>■ (44) 



336 Mr. L. C. Jackson on 



whence 



a | 2a (- + aV)-« 2 (6-™ 2 + S) \ ib-m 2 -8 I 1 

 H | a 2 (&-m 2 -8)-2tf(--f«v)} j/,-m 2 + SJ 



E 2a(-+a 2 p)- a 2 (£--m 3 + S) 

 F a*(j— m «-S) -2a /- + a 2 ^ 



III. Relations among Variables. 



The relations between the coupling 7 and either the values 

 of a (the ratio of the distance from the base of the elastic 

 pendulum to the point of suspension of the gravity pendulum 

 to the whole length of the elastic pendulum) or the ratio of 

 the frequencies of the superposed simple harmonic vibrations, 

 i. e. p/q, may be more conveniently visualised by means of a 

 graph. 



In fig. 1 the graph showing the relation between 7 and a 

 is plotted for the three cases given in the Tables I. to III., 

 a separate graph being needed for each combination of 

 p and 7]. 



Table I.— Masses 3 : 2, Periods 12 : 7. 



Coupling 



7- 



Per cent. 







Length Ratio 

 a. 







Frequency Ratio 



p/q. 



1-339 



29-01 



0-324 



1-563 



3672 



0-422 



1-682 



43-74 



0-520 



1-839 



50-25 



0-618 



2014 



'ABLE Il.- 



-Masses 1 : 1, Pe 



riods 12 : 13. 



Coupling 



7- 



Per cent. 







Length Ratio 

 a. 







Frequency Ratio 



p/q. 



1-041 



22-81 



0-225 



1-266 



31-95 



0-324 



1*393 



40-22 



0-422 



1-539 



5410 



0-618 



1-862 



