[UAWES] A REVERSIBLE PENDULUM 127 



make electrical contact in order to use a coincidence method of 

 evaluating the period. The bar carries two sliding weights E, E, 

 by which the period may be altered. These weights are accurately 

 equal in dimensions and weight and are intended to be used at equal 

 distances from the centre thereby maintaining the symmetry of 

 figure. By this construction the Centre of Gravity of the pendulum 

 remains unaltered as the weights are moved since the Centre of Gravity 

 of the two iveights is always the fixed poitit midway between the Centres 

 of Gravity of the individual weights. On account of this property of 

 the construction the relation between the squares of the periods about 

 either knife edge and the squares of the corresponding distances between 

 the centres of the weights \s rectilinear, as will be shown below (Section 4). 

 The determ.ination of the equality period from two pairs of observa- 

 tions is therefore a sim.ple one. 



3. Dimensions of Pendulum. 



124.5 cm. 



& S.) 



c. 



The dimensions were chosen so as to give a distance of 40 cm. 

 between centres of adjustable weights for equality of period. On 

 account, however, of the uncertain values of the weights of the knife 

 edges and their mountings, end caps, and cuttings in the making it was 

 not possible to calculate the exact position very accurately in the 

 designing stage. It turns out to be about 34 cm. as will be seen from 

 the records given below. 



4. Theory. 

 m is the mass of each sliding weight, wF its moment of inertia 

 about axis through its centre of gravity parallel to the knife edges. 

 If X is the distance from the C. G. of the weight to the Centre of 

 Symmetry of the pendulum, m^k'+x"^) is its moment of inertia about 

 parallel axis through the C. S. and 2m{k--{-x~) the moment of inertia 

 of the two^^sliding weights about this axis. 



Since the C. S. of the pendulum is also the C. G. of the pair of 

 weights and this point is distant L/2 from either knife edge (L being 



