Vibrations elucidated by Simple Experiments. 265 



the cord and lath pendulum assume simpler forms. It is 

 particularly noticeable that the couplings in the two cases 

 are then given by 



7 2 = /3 2 P/Q (101) 



and 7 2 =* 2 P/Q (102) 



thus reducing to the same form for each type of pendulum. 



VIII. Experimental Methods and Results. 



Double-Cord Pendulum. — This pendulum was arranged 

 with its bobs near the floor, along which a black board on 

 wheels was slowly pulled by cords so as to receive sand- 

 traces. The board with the sand-traces was then placed on 

 the floor at the foot of a rising stand carrying a camera by 

 which the photographs were taken. 



The relations were calculated from the theory already 

 given so as to obtain any desired values of the couplings. 

 The total height BD (see fig. 1) was 229 cm. The results 

 are shown in Table I. 



Table I. — Double-Cord Pendulum. 



Coupling 



Ratio 

 CD : BC, or 



l- 7 



Ratio 

 CD : BD*, or 



£ _ 2y 

 1+/3 1+7* 



Actual Droop 

 CD* for 



Frequency 

 Ratio 



Amplitude 

 Ratio when 

 bob is struck. 



y- 



BD=229 cm. 



!=V(l+/3). 



5=(1+0T*. 



Per cent. 







cm. 







5 



2/19 



0095 



21-81 



ro5i 



0-952 



10 



2/9 



0-182 



41-63 



1-105 



0-905 



15 



6/17 



0-261 



59-77 



1-163 



0-860 



20 



1/2 



0-333 



76-33 



1-225 



0-816 



25 



2/3 



0-400 



9160 



1-291 



0-775 



33^ 



1 



0-500 



114-5 



1-414 



0-707 



40 



4/3 



0-571 



130-86 



1-527 



0654 



50 



2 



0-667 



152-7 



1-732 



0-577 



60 



3 



0-750 



171-5 

 Length 



2 

 Found to give 



0-500 



>60 







173 



2 





* For Laboratory work it would be convenient to have a lath of length BD 

 with the positions of C marked on it for each desired coupling. 



Plate Y. shows sixteen reproductions of the double traces 

 obtained from this pendulum. The couplings used are in- 

 dicated on each figure as a percentage. The letters F or W 

 indicate that one pendulum-bob was started by a blow from 

 the finger or from a toood-block. A small circle and stroke 

 show that one pendulum-bob was drawn aside and let go 



