aide, the pulley, the veJijc, 

 and the ernr, were derived. The simple means here indicated would 

 be sufficient, with the aid of manual labour, to build up the most 

 iir cyckipeaa edifice ; aad even the vast materials which form the 



MECHANICS. us 



roofs of the Egyptian temples may have been raised to their places by 

 means of inclined planes, formed of earth for the purpose, on the 

 exterior of the walls, and afterwards removed. 



The steps by which the art of constructing machines advanced have 

 not been distinctly recorded ; and the work of Yitruvius on archi- 

 tecture is almost the only source whence can be obtained an account 

 of such as were in use in and before the time of that engineer (the age 

 of Augustus or Vespasian). From the descriptions there gi- 

 appears that among the mechanical powers then in use were the lever, 

 the windlass, and the assemblage of pulleys. Vitruvius also mentions 

 some ingenious contrivances for transporting heavy blocks of stone 

 from the quarries, and a f arcing-pump, the invention, of which he 

 ascribes to Ctesibius, for supplying the public fountains. He describes 

 a complex machinery, consisting of ichetlt driving each other by o/.< or 

 te-tli, which was applied to carriages or ships for the purpose of 

 measuring the distances travelled or sailed ; and he enters fully into 

 the construction of enyiat* for throwing darts or masses of stone. The 

 muicular itrenyth of men was then employed as a moving power in 

 turning mills : whreli impelled by rirer currenli acting on float-boards 

 ) gave motion to machinery for grinding corn ; and vhtdt 

 turned by men walking on them were used for raising water by buckets 

 or otherwise. Yitruvius generally mentions the names given by the 

 Greeks to the machinery ; and it might, without great risk of error, 

 be presumed that much of that which he describes was in use among 

 the latter people at, or even before, the time when the Parthenon wan 

 raised. There are no distinct intimations of the existence of mnctmillt 

 till the 12th century. The expansive force of tteam can only be said 

 to have become a moving power at the end of the 17th centin 

 then it was employed merely to raise water. Its general applies 

 machinery must be dated from the year 1768. 



In tracing the progress of discovery concerning the mathematical 

 theory of mechanical action, we shall have little to notice till we come 

 to the 16th century ; for the ancients, who devoted themselves v 

 much ardour to the researches of pure science, almost entirely neglected 

 the application of the latter to subjects which appeared to them to 

 terminate in mere practical utility. It must be observed li 

 Aristotle, who left no department of nature untouched, has not; 

 his mechanical questions, the equilibrium of unequal weights on the 

 unequal arms of a balanced lever, though he gives a very unphilo- 

 sophical reason for the fact. But in his ' Physics ' he states correctly 

 that if two forces move with velocities reciprocally proportional to 

 their intensities, they will exert equal efforts : this may apply to a 

 well-known property of the lever, but it may have been meant to refer 

 only to the effect of two unequal bodies moving with unequal velocities, 

 and striking each other or a third body. 



Sicily enjoys the honour of having given birth to the first philosopher 

 who can properly be said to have been a theoretical mechanician : we. 

 allude to Archimedes, who died about 212 B.C., and in whose works 

 there is direct evidence of an effort to determine the principle of 

 equilibrium in machines. Commencing, in the treatise whose Latin 

 title is ' De ^Equiponderantibus,' with the axiom that two equal weights 

 balance each other on a lever (of uniform dimensions), when at equal 

 distances from the fulcrum, he supposes the weights to be divided into 

 an equal number of equal parts, and that the parts are removed to 

 equal distances from the point of support ; observing then that the 

 equilibrium still subsists, lie proceeds, by the method of exhaustions, 

 to show that it always will take place provided the bodies are inversely 

 proportional to their distances from the fulcrum. Archimedes thence 

 concludes that there must exist in every one body, considered as an 

 assemblage of smaller bodies, a centre of force (that is, a centre of 

 gravity) corresponding to the fulcrum in the former case ; and he pro- 

 ceeds, by the analysis of that day, to investigate the seat of the centre 

 of force in a triangle, a parabola, and a paraboloid. 



This philosopher has obtained celebrity by the contrivances which 

 he is said to have adopted for the defence of Syracuse. No precise 

 account is given of the machinery which he employed to raise up and 

 destroy the galleys of the enemy, and the effects are probably exagge- 

 rated. The vessels must have been close to the walls, and it is con- 

 ceivable that, by hooks at the ends of chains which were suspended 

 from levers on the ramparts, the rigging, or some parts of the turrets 

 erected as usual on the decks, in order to enable the assailants to pass 

 over the parapets, might be caught ; then, the levers being raised by 

 the force of men or otherwise, the vessels or the turrets would be easily 

 overturned. 



During about 1800 years, which elapsed between the time of Archi- 

 medes and that of Cardan, we have no other notices concerning the 

 theory of mechanics (beyond those which occur in the writings of the 

 former mathematician), than such as are contained in the ' Mathe- 

 matical Collections ' of Pappus, which amount merely to a statement 

 that the ancients had reduced the theory of every machine to that of 

 the lever, and an unsuccessful attempt to explain the cause of the 

 equilibrium of a body on an inclined plane. It is remarkable moreover 

 that both Cardan and, subsequently, the Marquis Ubaldi (the hitter of 

 whom published, in 1(77, a treatise in which lie explains at length the 

 combinations of pulleys, and reduces their theory to that of the lever) 

 should also have given erroneous solutions of the problem concerning 

 that equilibrium. The discovery of the true theory of the inclined 

 plane was however, about the same time, made by Stcvinus, a native 



