16 TKENCHING AND SUBSOILING 



revolving in two sockets. Levers L are fixed through the 

 cylinder, and it is by acting on these levers that power is 

 applied. 



A rope or cable C wound OD the drum, supports a bucket, 

 the weight of which is the resistance to be overcome. The 

 friction of the axle-trees and the rigidity of the rope not 

 being taken into consideration, 



P, being the effort exerted tangentially at the extremity 

 of the lever L. 



/, the length of the lever, measured from the axis of the 

 cylinder. 



Q, the weight to be raised, or the resistance. 



r, the radius of the cylinder around which the rope is 

 wound ; it is shown in mechanics that 



P r r 



Q = T' orp = Q x T ; 



that is to say, that the motive power is to the resistance as 

 the radius of the cylinder is to the length of the lever, or, in 

 other words, that the motive power is a fraction of the re- 

 sistance equal to the ratio between the radius of the cylinder 

 and the length of the lever. The smaller r is in relation to 

 to /. the greater Q may be in relation to P. If for instance, 



r \ 



T To, 



we may, with an effort of 10 Ibs. raise a weight of 100 Ibs. 

 Practically, we must take into account the friction of the 

 axle-trees and the rigidity of the rope, so that the useful 

 resistance Q' overcome by the windlass, is a little less 

 than Q, which, theoretically, is in equilibrium with P. We 

 will see the importance of these passive resistances, also 

 called detrimental forces, in the machines we are going to 

 study. 



In mechanics we always lose in velocity what is gained in 

 force, and reciprocally. If the windlass equilibrates a great 

 resistance by a small motive power, it is only at the expense 

 of the velocity or rate. We see that the path traversed at 

 each revolution of the windlass by the moving power is 

 equal to 2 tr I; that traversed by the resistance is 2 ?r r. 

 These two paths traversed in the same lapse of time are, 

 therefore, in inverse ratio of the effort developed to the 

 resistance overcome. We may, with a moving force of 

 10 Ibs. raise 100 Ibs., provided r be ^ of /, but the weight, 



