MECHANICS. 



ed by any algebraic equation ; and so 

 stands contra-distinguished from algebraic 

 or geometrical curves. 



Leibnitz and others call these me- 

 chanical curves transcendental, and dis- 

 sent from DCS Cartes in excluding" them 

 out of geometry. Leibnitz found a new 

 kind of transcendental equations, where- 

 by these curves are defined ; but they 

 do not continue constantly the same 

 in all points of the curve, as algebraic 

 ones do. 



MECHANICS, is the science which 

 treats of the laws of the equilibrium and 

 motion of solid bodies ; oi the forces by 

 which bodies, whether animate or inani- 

 mate, may be made to act upon one ano- 

 ther; and of the means by which these 

 may be increased, so as to overcome such 

 as are most powerful. As this science is 

 closely connected with the arts of life, 

 and particularly with those which existed 

 even in the rudest ages of society, the 

 construction of machines must have been 

 practised long before the theory upon 

 which their principles depend could have 

 been understood. Hence we find in use 

 among the ancients, the lever, the pulley, 

 the crane, the capstan, and many other 

 simple machines, at a period when mq- 

 chanics, as a science, were unknown. In 

 the remains of Egyptian architecture are 

 beheld the most "surprising marks of me- 

 chanical genius. The elevation of im- 

 mense and ponderous masses of stone to 

 the tops of their stupendous fabrics, must 

 have required an accumulation of me- 

 chanical power, which is not in the pos- 

 session of modern architects. We are in- 

 debted to Archimedes for the foundation 

 of this science : he demonstrated, that 

 M hen a balance with unequal arms is in 

 equilibrio, by means of two weights in its 

 opposite scales, these weights must be 

 reciprocally proportional to the arms of 

 the balance. From this general princi- 

 ple the mathematician might have deduc- 

 ed all the other properties of the lever, 

 but he did not follow the discovery 

 through all its consequences. In demon- 

 strating the leading property of the lever, 

 he lays it down as an axiom, that if the 

 two arms of the balance are equal, the 

 weights must be equal, to give an equi- 

 librium. Reflecting on the construction 

 of the balance, which moved upon a ful- 

 crum, he perceived that the two weights 

 exerted the same pressure on the ful- 

 crum as if they had both rested on it. He 

 then advanced another step, and consid- 

 ered the sum of these two weights as 

 combined with a third, and then the sum 



of the three with a iburth, and so <" 

 perceived that in every such combination 

 the fulcrum must support their united 

 weight ; and, therefore, that there is in 

 every combination of bodies, and in every 

 single body which may be considered as 

 made up of a number of lesser bodies, a 

 centre of pressure or gravity. This disco- 

 very Archimedes applied to particular 

 cases, and pointed out the method of 

 finding the centre of gravity of plane sur- 

 faces, whether bounded by a parallelo- 

 gram, a triangle, a trapesium, or a para- 

 bola. See CENTRE of gravity. 



Galileo, towards the close of the six- 

 teenth century, made many important 

 discoveries on this subject. In a small 

 treatise on statics, he proved that it re- 

 quired an equal power to raise two dif- 

 ferent bodies to altitudes, in the inverse 

 ratio of their weights, or that the same 

 power is requisite to raise ten pounds to 

 the height of one hundred feet, and 

 twenty pounds fifty feet. It is impossible 

 for us to follow this great man in all his 

 discoveries. In his works, which were 

 published early in the seventeenth cen- 

 tury, he discussess the doctrine of equa- 

 ble motions in various theorems, contain- 

 ing the different relations between the 

 velocity of the moving body, the space 

 which "it describes, and the time employ- 

 ed in its description. He treats also of 

 accelerated motion, considers all bodies as 

 heavy, and composed of heavy parts, and 

 infers that the total weight of the body is 

 proportional to the number of the parti- 

 cles of which it is Composed. On this 

 subject he reasons in the following man- 

 ner : " As the weight of a body is a power 

 always the same in quantity, and as it 

 constantly acts without interruption, the 

 body must be continually receiving from 

 it equal impulses in equal and successive 

 instants of time. When the body is pre- 

 vented from falling, by being placed on a 

 table, its weight is incessantly impelling 

 it downwards ; but these impulses are de- 

 stroyed by the resistance of the table, 

 which prevents it from yielding to them. 

 But where the body falls freely, the im- 

 pulses which it perpetually receives are 

 perpetually accumulating, and remain in 

 the body unchanged in every respect, 

 except the diminution which they expe- 

 rience from the resistance of the air : 

 hence it follows, that a body falling free- 

 ly is uniformly accelerated, or receives 

 equal increments of velocity in equal 

 times. He then demonstrated that the 

 time in which any space is described by 

 a motion uniformly accelerated from rest. 



