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By the use of the reversion method certain types of ordinary nonlinear differential equations can be reduced to a set of ordinary linear differential equations which may conveniently be solved by the Laplace transform. The expression for the general member of the linear set is developed and written out in detail for certain illustrative terms. The method is applied to two simple problems for which the answers are exactly known so that some idea may be obtained as to the excellence of the approximations supplied by this method.

In this paper the method developed by J. R. Wait to determine th e fi elds produced by an aperture in an infinite coated-metal cylinder is extended to obtain the s olution for the fields produced by an apert ure in an infinite coated-m etal plane. Although t he fi elds at any point can be found by this method, this paper treats only the radi rLt ion fi elds (a futur e paper is planned which will treat the near fields and input admittance of the aperture). It is shown that the ra diation fi elds produced by a given aperture for t he coated case are related to those of the uncoated case, for the same apertu re excitation , by simp le multiplicative functions which depend only on the parameters of the coating a nd the off-axis a ngle. Th ese findin gs, combined with exp erim en tal results for finite s ize uncoated and coated plates in conjullction with se mi-empirical a nd empirical tlleories, resp ectively, are then ge nera li ze d to obtain t h e ra di ation fi elds produced b.v a slot in a coated finite metal p late . Th e sh a rpe ning a nd broa de ning effects on the radiation p a tterns du e to a losslesl; plasma coating are a lso obtained from the general solution.List of Symbols E = vector elecLl'ic fleld in tensity, volts/met er H = vector magnetic field intensity, amperes/meter E,, = x component of E, eLc. ] = double Fourier transform of the fun ctionj(x, y) P -I= double inverse Fourier Lransform opera Lor Et = dou ble Fourier transform of forward goin g f1xial electric field in region 1, etc. El = double Fourier tra nsform of backward goi ng axial elecLric field in re gion 1, etc. c= cosine S=Sltle j3v= W~= 2' 71-jA v= phas e fa ctor in vacuum J-Lv= permeability of vacLlum = 47r·1Q-7 henries/meter €v= permittivity of vacuum = 1/367r·10 9 farads /meter Av= wavelength of source in vacuum ' YI = propagation factor in coating j32=phase factor in region external to coating { j32~ ~ + 'Y2 in coa ting j3~= e + 7)2=squar e of cutoff phase factor = ~ r : . 1 .• j3;,-j3'2 lil reglOn external to coatmg ~= wave number in x direction 7) = wave number in y direction MT = complex relative permeability of coating ~r = complex relative dielectric constant of coating d = thickness of coating jp = wp/27r= pI asma frequency"'" g{n cycles/second n =electron density, electron/meter 3 (All other symbols are defined as they are introduced.) 363