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LII. On Curved Di fraction-gratings. — II. 
By R. T. Glazebrook, M.A., F.R.S.* 
IN the September number of the Philosophical Magazine 
there is a paper by Prof. Rowland on my paper read 
before the Physical Society bearing the above title. In that 
paper (Phil. Mag. June 1883) I investigated the aberration 
of a curved diffraction-grating ruled so that the spaces between 
the lines are equal when measured along the arc of the curve, 
and applied my results to Professor Rowland's gratings. 
Until Professor Rowland's paper (Phil. Mag. Sept. 1883), 
this assumption had been made explicitly or tacitly in all I 
have seen written on the subject. In that paper Prof. Row- 
land mentions (I think for the first time in print) that the 
spaces are equal, not along the arc, but along the chord of the 
arc, and therefore that my theory fails to apply to the gra- 
tings as he rules them. Owing to absence from home I have 
not until the present date (October 3) had an opportunity of 
reading Professor Rowland's paper carefully. I wish now to 
express my agreement with him so far as this criticism is con- 
cerned, and to show the concurrence of results between the two 
methods of attacking the problem followed by Professor Row- 
land and myself respectively when the gratings are ruled in 
the manner he has adopted. Another criticism is, that I have 
supposed the gratings to be ruled on a cylindrical instead of a 
spherical surface. To this I would reply (1) that Prof. Row- 
land does the same himself. " For the particular problem in 
hand," he says, " we need only work in the plane xy at pre- 
sent."" And throughout the paper he works in the plane xy. 
This is clearly equivalent to treating the surface as cylindrical. 
And (2) we are both quite right in so doing. 
For let Q (fig. 1) be 
the source of light, ABC ;pw \ % 
one of the lines of the 
grating, and Q' a point 
at which the illumination 
is required. Let be 
the centre of the grating. 
In the problem we con- 
sider Q, 0, and Qf lie in 
a plane which is at right 
angles to the lines of the 
grating, the plane xy with 
Prof. Rowland's nota- 
tion; let this plane cut 
* Communicated by the Author. 
