Furthermore, sub matrix [[A.sub.1]] represents the propagation effects to appear on the electrical device consisting of towers, ground wires and grounding systems, while sub matrix [[A.sub.2]] represents the relationship between electric currents and voltages at each node (deduced by the application of Kirchhoff's laws).
Thus, in the absence of the propagation along the ground wire and the vertical column of the tower only a lumped-constant circuit exists and the sum of three currents leads to the injected current (Kirchhoff's law).
In the first preface of his book The Theory of Heat Radiation Planck mentions that he has "deviated frequently from the customary methods of treatment, wherever the matter presented or considerations regarding the form of presentation seems to call for it, especially in deriving Kirchhoff's laws ..." [9; p.
Finally, Planck's treatment of Kirchhoff's law is examined in detail and the shortcomings of his derivation are outlined.
I have previously stated that Kirchhoff's law [20-22], and, as a necessary result, Planck's law [1, 2] and blackbody radiation, are not universal in nature [23-25].
In Planck's words (see [9; [section] 44]), Kirchhoff's law of thermal emission holds that: "With these assumptions, according to equations (46), (45), and (43), Kirchhoff's law holds, E/A=I = d[sigma] cos [theta] d[OMEGA] [K.sub.[upsilon]] d[upsilon], i.e., the ratio of the emissive power to the absorbing power of any body is independent of the nature of the body".
Given thermal equilibrium within an enclosure, Kirchhoff's law [20-22] states that the ability of an object to emit a photon is equal to its ability to absorb one.
In studying blackbody radiation, it will be demonstrated that radiation within an enclosed body is not necessarily black [25], as Kirchhoff's law erroneously dictates [20-22].
Agassi highlights the importance of Kirchhoff's law for astrophysics: "Browsing through the literature, one may find an occasional use of Kirchhoff's law in some experimental physics, but the only place where it is treated at all seriously today is in the astrophysical literature" [32].