Telescopes and Spectroscopes for Lines of Finite Width. 321 



change of temperature of the grating or of parts of the ruling- 

 engine of less than ^° 0. But the immense value that such 

 large gratings would have in rendering possible a more 

 detailed study of the complex character of spectral lines, and 

 a more exact determination of their wave-length under 

 varying conditions of production, would seem sufficient to 

 amply justify any expenditure of time and money necessary 

 to make their production possible and practicable*. 



It is worth while remarking that the independence of 

 resolving power of the fineness of ruling, already pointed out, 

 makes it possible to considerably reduce the time and diffi- 

 culties of ruling large gratings by very considerably increasing 

 the grating space, provided only that ruling-points can be 

 found (by trial) which will produce gratings sufficiently 

 bright in the higher orders. The two objections usually 

 urged to coarse-ruled gratings are the increased overlapping 

 of the different orders of spectra, and the increased accuracy 

 of spacing required. I have recently shown how the first 

 objection may be overcome by a very simple and efficient 

 optical device placed in front of the spectroscope slitf. The 

 second objection is not a valid one. It has been shown 

 (Rayleigh) that in a given grating the allowable error in the 

 spacing s is J s in the first order, J s in the second, -^ s in 



the third, or in general — - s. But for a given resolving 



for a given aperture and given position of 



i. e. 



m 



grating, we have from (4) — = constant, or for two gratings 



of the same aperture but of different spacing, s and s 1? 



m m l 



S Sj 



The limiting absolute error of ruling is therefore the same 

 in both fine and coarse-ruled gratings. If, for example, the 

 absolute error of spacing of the ruling-machine is fooooo ^ ncn ? 

 equally good definition would be obtained by ruling the 

 grating with 20,000 lines to the inch, and using the first 

 order spectrum only, or by ruling it 4000 lines to the inch, 

 and using the fifth spectrum. But' the last grating would 



* The writer has just finished the design of a large ruling-engine, the 

 money for the construction of which has been given by a friend of 

 science in Chicago. Work on it has been begun in the instrument-shop 

 of the Observatory, and every possible precaution will be taken to ensure 

 success. 



t The ' Astrophysieal Journal,' March 1896, vol. iii. p. 169. 



