THE 



LONDON, EDINBURGH, \xd DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



M A Y 1893. 



XXXIX. Gratings in Theory and Practice*. 

 By Heney A. Rowland f. 



Part I. 



IT is not my object to treat the theory of diffraction in 

 general, but only to apply the simplest ordinary theory 

 to gratings made by ruling grooves with a diamond on glass 

 or metal. This study I at first made with a view of guiding 

 me in the construction of the dividing-engine for the manu- 

 facture of gratings, and I have given the present theory for 

 years in my lectures. As the subject is not generally under- 

 stood in all its bearings I have written it for publication. 



Let p be the virtual distance reduced to vacuo through 

 which a ray moves. Then the effect at any point will be 

 found by the summation of the quantity 



A cos b (p —Yt) + B sin h (p—Yt) , 



in which b = -y-, I being the wave-length, V is the velocity 



A 



reduced to vacuo, and t is the time. Making 6 = tan -1 ^ 



* Reprinted from a separate copy from the 'Astronoru. and Astero- 

 Physics ' for February communicated by the Author. 



t I am much indebted to Dr. J. S. Ames for looking over the proofs of 

 this paper and correcting some errors. In the paper I have, in order to 

 make it complete, given some results obtained previously by others, 

 especially by Lord Rayleigh. The treatment is, however, new, as well 

 as many of the results. My object was originally to obtain some guide 

 to the effect of errors in gratings, so that in constructing my dividing- 

 engine I might prevent their appearance if possible. 



Phil. Mag. S. 5. Vol. 35. No. 216. May 1893. 2 E 



