24 MR. J. H. POYNTING ON THE 



but was obliged to adopt the method described in this paper. 

 Stated generally^ it consists in treating the balance as a 

 pendulum. Knowing the nature of the pendulum (that is 

 its moment of inertia) and its time of vibration, we can 

 calculate what force acting at the end of one arm of the 

 beam will produce a given angular deflexion. It is, in fact, 

 an application to the common balance of the method which 

 has always been used with the torsion-balance when it has 

 been necessary to calculate the forces measured in absolute 

 measure. I cannot find any record of a previous applica- 

 tion of the method ; and as it might be of use in very 

 delicate weighings or in verifying the small weights in a 

 laboratory, I have thought it worth while to give a full 

 account of it. 



When small quantities of the second order are neglected 

 and the oscillations are of the first order, it will easily be 

 found that the equation of motion of the beam of the 

 balance is 



fMl'-+^:^\e + {2Vh + Mffk)e=ap, . . (i) 



where MI^ = moment of inertia of beam about central 

 knife-edge, 

 M == mass of beam, 



a =half length of beam, 



P=weight of either pan and the mass in it, 



A = distance of line joining terminal knife-edges 

 below the central knife-edge, 



A; = distance of centre of gravity of beam below 

 central knife-edge. 



j9 = small excess in one pan. 



6 = angular deflection in circular measure pro- 

 duced by p, 



^= gravity. 



