APPLICATION OF GRAPHIC METHODS 273 



machines, it has been found necessary to begin by some ele- 

 mentary definitions. 



2. Elements of Machines. All machines consist of parts so 

 joined that any change in the force with which one part presses 

 against another will produce some change in the force with 

 which the other parts are pressed or held together. This con- 

 dition obviously holds good when the parts are rigid, and it 

 constitutes the test whether flexible ties or elastic fluids form 

 part of a given machine. 



A loose coil of rope cannot by this definition form part of a 

 machine, but a rope is part of a machine, whenever a change in 

 the tension of the rope changes the pressures or tensions between 

 other parts of that machine. Similarly, steam or water forms 

 part of a given machine whenever a change in the pressure of 

 that steam or water changes the force exerted between ether parts 

 of that machine. This relation between the parts of a machine 

 is dynamic, and is more general than the kinematic relation 

 which exists between the rigid or inextensible parts of a machine. 

 A definite position or motion of one part of a machine is not in 

 every case accompanied by a definite motion or position of 

 another part, irrespective of the forces in action, neither does 

 the same relative position of all the parts of a machine neces- 

 sarily imply the same forces between the parts, but a change in 

 the force exerted between any two parts always implies a 

 change in the forces between the other parts. 



The word element will in this paper be used to designate the 

 continuous parts of machines. Each solid element is a part 

 which is continuous in respect that no portion can slide upon or 

 break away from another portion in immediate contact with it. 

 Any rigid bar or structure in a machine is an element, as, for 

 instance, the connecting rod of an engine, the cylinder and bed 

 plate, the crank and fly-wheel. A belt between two pulleys, or 

 a rope on an axle, when these form parts of machines, are sepa- 

 rate elements. A slack belt or a slack rope forms no part of a 

 machine, since it does not fulfil the first condition of altering 

 the force at one end when the tension is altered at the other. 

 A continuous fluid forming part of a machine will be called a 

 fluid element. ,A portion of fluid is continuous when a change 

 of pressure at one place is transmitted by the fluid so as to change 



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