Vibrations : Both Masses arid Periods Unequal. 43 



aside and the heavy one allowed to hang freely. Figs. 11 

 and 12 were obtained with the heavy boh drawn aside and 

 the light one held in its zero position. It may be seen that 

 fig. 6 in Paper II. is more like fig. 7 than like ng. 1, both 

 of the present paper. On the other hand, fig. 21 o£ Paper II. 

 is less like fig. 7 than like fig. 1, both of this paper. This is 

 because the separate frequencies of the component pendulums 

 are more nearly in tune with each other. Fig. 10 shows the 

 effect of drawing aside the lighter bob, little energy is given 

 to the heavy bob and there is but little action or reaction o£ 

 the one bob on the other. Fig. 12 is almost identical with 

 fig. 5 of the present paper and with fig. 9 of Paper II., and, 

 the couplings in all cases are very nearly the same. 



Masses 20 : 1, Lengths 3:4 (77 = 4 : 3). — Table III. shows 

 the frequencies, couplings, and bridle droops with bob> 

 masses 20 : 1 and pendulum lengths 3 : 4, the longer one 

 having the lighter bob, and its length being 137 cm. i£ 

 the bridle droop were zero. 



Table III.— Masses 20 : 1, Lengths 3 : 4. 



Coupling 



Bridle Droop 



Frequency 

 Eatio 



Eatio of Amplitudes. 





— 7- 



Short Pendulum Length. 



p:q. 



E:F. 



G:H. 



Per cent. 

 







1-154 



00 ■ 



Indeter- 

 minate. 



1-76 



o-i 



1-106 



104-6 



-0809 



3-37 



0-2 



107 



12-9 





4-85 



0'3 



1-054 



2-283 



-0-893 



6-3 



4 



1065 







7-5 



0T> 



1-09 



0-2875 



-0-836 



99 



07 



1-154 







1297 



1-0 



1-243 



00696 



-0-640 



3147 



4-0 



1-952 





i 



The figures illustrating the cases in Table III. were 

 obtained with the new portable apparatus shown in fig. 13 

 (PI. V.) and which is described in detail later. Figs. 14-22:: 

 (Pis. IV. <fc Y.) show traces taken with masses 20 : 1 and the 

 length of the pendulum with the heavy bob 3/4 of that with 

 the light one. Figs. 14-21 were obtained by drawing aside 

 the heavy bob and allowing the light one to rest in its more 

 or less displaced position. In figs. 14-17 it is seen that the 

 light bob is almost undisplaced. In fig. 22 the light bob 

 was held undisplaced while the heavy one was drawn aside. 



It is noticeable that with couplings between 2 and 13 

 per cent, the fluctuations of amplitude of the heavy bob are 



