TH E 

 LONDON, EDINBURaH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



MAY 1889. 



XLV. The Concave Grating in Theory and Practice. By 

 Joseph Sweetman Ames, Assistant in Physics in the Johns 

 Hopkins University*. 



[Plate VIII.] 



SINCE the invention of the concave grating in 1881, it has 

 been universally I'ecognizecl as one of the most valuable 

 instruments for spectroscopic work at our command. Owing 

 to difficulties in their ruling, however, it is only recently that 

 they have come at all into common use. Thinking that the 

 experience of many years might be useful, at Professor Row- 

 land's request I write this explicit description of the appa- 

 ratus at the Johns Hopkins University and the adjustments 

 found necessary for its accurate use. 



General Theory. 

 The general theory of a concave spherical grating gives (see 

 Rowland, Phil. Mag. vol. x\'i. p. 197, and Amer. Journ. Sci. 

 vol. xxvi. p. 91) as the radius vector of the focal curve (see 

 PI. VIII. fig. I.), 



Rp cos^ u. 



v= J 



R (cos /X. + COS v) — /9 COS^ V 



it being referred to the centre of the grating as origin, /a is 

 the angle r makes with p the radius of curvature of the gra- 

 ting ; and R and v are the coordinates of the source of light. 

 For any given value of R and v there is thus a curve defined 



* Communicated by the Autlior. 

 Phil. Mag. S. 5. Vol. 27. No. 168. May 1889. 2 B 



