516 



Prof. Arthur Schuster on 



the maxima and minima of light produced by interference in 

 what we have called regular white light, it is found that, just 

 as in the case of the single impulses, there is a definite limit 

 of retardation, depending on the resolving power of the 

 spectroscope, and if the retardation is increased beyond that 

 limit, the spectrum is perfectly uniform. We shall arrive, 

 therefore, at the conclusion that, both for small and for large 

 resolving powers, any hypothesis we make as to the original 

 production of luminous vibration will lead to the same con- 

 clusion. There is no distinction between regular and irregu- 

 lar light beyond that which is brought out by the distribution 

 of intensity in the spectrum. If the intensity vanishes except 

 for a definite wave-length, we must call the vibration com- 

 pletely regular ; if the intensity is the same for all vibrations, 

 it will appear that we must call it completely irregular. 



We are prepared now to deduce a formula which will allow 

 us to calculate the disturbance at F (fig. 1), given the dis- 

 turbance at Gr. 



8. It is convenient to introduce what may be called a 

 " simple grating/' An imaginary grating of this kind has 



Fig. 2. 





B L 





r 



d/ST 



C 











Lyj I I " 



a/ \\\ : 



P 





already been made use of by Lord Rayleigh in his article 

 in the Encyclopedia Britannica*. A simple grating has 

 properties such that a disturbance of unit amplitude is reflected 

 as a disturbance of amplitude cos q s, where q is a constant 

 and s is measured along the grating at right angles to its 

 " lines." In whatever manner the lines of an actual grating- 

 are ruled, we may always express the amplitude of the reflected 

 ray as a function of s and obtain that function by means of 

 Fourier's theorem as a sum of terms, one being constant and 

 the others simply periodic ; so that every grating may be 

 treated as a superposition of a number of simple gratings and 

 an ordinary reflecting surface. 



* " Wave Theory," § 15. 



