Coupled Circuits used in Wireless Telegraphy. 587 



whose common frequency is &> l5 the lower of the two 

 resultant frequencies of the system. 



In the pendulum system this motion is stable, and it is 

 therefore probably stable in the electrical system. Its sta- 

 bility increases if the friction of the beam is increased ; in 

 fact i£ there is much frictional resistance to the motion of the 

 beam, any kind of motion o£ the pendulums even when 

 they differ much in length quickly degenerates into this 

 motion. 



This suggests that the pendulum model might be used to 

 illustrate some of the problems that arise in the paralleling 

 o£ alternators. 



Substituting from the equation of condition, 



(s-b^-pJE^O, 



in the general expressions for V 1 and V 2 , we find that the 

 equations of motion take the simple forms 



Vx^E! cos ct)^, Y 2 = E 2 cos corf, 



C x = — o^KjEi sin co^t, C 2 = — <w 1 K 2 E 2 sin co^. 



Thus there is no transfer o£ energy from one circuit to 

 the other, and it can be shown that 



i Lid 2 + MCA + i L 2 C 2 2 = i (KiEi 2 4- K 2 E 2 2 ) sin 2 atf, 

 i K^ 2 + i K 2 Y 2 2 = i (K^ 2 + K 2 E 2 2 ) cos 2 atf. 



13. The model can be modified so as to be the exact 

 analogue to the coupled circuits o£ a wireless receiver when 

 receiving signals. 



The first pendulum, instead of being a simple one, is now 

 a compound one, triangular in shape. The base of the 

 triangle is fitted with knife-edges which rest on suitable 

 planes on the upper surface of the beam, while the vertex of 

 the triangle hangs downwards. 



The disturbance arriving at the receiver is imitated by a 

 periodic pure couple transmitted to this pendulum from the 

 beam by means of a simple electromagnet device which can 

 be energized through light and very flexible wires. A 

 suitable arrangement is to attach to the pendulum a short 

 permanent bar-magnet, above and perpendicular to its knife- 

 edge, and to fix vertically to the beam two short straight 

 electromagnets, one under each pole of the permanent 

 magnet, and with their windings in the same direction. 



There are well-known methods of obtaining an alternating' 

 current of small and adjustable frequency, suitable to operate 



