ON THE ASTIGMATISM OF KOWLAND'S CONCAVE GRATINGS. 7 



Hence by addition we find for the difference A of the two pattis 

 DKE — DBE 



A=/ 3 



1 -|- COS V 



U^_,(g+*V 



2q ' 2R ' 2r/ \R 



Now if indeed D and E be conjugate foci, A must vanish for 

 every value of I, and both the factors included in brackets must 

 be = 0. So the first factor gives for the relation of the distances 



1 1 1-1- cos v 



s+-=— — 



it r Q 



as with a mirror of q/(1 + cos v) focus; the second makes 



zj R 



so that the heights of the images are proportional to the distances 

 as in common optics. 



I think I have shown that the astigmatism of the grating, while 

 securing to the instrument some precious qualities, is no impediment 

 against a method of observation that seems to be reputed incompat- 

 ible with astigmatism. On the other hand the valued quality of 

 the concave grating, that it shows no dust- lines, and that the image 

 of a star or a spark on the slit is broadened out into a band, may 

 be imparted to a dioptric spectroscope by giving a slight convex 

 spherical curvature to one side of one of the prisms, so that the 

 instrument becomes slightly astigmatic. 



Dec. the 28 th 1893. 



