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Til. Note on the Application of Cornu's Spiral to tlie Dif- 

 fraction-Grating. — A Geometrical Method of obtaining the 

 Intensity Formula for a Flat Diffraction- Grating. By 

 Arthur L. Kimball, Ph.D., Professor of Physics in 

 Amherst College*. 



IT is well known that the graphic method of Cornii furnishes 

 a useful method of discussing many diiFraction phenomena, 

 notably the case of a single narrow slit ; but, so far as I am 

 aware, the formula for the intensity of the light diffracted by 

 a grating of n lines has not been obtained without involving 

 the summation by analytic process of the trigonometric series 



sin X + sin [oc-\-y)-\- sin (x + 2y) -f &c. . . . sin (x + (?i — 1) ?/) . 



In the following note it is shown how, by a simple geo- 

 metrical device, the result may be obtained at a stroke ; and 

 the method besides giving immediately the desired summation 

 makes the discussion of the result particularly direct and 

 simple. When a flat wave falls on a flat difi'raction-grating 

 made up of alternate bars and spaces, the graphic expression 

 of the amplitudes and phases of vibration due to the waves 

 through the several slits, is a series of chords of Cornu's 

 spiral. 



In case the resultant amplitude is sought at a point at an 

 infinite distance from the grating, or for a point in the focal 

 plane of the observing telescope, Cornu^s spiral becomes a 

 circle. 



Thus the chord cd will represent the amplitude and phase 

 of motion due to the first slit, ef that due to the second, gh 



c 



that of the third, &c., and if the slits are all equal and 

 equally far apart, the amplitudes will be a series of equal 

 chords at equal distances apart around the circle, and the 

 resultant amplitude is the geometrical sum of these chords. 

 * Communicated by the Author. 



