332 nSTUAL M:LOCITIES. i-:x AMPLE. 



And since {(&c) f + ($y) f -f (82)'] * = 2p sin \0, 



X {(yn-*m) f + (zJ-a*) + (xm-yl)*}* = 2p si) 



or X {a- 1 + y* + **-(& + roy + n2) f j 4 = 2/>sin 0; 



fore X=0 ........................... (2), 



neglecting s and higher powers of 0. 



Suppose the body to be further displaced, so that cadi 

 particle moves over spaces a, b, c parallel to the co-ordinate 

 axes; if &c, By, &z denote now the u-hole displacement <>t' the 



particle whose original co-ordinates were x, y y z> we ha 



&x = (yn zm) + a, 

 $y = (zl-xn) + b, 

 Sz = (xm-yl) + c. 



^Multiply the six equations in Art. 73 by a, J, c, - 10, - 

 - n0, respectively, and add, then 



255. We shall illustrate the princ-iple of virtual , 

 in the solution of the folio win in. 



A beam in a vertical plain- rests on a post // jist a 



wall at J ; required the circumstances of equilibrium. 



Let the distance of B from the wall = I ; let G be the << 

 of gravity of the beam ; AG = a; and the inclination of the 

 beam to the wall = ^. The reaction (P) of the post at /; is 



perpendicular to the surfaces in contact, and therefore to the 

 team; the reaction (R) of the wall is perpendicular to the 

 wall for the same reason ; let IT L-- the weight of the beam. 

 may consider the beam in equilibrium under the action 

 of P, R, W t and suppose tl. -/all remu 



