176 



Prof. Barton and Miss Browning on 



and r constant throughout the series but vary the natural 

 periods. For quantitative work it is also desirable to keep f 

 constant throughout. 



Now the period depends upon s = mp 2 ~mg/x where x is 

 the length JK of the pendulum in question. Further, 

 F = m^x (inclination of JK) due to full amplitude of heavy 

 driving bob D. 



Now this inclination of JK (to the vertical) is the dis- 

 placement of J divided by the length JK = <2?. Hence to keep 

 F and / of same value for all the responding pendulums 

 we must have their inclinations equal for a given displacement 

 of D. And this is obviously obtained by arranging the bobs 

 so that the straight line AK passes through them all as shown 

 in fig. 2. For when the pendulum length is halved the dis- 

 placement of the point of suspension is halved also, and thus 

 the inclination retains the same value. 



Fio-. 2. 



Forced Vibration Apparatus with Equal Forces. 



Again, to have on the photographic plate coincidence of 

 all the points J we must have the camera-lens in the line 

 A JO when all is at rest. This coincidence is desirable so 

 that the length x for each pendulum shall reckon from a 

 definite invariable origin. Further, to have the displacements 

 of the bobs K measured from the same vertical line on the 

 plate, we must have the centre of the camera in the vertical 

 plane through ABCD when at rest. But this has already 

 been secured. 



