50 Mr. S. K. Mitra on the Problem of 



resonance potentials have been considered from a critical 

 standpoint. In conclusion, the writers desire to acknow- 

 ledge their indebtedness to Prof. F. A. Saunders, of Viissar 

 College, for suggestions in the preparation of the manu- 

 script. 



Bureau of Standards, 



Washing-ton, D.C. 

 April 18, 1918. 



Note added Nov. 11, 1918. 

 Since the above paper was written the writers have studied 

 electronic discharge in sodium vapour below the ionization 

 potential and have reported upon this work in J. Wash. 

 Acad. Sci. viii. p. 513 (1918). Both D-lines appear in the 

 normal ratio of intensities at the resonance potential. 



IV. On SommerfeUV s Treatment of the Problem of Diffrac- 

 tion by a Semi-infinite Screen. By SlSlR Kumar MlTRA, 

 M.Sc, Lecturer in Physics at the Calcutta University* . 



[Plate II.] 



Introduction. 



THE rigorous treatment of the effect of obstacles on the 

 propagation of light, considered as a boundary-value 

 problem in analysis, has received much attention from mathe- 

 matical physicists during recent yearsf. The particular case 

 of the diffraction of light by a semi-infinite perfectly reflecting 

 screen, for which the complete solution was first given by 

 SommerfeldJ (and later by Carslaw§), has been more recently 

 dealt with by Lamb|| in a paper characterized by very simple 

 and elegant mathematical analysis. As remarked bv Lamb 

 in his paper, the principal interest to the physicist of investi- 

 gations such as these lies in the fact that they afford a check 

 on the accuracy of the results obtained by less rigorous 

 methods, and also enable a comparison of the theory with 

 experiment to be carried out for cases in which the ordinary 

 treatment can hardly be regarded as applicable. A com- 

 parison of the results of the approximate theory with those 



* Communicated by Prof. C. V. Raman. 



t An excellent summary of the literature of the subject with refer- 

 ences to the original papers will be found in the article by Epstein in 

 the Encycl. Math. Wish, (section on Wave Optics, 1914). 



X Sommerfeld, Math. Annal. vol. xlvii. p. 317 (1895). 



§ Carslaw, Proc. Lond. Math. Soc. vol. xxx. p. 121 (1899). 



|| Lamb, Proc. Lond. Math. Soc. (2) vol. iv. p. 190 (1906). 



