Forced Vibrations Experimentally Illustrated. 175 



pass to pendulums shorter or longer than this one, we 

 gradually change to like phase with the driver or opposite 

 phase respectively. Hence the horizontal ordinates of the 

 curve rapidly diminish from their maximum both because 

 the amplitude is less and the phase is not right to exhibit it 

 fully. The comparison of fig. 5 with fig. 2 makes this 

 point clearer. 



Special interest attaches to the instantaneous view shown 

 in fig. 6, and taken when the driving bob was at one end of 

 its swing. The responding bob of about the same length as 

 the driver is then at the centre, the much shorter responders 

 are nearly in phase with the driver, the much longer ones in 

 the opposite phase nearly. The resulting curve may be 

 approximately represented by 



Other powers of x would be needed to represent more pre- 

 cisely the exact curve for any given arrangement of the 

 experiment. This will be dealt with later. 



To exhibit these instantaneous effects to a single observer 

 stroboscopic vision is desirable. This was easily arranged by 

 using a card with a vertical slit in its centre, each end of the 

 card being carried by a pendulum. The period of this 

 pendulum should bear a simple relation to that of the driver. 

 In the actual experiments it was made of four times the length 

 of the driver, as that suited the position of a purlin in the 

 roof. The moving slit at the middle of its swing passes a 

 slit of the same size in a fixed card. The period of coin- 

 cidence of these slits can be shortened at will by increasing 

 the amplitude of the pendulums carrying the moving card. 

 For about six observers we may use a camera and focussing 

 screen instead of a fixed slit. For a larger audience the 

 same arrangement of fixed and moving cards may be used as 

 for a single observer, but the light from an arc-lamp should 

 be passed through the slits on to the bobs while the room is 

 otherwise in darkness. 



IV. Detailed Theory. 



Let us now pass from general ideas as illustrated by the 

 apparatus in fig. 1 to an experimental arrangement more 

 suitable for a strict quantitative examination of the phenomena 

 involved. Referring to equations (1) to (3) we see that in 

 the set of responding pendulums we naturally keep m 



