528 Prof. Arthur Schuster on 



which holds as long as the retardation is smaller than the 

 product of the wave-length into the number of lines (2N) 

 on the grating. If D = 2N\ the equation shows that there is 

 no difference between the minimum and maximum, and this 

 continues for greater values of D. The importance of the 

 equation lies in the fact that it is applicable whatever the 

 nature of the light, as long as the intensity does not change 

 rapidly along the spectrum. We may write the expressions 

 in a form in which they are applicable to the spectra of 

 different orders and also to spectra formed by prisms. If 

 we take as the limit of revolution of two lines of wave- 

 lengths X and X 4- dX that in which the principal maximum 

 of one falls on the first minimum of the other, Rayleigh has 

 shown * that in the first-order spectrum two lines are resolved 

 when 



dX_ J_ 



X ~~ 2N' 



If we take X/dX as the measure of the resolving power (R) 

 of the spectroscope we may write R for 2N. If we further 

 express the retardation N in terms of wave-length, so that 

 T)z=nX where n may be a fraction, the distribution of in- 

 tensity in the spectrum may be written 



E = C[|-+2(l-g)cos 2 w7r]^==0[l+(l-g)cos2w7r]rfX, 



where is a constant and the relation between the maxima 

 and minima becomes 



-L^ TYIfl.T . « -'-*' 



'max 



n 



(4) 



15. I have treated, so far, only of grating spectra. The 

 investigation in detail of the effects produced by prisms is 

 more complicated, but it is easy to see that there can be no 

 essential difference between the two cases. If we possessed 

 a substance which, when cut into the form of a prism, would 

 separate the wave-lengths laterally according to the same law 

 as the grating, the disturbance at the focus of the telescope 

 attached to a prism spectroscope would be exactly the same as if 

 the prism were replaced by a grating of the same resolving power. 

 But whatever the law of dispersion the condition is approxi- 

 mately fulfilled within that small region of wave-lengths 

 which adds appreciably to the disturbance at any point. A 

 separate treatment of prisms would therefore seem unnecessary. 



* Encyclopedia Britannica, " Spectroscopy." 



