750 BELL SYSTEM TECHNICAL JOURNAL 



of light of equal amplitude intersect one another; and this we will 

 now consider. 



Designate hy 26 the angle at which the two beams are inclined to 

 one another, and draw the x-axis to bisect it; then the two wave- 

 functions are 



s' = A sin {nt — mx cos 6 — my sin 6), 

 s" — A sin {nt — nix cos 6 + my sin 6) 



and their sum ^ is 



s' -\- s" = s = 2A cos {my sin 6) sin {nl — mx cos 9). (14) 



W'e see immediately that this is a situation in which the wave-theory 

 of light predicts a peculiar and characteristic variation of amplitude 

 from point to point in space, which can be tested in detail, and of 

 which a favorably-resulting test has evidential value; whereas in 

 either beam separately the amplitude is constant, and nothing is 

 •observable which demonstrates that there are waves. Here, in the 

 region where the beams overlap, the amplitude varies sinusoidally 

 between zero and the maximum value 2A ; the distance between two 

 consecutive loci of zero amplitude, which are planes perpendicular 

 to the axis of y, being 



d = TJm sin 6 = ^X/sin 6. (15) 



The presence of a series of equally-spaced planes of darkness, their 

 separation varying inversely as the sine of the angle between the 

 beams, is then to be taken as evidence that light is undulatory; and 

 from their separation and the angle between the beams one may 

 compute the wave-length of the light. A more thorough test, made 

 by measuring the distribution of light-intensity between two such 

 planes, would lead (anyway it ought to lead) to the conclusion already 

 known, no doubt, to all the readers of this paper: that the intensity 

 of the light varies as the square of the amplitude of the waves. 



To produce this effect of interference, the two intersecting beams 

 must have started from the same source of light, and at very nearly 

 the same instant — that is to say, the optical paths from the source 

 along the two beams to the region of overlapping must be the same 

 within a few millions of wave-lengths, or a few hundreds of centimetres. 

 By the wave-theory, this is easily understood. We must think that 



*To add them thus implies that the quantity denoted by s is either a scalar, or 

 a vector perpendicular to the .vj-plane. Since light is not adecjuately described by 

 either assumjjtion, we must anticipate defects in the theory, more i)romiiK'nt the 

 larger the angle 0. In practice is evidently always so small that there is no trouble 

 from this source. 



