Vibrations elucidated by Simple Experiments. 267 



masses o£ the bridle cords ACA, A'C'A', and connector GC 

 were negligible. Now for the higher values of the couplings 

 where the droops are very great this can hardly be the case. 

 Hence it is not surprising to find that the droop had to be 

 made (as shown in the Table) 173 cm. instead of the cal- 

 culated 171*5 cm. to give the exact 2 : 1 ratio. This arrange- 

 ment furnished fig. 10, in which the kink scarcely wanders 

 perceptibly. The board was also turned through a right 

 angle and left stationary while the pendulums were used as 

 Blackburn's pendulums. They thus gave simultaneously the 

 patterns in the right-hand top corner of the figure and 

 retraced them almost perfectly about ten times. 



The gradual change from the case of beats in fig. 1 to the 

 exact tone and octave of fig. 10 is very instructive. It also 

 shows the advantage of taking traces, for in watching the 

 motions of the intermediate cases the eye fails to realize 

 exactly what is happening, though the extremes are easy 

 to recognize. 



Several of the remaining traces for this pendulum are 

 for the same coupling, but are varied only by different initial 

 conditions: 



Thus fig. 11 has the bob held at zero while the other is 

 pulled aside, then both let go together. (See equations 

 (51)-(54).) In fig. 1 one is allowed to hang freely at rest 

 (but somewhat displaced), while the other is held aside and 

 then let go. (See equations (47)-(49).) Figs. 13 and 14 each 

 show simple vibrations instead of two superposed. Fig. 13 

 was obtained by starting with unlike equal displacements due 

 to a connecting thread, which was burnt when all was still. 

 Fig. 14 was obtained by swinging with the hands till the 

 amplitudes were equal and phases alike instead of opposite as 

 in the previous case. Pains were taken to draw the board 

 at the same uniform rate by scale and stop-watch in figs. 13 

 and 14. Thus the relation of periods 1 : 2 is correctly 

 exhibited along with the phases. 



Figs. 15 and 16 show for two important couplings the 

 initial conditions of double displacement, one bob pulled 

 aside the other hanging freely at rest as in fig. 12, but here 

 the board was moved before the bob was let go, as seen by 

 the traces. 



In every case in which we tested them the traces were 

 found to give a satisfactory agreement with the theory both 

 qualitatively and quantitatively. These tests were carried 

 out by plotting on squared paper the theoretical curves to 

 be expected and then comparing them with the sand-traces 

 obtained. 



