72 THE HUMAN MOTOR 



As to the condition of equilibrium, the work done by the power 

 for a virtual displacement corresponding to the angle a will be 



T, = moment of P X angle a = P X A/>a. 

 The virtual work of the resistance will be : 



T p = moment of Q X a = Q X Ar a. 

 According to Alembert's theorem. 



P X Aa = Q X Ara, 

 or, calling the arms of the lever / and /' 



P /' 

 PI = Q/', or again Q=J' 



which is expressed thus : the motor work P/a is equal to the re- 

 sistant work Q/a, or the moment PI is equal to the resistant 

 moment Ql, or, finally, the power and the resistance vary in 

 inverse ratio to the arms of the lever. As a result of this last ex- 

 pression, HI = IW, the power could be 10 times smaller than the 

 resistance and equilibrium 

 would be maintained. The ^?/ 



paths traversed vary inversely 

 as the forces, whence the pro- / *\^ 



verb, "What is gained in ^./ ^\ K* t^/ 



force is lost in speed " (Gal- / """""".... r-^ 



ileo). Force is also gained in B j ' "'-'i->b 



levers of the second order, ^ 



because there the power al- I 



ways acts on an arm longer ^ 



than that of the resistance. Fl - 87 - 



But there is a loss of force in 



levers of the third order where the lengths of the arms are 



reversed. It will be noted that, in this last case, the machine 



displaces the resistance with an amplitude which is inversely 



proportional to the length of the arm to which the power is 



applied. If the power acts at the position P a displacement 



BB ' of the resistance results, but if the power acts at the position 



P lt the displacement BB X will be much greater (fig. 87). It will 



be understood that to realise this increased amplitude, it will be 



necessary to lose in force. 



52. (2) The Inclined Plane. This is a rigid plane which is pre- 

 sumed to be perfectly smooth. The load (resistance Q) placed 

 on the plane has a normal component N, and a component 

 parallel to the plane, F. The power P, to balance the load, will 

 be : P = F. It is easy to see that F depends on the angle a, 

 or the inclination of the plane, then 



F = Q sin a. 



