IMPEDANCE CONCEPT AND APPLICATION 47 



and the refracted field is such as could be produced by a current element 

 of moment 2r]Jll{-qi + 772), occupying the same position as the source. 

 In calculating these fields a uniform intrinsic impedance- r}i is assumed 

 throughout the whole space. 



Since the current / in the element implies two point charges, — I/ioo 

 and I/ico, at its terminals, we can interpret the above rule of images in 

 terms of the charges. The image of a point charge q for calculating the 

 refiected field is (772 — Vi)qKv2 + ^1). For calculating the refracted field 

 a charge 2rjiq/{r]i + 772) must be assumed in the same position as the 

 original charge. For perfect dielectrics the expressions of the image 

 charges reduce to those given by electrostatics. 



ACKNOWLEDGMENT 



I wish to express my appreciation to Dr. T. C. Fry for his valuable 

 criticism in the preparation of this paper. 



AN HISTORICAL NOTE 



The following memorandum written in 1932 by Dr. G. A. Campbell, 

 formerly of the American Telephone and Telegraph Company, repre- 

 sents an interesting historical comment and it is reprinted with Dr. 

 Campbell's permission. 



A letter discussing the characteristic impedance of free space, written to 

 me seven years ago by Dr. H. W. Nichols, is of possible interest in con- 

 nection with both this impedance and the question of superfluous units. 

 He derives the impedance from the Poynting vector by simple substitu- 

 tions. Specific use is made, however, of five systems of units. The letter 

 also supplies an illustration of confusion arising from the multiplicity of 

 units in use. Apparently, Heaviside's 30 ohms ("Electrical Papers," ii, 

 p. 377, 1888) was in ordinary ohms and not in Heaviside's own units, as 

 Nichols quite naturally assumed. The correct explanation of the 30 ohms 

 seems to be that Heaviside's "resistance-operator of an infinitely long tube 

 of unit area" was not intended to be the characteristic impedance, as I 

 define it. 



In definitive units the characteristic impedance of free space equals the 

 square of the effective volts per meter, in a plane electromagnetic wave, 

 divided by the transmitted watts per square meter. For a numerical ex- 

 ample, take the figures for strong sunlight (Maxwell, ii, footnote p. 441) 

 which correspond to 666.1 effective volts per meter and 1176 watts per 

 square meter. The characteristic impedance of free space implicitly as- 

 sumed was thus 377.3 ohms, which checks well with my 376.54 international 

 ohms. 



If free space could be bounded in one direction by a thin, plane film 

 having surface resistivity equal to the characteristic impedance of space, 

 a normally incident plane wave would be completely absorbed by the film; 

 there would be neither reflected wave nor transmitted wave beyond the 



