MECHANICS. 



TREATISE II. 

 ELEMENTS OF MACHINERY. 



CHAPTER I. Machines Power and 

 weight Principle of virtual veloci- 

 ties Simple Machines or Mechanic 

 Powers. 



(1.) NATURE has placed at the disposal 

 of man various mechanical agents, 

 endued with different kinds and degrees 

 of power. The weight of solid bodies, 

 and their momentum when in motion ; 

 the weight and pressure of liquids ; the 

 weight and pressure of air and other 

 gases; the elastic force of vapour raised 

 from liquids by heat ; the elasticity of 

 springs, and the muscular strength of 

 animals, furnish striking examples. In 

 applying these forces to'overcome resis- 

 tances, or to communicate motion to 

 bodies, it seldom happens that, without 

 some previous modification, they are 

 capable of accomplishing the end we 

 desire to attain. The power which we 

 may happen to have at our disposal 

 may not act in the proper direction, or 

 may not have that velocity or intensity 

 which suits our purpose ; and some con- 

 trivance must be found by which, in 

 transmitting it to the working point, its 

 direction, velocity, or intensity, may be 

 regulated in such a manner as to be 

 suitable to the purpose to which it is to 

 be applied. Such a contrivance is called 

 a Machine. 



(2.) Notwithstanding the infinite va- 

 riety of ways in which machinery is 

 employed, a'nd the great diversity of 

 ends which it appears to attain, yet it 

 will be found that every machine, 

 whether simple or complex,"can only be 

 designed to produce one or more ot the 

 three following effects: 1. To change 

 the direction of the moving power so as 

 to accommodate it to overcome a given 

 resistance, or to produce in some body 

 to which it is applied a given species of 

 motion. 2. To render a power which 

 has a certain velocity capable of pro- 

 ducing a different velocity in the work 

 to be performed or the body to be 

 moved. 3. To render a power of a cer- 

 tain intensity capable of overcoming a 



resistance or of exerting a force upon 

 the body to be moved of a different in- 

 tensity, and frequently of a much greater 

 intensity. 



(3.) In order to simplify the develop- 

 ment of the nature and properties of 

 Machinery, we shall consider the mov- 

 ing power, as well as the resistance to be 

 overcome, as represented by equivalent 

 weights ; that weight which is taken to 

 represent the moving force being techni- 

 cally called the power, and that which 

 represents the resistance being called 

 the weight. It is easy to conceive that, 

 whatever species of force the moving 

 power and the resistance may be, 

 weights equivalent to them can be as- 

 signed. Thus, if the moving power be 

 the elastic force of steam pressing upon 

 a piston, we familiarly say that the pres- 

 sure amounts to so many pounds per 

 square inch, meaning that it produces 

 the same effect in forcing the piston 

 through the cylinder as a weight 

 of so many pounds laid upon the 

 piston would produce. Again, it' the 

 resistance be that which timber offers to 

 the wedge which splits it, there is no 

 difficulty in conceiving a weight acting 

 against the wedge so as to offer an 

 equal resistance. We shall therefore 

 henceforward express the moving power 

 and the resistance to be overcome, 

 whatever be their nature, by the terms 

 power and weight. 



(4.) In transmitting the influence of 

 the power to the weight through the in- 

 tervention of a machine, it has various 

 resistances to encounter which oppose 

 its action, and which impair its effects. 

 Such are, for example, the roughness of 

 surfaces which move in contact, the 

 stiffness of cordage, the yielding or 

 flexibility of bars, and numerous others. 

 If the calculation of the effects of these 

 forces were introduced into the elements 

 of the science, and constituted a part of 

 our first investigations of the proper- 

 ties of machines, the investigations 

 would become- extremely complex, and 

 present difficulties which most students 

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