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XLV. A Simple Treatment of the Secondary Maxima of 

 Grating Spectra. By R. W. Wood, Professor of Experi- 

 mental Physics, Johns Hopkins University *. 



THE usual method of treating the diffraction spectra pro- 

 duced by gratings is so involved, that the student is apt 

 to lose all idea o£ the physical significance of the expressions. 

 An elaborate formula, involving double integrals, the develop- 

 ment of which requires several pages of pure mathematics, 

 and is finally solved by graphical methods, shows that between 

 the principal maxima produced by the grating, there are 

 present (n — 2) secondary maxima, where n is the number of 

 lines of the grating. As an example we may take the case 

 where the curves x = nt?iuz\ y = Uinnz are plotted, the 

 secondary maxima being given by the points of intersection 

 of the two curves. It has been my experience that students 

 go through this treatment without having the faintest idea 

 as to why secondary maxima are produced at all, though 

 each step is fully understood from a purely mathematical 

 standpoint. 



A method occurred to me during a lecture last winter, by 

 which the whole thing could be discussed without any mathe- 

 matics at aU, the relative intensities of the principal and 

 secondary maxima, their position and number being computed 

 with the greatest ease, from most elementary principles. We 

 shall make use of the well-known method of compounding 

 vibrations, which is employed in the elementary development 

 of Cornu's spiral, and shall show that we have minima equal to 

 zero whenever the amplitude lines form a closed symmetrical 

 figure, or mutually annul each other in pairs. The closed 

 figures are either triangles, squares, regular polygons or 

 star-shaped figures, which can be plotted in a very simple 

 manner, described later on. 



The method is somewhat similar to that employed by 

 Kimbal (Phil. Mag. July 1903), whose discussion, however, 

 is not always easily followed by students, and is not wholly 

 devoid of mathematics. 



It is so simple that I shall be surprised if others have not 

 used it before, but I have found it so helpful myself, that I 

 believe that every teacher of elementary or advanced optics 

 can employ it to advantage in class work, and that on this 

 account it is worth putting on record. 



Fraunhofer's treatment shows that a single slit produces 

 maxima and minima, which recede from the centre and 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 14. No. 82. Oct. 1907. 2 K 



