VIRTUAL VELOCITIES EXAMPLE. 



Now the ol m might be, solely to deter* 



!' r<juilil>rium, or also to det /' and 



to determine both P and R and also 



\Vc shall solve the problem by 



H under these four suppositions, 



i the met IKK! of proceeding to as to avoid 



us possible according to the nature of the 



(1) Suppose the position of equilibrium only required. 

 Wo must then give the beam a small arbitrary geoin 

 motion .< unknown pressures P and R shall not 



; the beam must 

 .;iin in contact with the wall and the post, as 



Let $0 be t' rise of 6 owing to t ' icmirnt. 



of O above the horizontal straight lin<- 

 igh /?, (or r), before displacem 



t after displacement is found by changing int<> 

 0+0 in this expression ; therefore, the vertical space described 

 by G or os 



-acos 



l>y the principle of virtual velocities, TFoz 0; therefore 



i-asin'0-0, 

 and this determines the position of equilibrium. 



(2) But suppose we wish to find the pressure P as well 

 as the po- ^ 



must in this case move the beam off the post, in order 

 that the virtual velocity of B with respect to /* may not 

 vanish, and cons, /'not disappear as in the first 



Let jLl'-c, and let, SB before, $0 be the change of 0. 



