102 BELL SYSTEM TECHNICAL JOURNAL 



the region containing the sources of the wave functions. In the 

 Theory of Sound the wave function represents the excess pressure or 

 the velocity potential and Kirchhofif's theorem is valuable in the 

 analysis of diffraction phenomena. Kirchhoff's theorem is also used 

 in dealing with optical diffraction. We may also remark that Kirch- 

 hoff's formula is a mathematical expression of a principle governing 

 compressional wave motion. This principle was first formulated by 

 Huygens in the following form: each particle in any wave front acts 

 as a new source of disturbance, sending out secondary waves, and these 

 secondary waves combine to form the new wave front.'' 



Let us now examine one of the familiar diffraction problems in the 

 light of the Equivalence Principle. Consider a source 5 and a per- 

 fectly absorbing screen (Fig. 5a). Such a screen will be defined in the 

 usual manner: the impressed wave enters it without reflection but 

 does not pass through it. If the screen is infinitely thin, this definition 

 implies the existence of electric and magnetic currents in the screen 

 whose densities are given by the postulated discontinuity in the field. 

 In reality the "black bodies" absorb not by virtue of the coexistence 

 of electric and magnetic currents but by virtue of electric currents 

 alone with the aid of reflections taking place between atomic layers. 

 The true mechanism of absorption is complex and requires more than 

 a mere surface. In diffraction studies it has become a habit with us 

 to ignore the precise nature of absorption and confine outselves to its 

 implications; but it is just as well to know the nature of the ideal 

 mechanism which we are substituting for the true mechanism. 



We can apply the Equivalence Principle to the present problem in 

 two ways. W^e can choose as our surface C a surface (1234) just on 

 the other side of the screen. The part (23) contributes nothing; the 

 equivalent distribution of sources S' over the parts (12) and (34) gives 

 us a complete field to the right of the screen. On the other hand if 

 S" is the field due to the electric and magnetic currents in the screen 

 induced by S, the total field is 5 + S" . The choice of the "surface 

 C" that would yield this result is shown in Fig. Sb although the con- 

 clusion is obvious without recourse to the Equivalence Principle. 

 Since to the right of C in Fig. 5a the two alternative fields must be 

 the same, we have 



S' = S + S" and S' - S" = S. (20) 



Incidentally the last equation is the expression for the Equivalence 

 Principle as applied to S in the absence of the screen since — 5" is 



» A. E. Caswell, "An Outline of Physics," p. 544 (1929). 



