492 BELL SYSTEM TECHNICAL JOURNAL 



where the /'s are the currents in the various sections of the antenna and the 

 F's are the impressed voltages. The Z's are the self -impedances and the 

 mutual impedances, and are calculated from the law of force between two 

 charged particles. In a transmitting antenna the impressed voltage is zero 

 everywhere except in a restricted region. In the receiving antenna the 

 voltage is impressed on all sections; but one section, the "load," has a very 

 different self-impedance from the remaining sections. 



When n is finite, our equations are approximate. If we make n infinite 

 and introduce the impressed electric intensity, that is, the impressed voltage 

 per unit length, we convert equations (2) into a single integral equation. 

 More generally we may have to consider the transverse dimensions of the 

 antenna and divide the entire surface of the antenna into elementary surface 

 elements, each of which will represent two meshes in our network. We have 

 to have two meshes for each surface element because the current may in 

 general change its direction from point to point and in order to specify it 

 completely w^e must consider two components of the current. These may 

 be taken as tangential to some Gaussian coordinate lines drawn on the 

 surface of the antenna. The exact network equations will appear as a 

 system of two integral equations involving double integrals. 



In this discussion, we have assumed that the medium outside the antenna 

 is homogeneous. No difficulty is presented by the simultaneous inclusion 

 of a transmitting and a receiving antenna. The two form just one network 

 and the voltages impressed on the various meshes of the receiving antenna 

 represent simply the coupling between these meshes and the meshes of the 

 transmitting antenna. All the mutual impedances are calculable from the 

 general equation, 



£= -M^-gradF, (3) 



representing the force per unit charge due to a given moving charge. If we 

 so desire, we can take equation (3) with the explicit expressions for A and V 

 in terms of electric current and charge as the fundamental equations of 

 electromagnetic theory and dispense with Maxwell's differential equations 

 altogether. This course is feasible but inexpedient. Actual applications of 

 this equation turn out to be much too complicated in the great majority of 

 practical problems. It is only when we already know the current and charge 

 distribution that (vS) becomes really useful. Thus in the accepted develop- 

 ment of electromagnetic theory {?>) is subordinated to Maxwell's equations 

 and derived from them. 



