MACHINES. ROBEKVAI.’s BALANCE.
79
Q./IC- W.CG-P.CN=0;
w
CN+ — .CG
Take the point D, so that CD = — CG;
Now let the arm DB he graduated by taking Da x , Z)a 2 ,
Da 3 , .equal respectively to AC, 2AC, 3AC, .let the
figures 1 , 2 , 3 , 4 , .be placed over the points of graduation,
and let subdivisions be made between these. Then by ob-serving the graduation at N we know the ratio of Q to P;and this latter being a given weight we know the weight of Q.In this way any substance may be weighed.
99- There is a remarkable balance called after its inventorRoberval’s Balance: a representation of it is given in fig. 35 .DC' is a frame of which the opposite sides are equal, and theextremities are connected by pins at D, C, D\ C’ so as toallow of free motion: this frame is supported by a standEE'A, being connected to it by pins at E and E' so as to allowof free motion about those points: EE' must be parallel to DCand D'C', but not necessarily equi-distant from them: armsare fixed at right angles to the sides DD', CC' to supportweights Q and P. The peculiarity of this machine is, that ifP and Q balance in any given position on the horizontal arms,the equilibrium will remain undisturbed if we shift P or Q orboth of them along their arms in either direction: also if wepush one arm down and consequently raise the other the wholewill remain at rest in the position in which it is left. Weshall prove these facts, and explained the paradoxical cha-racter of the machine in the Chapter of Problems. We mayhowever easily prove by the Principle of Virtual Velocitiesthe facts mentioned above, though the paradox will not beremoved.