Coupled Circuits used in Wireless Telegraphy, 575 

 where 



P2= r 



l± m 1 



l 2 M + mi 

 (see equations II. § 3). 



The motion o£ the beam is also the resultant of two super- 

 posed harmonic motions of frequencies coj and co 2 , and can 

 easily be obtained from the consideration that during the 

 motion, when the initial conditions are those assumed above, 

 the centre of mass of the system must remain fixed, hence 



(M + m x + m 2 ) x — l\m<fi x + l 2 m 2 6 2 = constant, 



6. It is interesting to consider the analogies between the 

 constants of the two systems. 



Taking as the starting point the correspondence between 

 Y and 0, then as the energy expressions must be equivalent, 

 that is 



■JKjVx 2 and iniigihO 2 , 



therefore 



Kx co m l l l g l 



K 2 co m 2 l 2 g 2 



where the symbol co means analogous to. 

 Again, as 



C 1 =K 1 DV 1 



Cx co -niil-igdi 



C 2 co m 2 l 2 gd 2 . 



As the frequency must be the same thing in both systems, 



1 M-f??ij + m 2 g 



Kj7x °° M + m 2 ' k 9 

 hence 



Lxco ~ 



1 M + w a 



g 2 mi(M + m x + ra 2 ) 

 T 1 M + mj 



-L 2 CO — 



g 2 ??i 2 (M + ?rii + ??i 2 )* 

 The coupling must be the same for both systems, so that 



m\m 2 



M 2 



CO 



LxL 2 (M + mx)(lVH-m 2 )' 

 hence 



M CO 0/ --, r. 



g*{ M + m 1 + m 2 ) 



