306 BELL SYSTEM TECHNICAL JOURNAL 



which can be integrated almost by inspection (the last term through 

 integration-by-parts) and yields the desired value: 



/ = 4x cos nt, (68) 



and Kirchhoff's theorem comes triumphantly through the test. 



It happens however that these conditions, to which we have applied 

 the theorem with so easy a success, are such that the result is of no 

 value whatever in testing the undulatory theory of light.* As I have 

 said already, the eye and the light-recording instruments register 

 amplitude only, not phase. In the train of plane parallel waves de- 

 scribed by (61), the amplitude is everywhere the same, and the instru- 

 ments must report an impression uniformly intense. Nothing could 

 be learned from them about the frequency or the wave-length of the 

 light, and indeed they could not even show that there is anything 

 periodic in the beam. The situation is no better in such a train of 

 spherical diverging waves as (55) describes. Here the amplitude varies 

 inversely with the distance from the centre of divergence, and the eye 

 must report a gradual smooth decline of intensity as it moves away 

 from that centre. In neither observation is there anything to reveal 

 a periodicity or a wave-length, nor anything to forbid the supposition 

 that a beam of light is a stream of straight-flying particles. What we 

 require is a situation in which the use of Kirchhoff's theorem leads to a 

 peculiar and striking variation of amplitude from place to place in the 

 radiation-field — an amplitude-pattern or vibration-pattern, so to speak, 

 depending in detail upon the wave-length of the waves, and so distinc- 

 tive that if such a pattern of intensity were actually to be found in a 

 field of light one could not but regard it as forceful evidence for the 

 undulatory theory. 



Situations which answer this requirement occur when a broad beam 

 of waves is intercepted by a screen pierced with small apertures. In 

 the space beyond the apertures there is a wave-motion of which the 

 amplitude varies from place to place in a remarkable way, depending 

 in detail upon the wave-length. When light falls onto a screen pierced 

 with small holes, the intensity beyond the holes varies remarkably in 

 space. The variations which are observed agree with those which are 

 predicted from the wave-theory, when the proper value of wave-length 

 is chosen; and this is the method of measuring wave-length. Also it 

 is the method of measuring frequency ; for the frequency of light can- 

 not be measured directly; it must be computed by dividing the wave- 



* In the actual theory of light there are several distinct quantities 5 — components 

 of electric and magnetic field strengths — each of which separately conforms to 

 equation (6), and which are interconnected in ways which need not yet concern us. 



