On the Spectra formed by Curved Diffraction-gratings. 183 



vapour, a consideration which it will be advantageous to present 

 in another connexion. It is to be remembered that all the 

 values here given are presented as approximate, and not as 

 final ones. 



In presenting these researches, on the part of the Allegheny 

 Observatory, I should state that the considerable especial 

 expenditures they have involved have been met by the gene- 

 rosity of a friend of that institution, whose aid, which alone 

 made them possible, I would gratefully acknowledge. 



In conclusion I desire to say that I have been aided through- 

 out them by Messrs. F. W. Very and J. W. Keeler of this 

 Observatory, with an efficiency and interest in their prosecution 

 without which they could hardly have taken their present form. 



Allegheny Observatory, Allegheny, 



Pennsylvania, December 30, 1882. 



XXIII. On the Spectra formed by Curved Diffraction-gratings. 



By Walter Baily*. 



[Plate II.] 



IN the curved diffraction-gratings invented by Professor 

 Rowland, he has pointed out that if a source of light be 

 placed at the centre of curvature, all the rays diffracted back 

 from the grating will have their foci on the circle which lies 

 in a plane perpendicular to the lines of the grating, and is 

 described on the radius of curvature as diameter. In this 

 paper I investigate the locus of these foci, and of those of rays 

 transmitted through a transparent grating for any position of 

 the source of light in the same plane. 



Let a plane grating be placed at D (fig. 1) with its lines 

 perpendicular to the paper and one of them passing through 

 D, and its plane perpendicular to C D, and let a D be an inci- 

 dent ray, of which a portion with wave-length \ Y is diffracted 

 along 1)%, and a portion with wave-length X 2 is diffracted 

 along Da 2 , a 1 Da 2 being a straight line. Let CDa = ^, and 

 CDa 1 = 6; and let a be the distance between the lines of the 

 grating. Let D / be the next line of the grating to D ; and 

 draw DV and a\D'a' 2 parallel to Da and a 1 Da 2 respectively; 

 and draw aa! ', a^a'^ a 2 a' ' 2 perpendicular to Da and aj)a 2 . 

 Then we must have 



aD + Da 1 = a / D / + T>W + nfa 

 and 



aD + Da 2 = a'W -f D V 2 + n 2 \ 2j 



where n x and n 2 are integers. 



* Head before the Physical Society of London, January 27, 1883. 



