256.] THE PRINCIPLE OF VIRTUAL WORK. 157 



directly ; they must be controlled, guided, and transformed in various 

 ways to become useful, and this is done by interposing the machine 

 between the given driving force, commonly called the power, and the 

 force which is to do the final work, usually called the resistance, load, or 

 weight. We shall in general denote the " power " by P, the " weight " 



by Q. 



The term power is somewhat objectionable in this connection, being 

 here used to denote a force, while in Kinetics it is used for the rate of 

 doing work. 



255. The ratio Q/P of the weight to the power is called the mechani- 

 cal advantage of the machine. 



Under the action of the power P its point of application as well as 

 that of the weight Q is displaced. The corresponding work of the force 

 P may be called the available or total work; that of the force Q is 

 called the useful work. 



The ratio of the useful work to the total work is called the efficiency 

 of the machine. 



In all machines this efficiency is a proper fraction, owing to the fact 

 that the work done by P must balance not only the useful work, but also 

 the so-called wasteful work due to friction, stiffness of ropes, slipping of 

 belts, lack of rigidity, etc. 



256. For a more complete discussion of the principle of virtual work 

 the student is referred to MINCHIN'S Statics, Vol. I., pp. 78-96, 160-180, 

 and Vol. II., pp. 98-188; ROUTH'S Statics, Vol. I., pp. 146-197; 

 SCHELL'S Theorie der Bewegung und der Kr'dfte, Vol. II., pp. 166-211 ; 

 and J. PETERSEN, Statik fester Korper, iibersetzt von R. von Fischer- 

 Benzon, Kopenhagen, Host, 1882, pp. 114-124. 



