498 BELL SYSTEM TECHNICAL JOURNAL 



"dipole" is the source of the simplest spherical electromagnetic wave. We 

 may picture this dipole as a pair of small spheres connected by a thin rod. 

 Under the influence of an impressed force the charge is made to surge back 

 and forth between the spheres. We cannot have a simple source like a 

 uniformly expanding and contracting sphere as in the case of sound waves. 

 The electric charge is conserved, and the only way we can alter the charge 

 in one place is to transfer it to some other place. A more symmetrical 

 dipole would be a single sphere on the surface of which the charge is made 

 to move back and forth between two hemispheres. Let us call these 

 hemispheres respectively the "northern" and the "southern". When the 

 positive charge accumulates on the northern hemisphere, the radial dis- 

 placement current flows outwards from it. At the same time an equal 

 radial displacement current flows toward the southern hemisphere. The 

 situation is analogous to the balanced mode of transmission along parallel 

 wires, with the two half spaces acting as "the wires". The distance along 

 the line is the distance from the dipole. The radial transmission line is 

 capacitively loaded but the series capacitance increases as the square of 

 the radius and therefore the capacitive series admittance decreases as the 

 reciprocal of the square of the radius. Hence, at some distance from the 

 dipole, the wave propagation will be quite unimpeded just as in ordinary 

 transmission lines free from loading. Near the dipole the series capacitance 

 is high, and the power carried by the wave in comparison with the energy 

 stored is small. 



In the next spherical mode of transmission the polar regions of the spher- 

 ical generator are similarly charged while the opposite charge is concen- 

 trated in the equatorial zone. The zonal character of the radial current 

 distribution persists at all distances from the generator. As might be 

 expected the reactive field in the vicinity of a small "tripole" generator is 

 even stronger than in the case of the dipole source. 



The sequence of zonal modes of transmission can be continued indefinitely. 

 Next we could imagine tubular modes in which the space surrounding the 

 generator is subdivided into conical tubes with the radial current in adjacent 

 tubes flowing in opposite directions. This picture is essentially physical; 

 but it corresponds very closely to the mathematical expansion of the general 

 solution of Maxwell's equations in spherical harmonics. 



Field Representation in Terms of Fields of Special Types 



From the mathematical point of view the method which we have just 

 been considering is based on the idea of representation of the general field 

 in terms of particular fields having certain relatively simple properties. 

 The method is analogous to that employed in circuit theorj^ when the 



