\ Il;l I'M, 



and one of the rods l.-'inir NJ m a horizontal ],. 



listened to it by an elastic -ining 



their middle jn.ints; determine the tension of this strr 



Let M" , .f the 



:. Sii])|M.se tin- system displace. I slightly s> that the 

 if rod descends vertically through a space ./. Then it 

 will be easily seen that the centre nt' gravity of each of the 

 t\v rods which arc adjacent t< the highest 



/j 



through a space -; and i n of gravity of each of the 



two rods which are adjacent to the lowest rod descends 



3x 

 through a space ; the point of application of the tension 



on the lowest rod descends through a space x. Therefore by 

 the principle of virtual velocities 



2TF? + 2TF + Wx-Tx = 0; 

 4 4 



therefore 7 7 =3TF. 



The mutual actions at the hinges disappear from the equation 

 furnished by the principle of virtual velocities, and thus the 

 required result is readily obtained. 



259. The following is the process by which we may de- 

 the equations of equilihrium of any system from the 

 principle of virtual vel>ci- 



Let P p P s , P s , ... denote the forces which act on a system ; 

 P.fyv Pji ir respective virtual moments for any dis- 



placement ; then, l.y the principle, 



P 1 V 1 + P,Sp, + P 8 S / 7.+ ... = (1). 



equation we proceed to develope. 



Let ctp ,, 7, be the angles which the direction of / 

 with the c<>-ordinate axes; x lt y^ z l the co-ordinates of the 

 point of application of 1\ ; then 



Spt = cos a^x, -f- cos /3fy l -f cos yf~ l (2) ; 



'-$ rigorously true, and similar equations hold for y? 2 , 



