300 Mr. L. C. Jackson on 



These values in (9) and (10) give the special solution 



— otq 2 b , ap 2 b 



y = (f^) C0S P t+ f^f cos $> 



Y • (35) 



(p 2 -m 2 )q 2 b (m*-q*)p*b 



z =(2 2fS- C0S ^ + 7~ 2 -A 9 cos at. 



(p 2 — q 2 )m 2 2 (p 2 ~q z )m 2 * J 



So 



F />» and K-{m 2 -q*)p>' ' " * (dbJ 



III. Relations among the Variables. 



Fig. 2 is a graph showing the relation between y and a, 

 the couplings being ordinates and the values of a abscissae. 



The data for the graph are given in the following 

 table : — 



Coupling. 



per cent. 







5 



10 



Values of a. 





 005006 

 0-1005 



Frequency ratio p 



1-000 

 1051 

 1-106 



15 



01517 



1-121 



20 



0-2041 



1-226 



25 



0-2582 



1-294 



30 



0-3145 



1-362 



35 



0-3737 



1-475 



40 



0-4364 



1-542 



45 



0-5039 



- 1-656 



50 



0-5780 



1-767 



55 



0-6586 



1-910 



60 



0-7499 



2-083 



65 



0-8553 



2-296 



70 



0-9802 



2-572 



It will be observed that, while the general solutions for 

 the present system are the same as those for the Cord 

 and Lath Pendulums, the equations for the couplings are 

 not the same, there being no term in a in the equation for 

 the gravity-elastic arrangement. 



Fig. 3 is a graph showing the relation between y 



and -. 

 9 



