MECHANICS -MACHINERY. 



'T^HE application of the laws of motion and 

 _L forces to objects in nature, or contrivances 

 in the arts, constitutes the branch of Natural 

 Philosophy usually treated under the head ME- 

 CHANICS, MECHANICAL POWERS, or ELEMENTS 

 OF MACHINERY. 



GENERAL DEFINITIONS. 



It is seldom that a force is made to act directly 

 on the body that is to be moved, or the resistance 

 that is to be overcome. In raising coals from a 

 coal-pit by steam-power, the expanding steam is 

 not put below the load of coals, and made to blow 

 it up the shaft, as it were. The steam first raises 

 a piston, which then moves a beam, which in its 

 turn moves a rod connected with a crank ; and 

 thus the motion is propagated from one piece of 

 matter to another until it arrives at last at the 

 load. During this transmission the force under- 

 goes various changes which make it act more 

 advantageously for the end in view. 



Instruments thus interposed between the moving 

 power and the resistance, with the view of chang- 

 ing the direction of the force or otherwise modi- 

 fying it, are called machines (Gr. mechane, con- 

 trivance) ; and to explain the laws of their action 

 and their various applications forms the subject of 

 the present treatise. Mechanics, in the narrower 

 sense of the term as here used, is understood to 

 treat of the abstract theory of machines, or those 

 general principles, mathematical and physical, on 

 which their action depends; the special applica- 

 tion of these principles is the subject of Practical 

 Mechanics, Mechanism, or Machinery. 



Machines are of various degrees of complexity ; 

 but the simple parts or elements of which they are 

 all composed are few. These are strictly only 

 three in number namely, i. The Lever; 2. The 

 Pulley; and 3. The Inclined Plane. These may 

 be called the Primary Mechanical Powers ; and 

 from two of them, the Lever and Inclined Plane, 

 other three are formed, as follows : i. The Wheel 

 and Axle, from the Lever; 2. The Wedge, from 

 the Inclined Plane; 3. The Screw, from the In- 

 clined Plane. These may be called the Secondary 

 Mechanical Powers. The six altogether form the 

 most usually occurring elements of complex ma- 

 chinery. 



THE LEVER. 



When a box, or other heavy body, is lifted in 

 the hands, the power is applied to the weight 

 directly ; it acts without the intervention of 

 machinery. But when a bar is used, as repre- 

 sented in the figure, resting on a support F, we 

 have an instance of a machine interposed between 

 the power and the weight. The effect of this 

 machine is to modify the power in more ways than 

 one. When the hand lifts the weight directly, it 

 pulls upwards at the same point and with exactly 

 the same force with which the weight pulls down- 

 14 



wards. But with the machine the hand pushes or 

 pulls downwards as well as the weight, and one 

 effect of the solidity of the rod and of the fixed 

 prop is to convert the downward force at P into* 



Fig. i. 



an upward force at the other end. And not only 

 this, but when the prop is nearer to the weight 

 than to the power, the power seems to be in- 

 creased ; a downward pressure of one pound at P, 

 causes an upward pull of, it may be, two or more 

 pounds at W. 



A rod or bar used in this way is called a lever, 

 from the French word for 'to raise.' The point 

 of support is called the fulcrum, and the distances 

 from the fulcrum to the points of the lever where 

 the power and the weight act, are called the arms 

 of the lever. The lever is the most important of 

 the simple machines, or mechanical powers, and, 

 in its various modifications, enters most extensively 

 into the composition of complex machinery. The 

 law by which it acts, therefore, deserves attentive 

 consideration. To comprehend thoroughly the 

 nature of the advantage conferred by the lever, is 

 to comprehend the fundamental principle of all 

 mechanics. 



In treating of the theory of the mechanical 

 powers, certain assumptions are made. Thus the 

 object of the lever is to move the weight ; but the 

 question really examined in the theory of the lever, 

 is not what power is necessary to move a certain 

 weight, but what power is necessary to balance it ;. 

 what force at P will just keep W at rest, or sus- 

 pended, if unsupported below. The subject is 

 thus considered as belonging to Statics, or the 

 doctrine of forces in equilibrium. It is obvious 

 that when P and W once balance one another, the 

 least additional force to P will suffice to begin 

 motion. Again, it is assumed that machines are 

 themselves without weight ; that the rod or lever, 

 for instance, is a mere rigid line. This is done for 

 simplicity ; in practice, the weight of the bar 

 itself has an effect on the resistance, and must be 

 allowed for. Another assumption is, that machines 

 move without friction. A certain amount of force 

 is always necessary to turn the lever about its 

 axis or point of support ; but this we do not take 

 into the account. The amount of power consumed 

 in overcoming friction, and the means of diminish- 

 ing it, are questions for practical mechanics. 



Law of the Lever. When the fulcrum of a lever 

 is placed as iri the annexed figure, so that one of 

 the arms, FA, is double the other, FB, it is found 

 by experience that a weight of one pound at P 



