ELECTROMAGNETIC FIELD ANALYSIS 491 



larly the currents in the other coils are Hx A.r and ILj A>'. It is to be noted 

 that the capacitors are associated with the corresponding longitudinal com- 

 ponents of the electric held while the inductors go with the transverse com- 

 ponents of the magnetic field. Applying Kirchhoff's laws to the network in 

 Fig. 1, w^e should and do obtain Maxwell's field equations. Similarly, we 

 can construct network lattices in the patterns of other coordinate systems, 

 cylindrical and spherical, for example. 



Among the obvious conclusions to be drawn from this analysis of the 

 network structure of the medium supporting the electromagnetic field is the 

 validity of certain general network theorems such as the Reciprocity 

 Theorem and Thevenin's Theorem. 



Reduced Network Models and Integral Equations of 

 LoRENTZ Type 



So far we have been concerned with the electromagnetic field in its en- 

 tirety. In order to visualize the medium as a three-dimensional network we 

 have selected the most direct cour£e : We have subdivided the medium into 

 blocks of displacement current, compressed them into capacitors, and 

 eliminated displacement currents from the rest of space; similarly, we have 



' 1 ' 2 ' 3 ' 4 ' 5 ' 'n-2'n-i ' n ' 



Fig. 2 — Subdivision of a straight antenna for its representation by 

 a reduced network with n meshes. 



swept the magnetic flux into neat little packages. But this is not the only 

 course open to us. We can suppress the medium just as completely as we 

 normally do in the analysis of elementary networks. In order to illustrate 

 this method let us consider a doublet antenna. Fig. 2. We shall divide it 

 into.w sections. The current and charge in any one section exert forces on 

 the charge in any other section. We can regard each section of the antenna 

 as a mesh of a network in which every mesh is coupled to every other mesh. 

 In each mesh the voltage which is necessary to compensate for the electro- 

 motive force of self-induction of the mesh itself, for the resistance of the 

 mesh (or rather for the internal impedance of the wire), and for the voltages 

 induced from all the other meshes, is the impressed voltage. The equations 

 assume the following form: 



Zn/i + Znh + Z13/3 + • • • + /i Jn - Vi , 



Z21/1 + Z22/2 + Z23/3 + • • • + Z2nln = V2 , (2) 



Znlh + Zn2l2 + Zrcdz + * * " + ZnrJn = ^'n , 



