Aberration of the Concave Grating, 121 



was iinsntisfactory. The aiitliors of tho paper suor^'(^st tliat 



this mioht have resulted from any one or more of the follow- 



ino- causes : — (1) an error of settino- the plane of dispersion 



in the correct i)osition-anole, (2) errors of following, (3) errors 



of focussing, (4) astigmatism. The grating used by Jewell 



and Humphreys* at the Sumatra eclipse was still larger than 



that us<h1 by Mohler and Daniel, having a ruled surface of 



20 cm. aperture and a radius of curvature of 915 cm. The 



ruling was defective on one side, and in actual use only 0*6 



of the whole aperture was employed, so that the effective 



semi-angular aperture /3 was about 0*0065. It is stated that 



in this case also the definition was unsatisfactory, the cause 



ascribed beino- an error of focussino-. 



. .... 



The grating used by the writer in his eclipse work at 



Union Springs in May 1900 was one ruled especially by 

 Prof. Rowland for the Allegheny Observatory. It has an 

 aperture of 13*2 cm., a radius of curvature of 175*3 cm., and 

 an unusually long ruling, 8 cm. The number of lines per 

 cm. is 1421. Hence the resolving-power in the first-order 

 spectrum is about 18,750, and the semi-angular aperture at 

 the centre of curvature is about 0-04. This grating gives 

 good definition at the centre of curvature, but when it w^as 

 used as an objective spectroscope at Union Springs the de- 

 finition was greatly impaired, both visually and photographi- 

 cally, so much so that I do not consider the spectrum plates 

 taken with the instrument mounted in the manner there used 

 good enough for accurate measurement of the wave-lengths 

 of the spectral lines. In this case the lack of definition can- 

 not be ascribed to errors of focussing or mal-adjustment of 

 the apparatus, and I have therefore been led to investigate 

 more rigorously than was at first done the effect of aberration 

 of a concave grating at its principal focus. The results of 

 this investigation show very clearly that the field and range 

 of action of the concave grating, when used as an objective 

 spectroscope with parallel incident light, is very much more 

 restricted than w^hen it is mounted in the usual manner 

 (Rowland method) ; and that in order to avoid injuring the 

 definition in the former case the anoles of incidence and dif- 

 fraction must never exceed certain limiting values, which are 

 rapidly varying functions both of the resolving-power and 

 the angular aperture of the grating. 



We will first consider the case in which the ruled surface 

 is spherical, the usual form adopted for concave gratings. 

 For a parallel incident beam of light the optical conditions 



* Ibid. vol. xvi. p, 3] 3, June 1902, 



