526 Prof. Arthur Schuster on 



But if the value of r exceeds that of I, the integrals have 

 different values. 



With the help of these equations we find, if r < I, 



As 

 E = —- [sin 2qr + 2ql+2q{l—r) cos 2qr] . 

 Iq 



The first term may be neglected compared to the two others 

 if the number of lines on the grating is great, and we may 

 without appreciable error write 



E = As[l+(l-r) cos2qr]. 



This equation, however, only holds when I exceeds r. If, 

 on the other hand, r>l, the definite integrals on which E 

 depends take different values, which give in that case 



E =Asl 



The expression for the energy here does not involve r, and 

 therefore whatever the retardation the energy is the same, and 

 the spectrum will show neither minima nor maxima. The point 

 at which interference ceases is given by r=l, that is by 

 r = yl/a ; yl being the difference in optical length between the 

 extreme rays which fall on the grating, the value of t is 

 identical with that for which interference ceases in the case 

 of a simple luminous impulse. Thus Grouy and Rayleigh's 

 proposition is proved for the case of a finite grating. Inter- 

 ference ceases completely for a given retardation of path 

 depending only on the resolving power of the grating and 

 not on the nature of the light. Our test case is therefore 

 disposed of, but it is not easy to see how we could have fore- 

 seen the result without the Complete analysis. 



14. The expression for the energy may with advantage be 

 transformed by taking as the area s that included within 

 a slit parallel to the lines of the grating, the edges of the 

 slit coinciding with the principal maxima of the two wave- 

 lengths A- and \+<i\. The illumination along the slit will 

 show maxima and minima distributed in a well-known 

 manner, the beam being limited by a rectangular aperture. 

 If x is measured along the slit and the intensity is taken as 

 unity at the central point, the intensity at any other point 

 will be 



irhx 



sin 2 



XF 



X 2 F 2 



