PROCEEDINGS OF SECTION A. 43 



Thus, there is no transfer of energy from one circuit to the other, 

 and it can be shown that 



iZiCi^ + MCyC2+ iL^Cz^ = HKiEi^ + K^E^^) sin2 u,^t 

 i^iFi^ + 1^2 Fa^ = M^i-E*!^ + ^2^2^) cos2 w^t. 



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

 the coupled circuits of a wireless receiver when receiving signals. 



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

 pound 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 dis- 

 turbance arriving at the receiver is imitated by a periodic pure couple 

 transmitted to this pendulum jrom the beam by means of a simple 

 electro-magnet 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 electro- 

 magnets, one under each pole of the permanent magnet and with their 

 windings in opposite directions. 



There are well-lcnown methods of obtaining an alternating current 

 of small and adjustable frequency suitable to operate the pendulum, 

 and when the electro-magnets are energized by such a current the 

 mutual stress between the beam and the pendulum will be approxi- 

 mately a pure couple. 



p? t 14. If the mutual stress between the beam and the pendulum be 

 the periodic couple P = p cos at the equations of motion of the system 

 can easily be shown to be 



{M + Ml + niz) X - iriihOi + mJ^^Q^ = ^ 



-X + ' -— «i + gd^ = 



h niih 



X + I2O2 + 5^02 = 



where wti is the mass of the first pendulum as before, k its radius of 

 gyration round its centre of mass, and h the distance of its centre of 

 mass below the knife-edges. 



k'^ + h^ 



Putting li for , the length of the simple pendulum 



h 



equivalent to the compound one, and proceeding exactly as in § 5, we 



obtain the following equations connecting 61, 62, and P. 



[D^ + tii^) 01 = - nDH2 + yP 



(1)2 + ^2^) ^2 = - P2^^^1 



