34 Triple Pendulums ivith Mutual Interaction. 



theory of coupled pendulums of unequal masses and resulted 

 In a satisfactory^ confirmation *. 



Table V. - 



a = 138 cms. t, , -p, , 



rn ce * Bobs Bobs 



""" 7 ~ "~^ Locked. Started. 



b. c. 



Z 134 cms. 116 cms. Q&E P 



b 134 ,. 116 „ Q&R Q&E 



a 134 „ 116 „ P&Q K 



d 104 „ 104 „ Q&R P 



e 104 „ 104 ,. Q&E Q&E 



z 80 ,. 40 „ none. Q struck. ' 



VI. Summary. 



1. The present work is carried out with a simpler arrange- 

 ment of three inter-connected pendulums than that used for 

 the preliminary experiments. 



2. This arrangement is subjected to analysis which shows 

 that the pendulums execute resultant vibrations each com- 

 pounded of two or three simple vibrations. Two of these 

 component vibrations have frequencies which are derivable 

 from the lengths in use, as in the case of simple pendulums. 

 The third component vibration has a frequency which is a 

 function of the three lengths concerned. 



3. Certain general relations between the amplitudes and 

 phases of the components are also derived. These take 

 special values for various initial conditions. 



4. A comparison between this mechanical case and the 

 triple electrical system to which it is somewhat analogous 

 reveals a strong general resemblance, but with a slight 

 variation in details. 



5. Thirty-six photographic records are given, each showing 

 triple traces, and on careful examination these are seen to 

 give a satisfactory confirmation of the theory. 



Nottingham, 



January 13, 1921. 



* To trace this confirmation, see pp. 67-68 of paper II., Phil. Mag. 

 January 1918. On these pages the following corrections need to be 

 noted: — 



Page 67, equations (41), second part, should read : 



(l + /3)p/ 

 -1+P+/3/ 

 This leads to changes in equations (42) and (43) on page 68, viz. : /3 and 

 p need interchanging in the numerators of the coefficients of the second 

 terms. Hence these numerators are (l-j-/3)p/, instead of as printed. 

 Consequently the coefficients of the e's are 

 -1 ^ 1 



T+J3 and (1+^ respectively. 



