Coupled Circuits used in Wireless Telegraphy. 589 

 and for the P.D.s of the condensers in the circuits are 

 rJ^V^-MK.DV. + D^P, 

 r 2 K. 2 Y 2 =-MK 1 T>Y l ; 



and as 



T D 2 + ^ 2 T D 2 + ^ 



^1 = ^1 j^ * ^2=^2 — JJ 



(damping being neglected), the latter become 



P 



(D' + ^V^-^D^ + f^ l_ ^ ^ _ (L) 



where 



2 _ 1 2 _ 1 



^ ~ KxW M2 ~ K 2 L 2 ' 



_ K 2 M _ KiM 



Pl ~ Ej? ^ 2 ~ K 2 L 2 ' 



as before in § 3. 



Thus, as the differential equations in § 14 connecting the 

 pendulum deflexions are identical in form with the differential 

 equations, given in this paragraph, connecting Y 1 and Y 2 for 

 the receiver coupled circuits when receiving, and as the 

 equations connecting the angular velocities of the one system 

 are also identical in form with those connecting the currents 

 in the other system ; and as all the variables and initial con- 

 ditions for one system can be expressed by the same symbols 

 as the analogous variables and initial conditions for the other 

 system, the modification of the mechanical model proposed is 

 an exact analogue to the coupled circuits of a wireless receiver 

 when receiving. 



16. When damping is taken into account, the different 

 variables in the case of the coupled circuits of a transmitter 

 satisfy the following differential equation (see § 2), 



{cos' 2 ^r) 4 4-2(X 1 + X 2 )D 3 + (a + 6 + 4X 1 X 2 )D 2 H-2(/>X 1 -haX 2 )D + a5}^, = 0, (I.) 



M 2 

 where a = fi^, b = {j, 2 2 -> sin 2 -dr — T ' , 



R-! _ R 2 



2\i — j— } 2X 2 — t 



1j l Li 2 



We will now proceed to investigate this case when squares 

 and higher powers of the damping coefficients are neglected. 



