3 8o SCIENCE PROGRESS 



menced to execute vibrations. The amplitude of these vibra- 

 tions remained practically constant throughout the course of 

 the experiment. The point of support E of the simple pendulum 

 participated in the motion of the compound pendulum, and 

 thus the simple pendulum was set into vibration. A horizontal 

 scale not shown in the diagram was fixed up close behind the 

 thread parallel to the direction of motion, and the maximum 

 value of the amplitude read. The cylindrical weight was then 

 clamped in another position and the measurement repeated. 

 The initial angle of the compound pendulum was the same 

 in each case. 



The results are represented by the smooth curve in fig. 2. 

 The abscissae give the period of the compound pendulum, and 

 the ordinates the square of the maximum amplitude of the 

 simple pendulum. The square of the maximum amplitude is 

 plotted instead of the maximum amplitude itself, because the 

 former, not the latter, is proportional to the energy acquired 

 by the simple pendulum. The curve has a maximum at 

 2*05 sec. falling away rapidly on both sides of this. In the 

 experiment recorded in the diagram, the spring clip was 

 attached a distance of 6 cm. below the knife-edge. The 

 relative value of the different ordinates does not depend on 

 the position of D, but their absolute value does, i.e. if the 

 distance of D below the knife-edge is increased, the ordinates 

 of the curve would increase everywhere in the same ratio. 



After the experiment with the ping-pong ball was com- 

 pleted, a similar one was carried out with a simple pendulum 

 consisting of a small " marble " at the end of a thread. This 

 time the clip was attached at a point 4 cms. below the knife- 

 edge, and the period of the simple pendulum was 1*99 sec. 

 The results are represented by the dotted curve in fig. 2, but 

 on only half the vertical scale that the other curve is plotted 

 on. If they were plotted on the same scale, the maximum 

 ordinate of the dotted curve would be more than twice the 

 maximum ordinate of the smooth curve. 



Both the curves are of the same type, the difference being 

 that the dotted one is narrower. This is because the marble 

 offers less resistance to the air than the ping-pong ball. The 

 smaller the frictional resistance, the narrower the curve, and 

 consequently the more perfect the resonance. 



3. Now let us apply the curves shown in fig. 2 to the 



