RESISTANCE OF MATERIALS 77 



56. (6) Screws. A screw engages in its n at by a rotary move- 

 ment. It advances through a linear distance equal to the pitch 



h for one complete turn 2^R. It will advance by h X -^5- or 



OC-tv 



a.h 



7> for a fraction of a turn aR, corresponding to the angle a so 



that the work done by the power will be : 

 P X R X oc 



if the lever of action is the radius R ; the resistant work ' will 

 be: 



The condition of equilibrium gives : 



PaR = QOL~ ; whence P = Q h 



Thus the power needed will be considerably reduced by employing 

 a long lever and a screw with a fine thread. 



57. Industrial Machines. The machinery employed in industry 

 is composed of simple machines. Their aim is the execution of 

 certain work, and they comprise, as a rule, three parts. 



(1) The receiver on which the motive force acts. That force 

 is a pressure ; thus the pressure of steam is a motive force, 

 whilst the steam itself, that is to say, the agent, is the motor 

 (latin movere, to move). The motor is, often, a machine called 

 a prime mover put into touch with the receiver or recipient 

 machine. From this is derived the name of motors, given to 

 engines which develop the power or motive force. 



According to the form oi energy utilised, engines may be classi- 

 fied as heat, hydraulic, pneumatic, electric, elastic or gravitational. 

 Live motors (man and animals) use muscular force, but the nature 

 of the agent which produces this force is not known for certain 

 (^345). 



(2) The operator, or the tool, is that part of a machine which 

 does the actual work. The tool is directed to the result which 

 it is desired to obtain, its movement being determined by that 

 direction. It is if it can be said " blind " compared with the 

 intellectual movements of man and animals. 



(3) Mechanism transmits the movement successively, from 

 the receiver to the operator. 



58. The principle which regulates the working of machines 

 is that of " vis viva" ( 30). Let a machine be in movement from 

 the instant ^ to the instant t 2 . In that interval, the powers have 

 done work T m and the resistances have done work T r , and it is 



